Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

Evidence of Sulfur Non-Innocence in [CoII(dithiacyclam)]2+-Mediated Catalytic Oxygen Reduction Reactions

In many metalloenzymes, sulfur-containing ligands participate in catalytic processes, mainly via the involvement in electron transfer reactions. In a biomimetic approach, we now demonstrate the implication of S-ligation in cobalt mediated oxygen reduction reactions (ORR). A comparative study between the catalytic ORR capabilities of the four-nitrogen bound [Co(cyclam)]2+ (1; cyclam=1,5,8,11-tetraaza-cyclotetradecane) and the S-containing analog [Co(S2N2-cyclam)]2+ (2; S2N2-cyclam=1,8-dithia-5,11-diaza-cyclotetradecane) reveals improved catalytic performance once the chalcogen is introduced in the Co coordination sphere. Trapping and characterization of the intermediates formed upon dioxygen activation at the CoII centers in 1 and 2 point to the involvement of sulfur in the O2 reduction process as the key for the improved catalytic ORR capabilities of 2

Spectroscopic Properties of a Biologically Relevant [Fe2(μ-O)2] Diamond Core Motif with a Short Iron-Iron Distance

Diiron cofactors in enzymes perform diverse challenging transformations. The structures of high valent intermediates (Q in methane monooxygenase and X in ribonucleotide reductase) are debated since Fe−Fe distances of 2.5–3.4 Å were attributed to “open” or “closed” cores with bridging or terminal oxido groups. We report the crystallographic and spectroscopic characterization of a FeIII2(μ-O)2 complex (2) with tetrahedral (4C) centres and short Fe−Fe distance (2.52 Å), persisting in organic solutions. 2 shows a large Fe K-pre-edge intensity, which is caused by the pronounced asymmetry at the TD FeIII centres due to the short Fe−μ−O bonds. A ≈2.5 Å Fe−Fe distance is unlikely for six-coordinate sites in Q or X, but for a Fe2(μ-O)2 core containing four-coordinate (or by possible extension five-coordinate) iron centres there may be enough flexibility to accommodate a particularly short Fe−Fe separation with intense pre-edge transition. This finding may broaden the scope of models considered for the structure of high-valent diiron intermediates formed upon O2 activation in biology

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics

Experimental assignment of long range magnetic communication through Pd amp; Pt metallophilic contacts

Record breaking magnetic exchange interactions have previously been reported for 3d metal dimers of the form [M Pt SAc 4 pyNO2 ]2 M Ni or Co that are linked in the solid state via metallophilic Pt amp; 8943;Pt bridges. This contrasts the terminally capped monomers [M Pt SAc 4 py 2], for which neither metallophilic bridges nor magnetic exchange interactions are found. Computational modeling has shown that the magnetic exchange interaction is facilitated by the pseudo closed shell d8 amp; 8943;d8 metallophilic interaction between the filled Pt2 5dz2 orbitals. We present here inelastic neutron scattering experiments on these complexes, wherein the dimers present an oscillatory momentum transfer dependence of the magnetic transitions. This allows for the unequivocal experimental assignment of the distance between the coupled ions, which matches exactly the coupling pathway via the metallophilic bridges. Furthermore, we have synthesized and magnetically characterized the isostructural palladium analogues. The magnetic coupling across the Pd amp; 8943;Pd bridge is found through SQUID magnetometry and FD FT THz EPR spectroscopy to be much weaker than via the Pt amp; 8943;Pt bridge. The weaker coupling is traced to the larger radial extent of the 5dz2 orbitals compared to that of the 4dz2 orbitals. The existence of a palladium metallophilic interaction is evaluated computationally from potential surface cuts along the metal stretching direction. Similar behavior is found for the Pd amp; 8943;Pd and Pt amp; 8943;Pt systems with clear minima along this coordinate and provide estimates for the force constant for this distortion. The estimated M amp; 8943;M stretching frequencies are found to match experimental observed, polarized bands in single crystal Raman spectra close to 45 cm amp; 8722;1. This substantiates the existence of energetically relevant Pd amp; 8943;Pd metallophilic interactions. The unique properties of both Pt2 and Pd2 constitutes an orthogonal reactivity, which can be utilized for steering both the direction and strength of magnetic interaction

