Onset of Synchronization in the Disordered Hamiltonian Mean-Field Model

We study the Hamiltonian mean field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite-size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution

Thirty Years of Turnstiles and Transport

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem over the past thirty years. Primary measures of transport for volume-preserving maps include the exiting and incoming fluxes to a region. For area-preserving maps, transport is impeded by curves formed from invariant manifolds that form partial barriers, e.g., stable and unstable manifolds bounding a resonance zone or cantori, the remnants of destroyed invariant tori. When the map is exact volume preserving, a Lagrangian differential form can be used to reduce the computation of fluxes to finding a difference between the action of certain key orbits, such as homoclinic orbits to a saddle or to a cantorus. Given a partition of phase space into regions bounded by partial barriers, a Markov tree model of transport explains key observations, such as the algebraic decay of exit and recurrence distributions.Comment: Updated and corrected versio

Quantum Breaking Time Scaling in the Superdiffusive Dynamics

We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as $\tau_{\hbar} \sim (1/\hbar)^{1/\mu}$ with the transport exponent $\mu > 1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one $\tau_{\hbar} \sim \ln(1/\hbar)$ with respect to $\hbar$

Ulam method for the Chirikov standard map

We introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately equal to the exponent of Poincar\'e recurrences in such systems. The eigenmodes show links with trajectories sticking around stability islands.Comment: 13 pages, 13 figures, high resolution figures available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text and fig. 12 and revised discussio

Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure

Triton 2 (1B)

The goal of this project was to perform a detailed design analysis