Spektroskopische Eigenschaften eines biologisch relevanten [Fe2 mu O 2] Diamond Core Motivs mit einem kurzen Eisen Eisen Abstand

Dieisen Kofaktoren in Enzymen vollziehen diverse anspruchsvolle Transformationen. Die Strukturen hoch valenter Intermediate Q in der löslichen Methanmonooxygenase und X in der Ribonukleotidreduktase sind Gegenstand aktueller Diskussionen, seit Fe Fe Abstände von 2.1 3.4 amp; 8197; eine Zuordnung zu geöffneten und geschlossen Kernen mit verbrückenden oder terminalen Oxido Gruppen in den aktiven Zentren ermöglichen. In dieser Studie berichten wir die kristallografische und spektroskopische Charakterisierung eines FeIII2 amp; 956; O 2 Komplexes 2 mit tetraedrischen 4C Zentren sowie einem geringen Fe Fe Abstand 2.52 amp; 8197; , der in Lösungsmitteln beständig ist. 2 zeigt eine gro e Fe K Vorkanten Intensität. Diese resultiert aus der starken Asymmetrie an den TD FeIII Zentren bedingt durch die kurzen Fe amp; 956; O Bindungen. Während ein Fe Fe Abstand von amp; 8776;2.5 amp; 8197; für sechsfach koordinierte Zentren in Q und X unwahrscheinlich ist, könnte ein Fe2 amp; 956; O 2 Kern mit vierfacher oder möglicherweise auch fünffacher Koordination flexibel genug sein, um eine kurze Fe Fe Separierung mit gro er Vorkanten Intensität zu ermöglichen. Diese Erkenntnis kann dazu beitragen, dass weitere Modelle für die Strukturen der hoch valenten Dieisen Intermediate, die sich im Zuge der biologischen O2 Aktivierung bilden, in Betracht gezogen werde

Field induced single ion magnet based on a quasi octahedral Co ii complex with mixed sulfur oxygen coordination environment

Synthesis and characterization of structure and magnetic properties of the quasi octahedral complex pipH2 [Co TDA 2] 2H2O I , pipH22 piperazine dication, TDA2 amp; 8722; thiodiacetic anion are described. X ray diffraction studies reveal the first coordination sphere of the Co II ion, consisting of two chelating tridentate TDA ligands with a mixed sulfur oxygen strongly elongated octahedral coordination environment. SQUID magnetometry, frequency domain Fourier transform FD FT THz EPR spectroscopy, and high level ab initio SA CASSCF NEVPT2 quantum chemical calculations reveal a strong easy plane type magnetic anisotropy D amp; 8776; 54 cm amp; 8722;1 of complex I. The complex shows field induced slow relaxation of magnetization at an applied DC field of 1000 O

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

TonB-dependent maltose transport by Caulobacter crescentus

We have shown previously that Caulobacter crescentus grows on maltodextrins which are actively transported across the outer membrane by the MalA protein. Evidence for energy-coupled transport was obtained by deletion of the exbB exbD genes which abolished transport. However, removal of the TonB protein, which together with the ExbB ExbD proteins is predicted to form an energy-coupling device between the cytoplasmic membrane and the outer membrane, left transport unaffected. Here we identify an additional tonB gene encoded by the cc2334a ORF, which when deleted abolished maltose transport. MalA contains a TonB box that reads EEVVIT and is predicted to interact with TonB. Replacement of valine number 15 in the TonB box by proline abolished maltose transport. Maltose was transported across the cytoplasmic membrane by the MalY protein (CC2283). Maltose transport was induced by maltose and repressed by the MalI protein (CC2284). In addition to MalA, MalY and MalI, the mal locus encodes two predicted cytoplasmic alpha-amylases (CC2285 and CC2286) and a periplasmic glucoamylase (CC2282). The TonB dependence together with the previously described ExbB ExbD dependence demonstrates energy-coupled maltose transport across the outer membrane. MalY is involved in maltose transport across the cytoplasmic membrane by a presumably ion-coupled mechanism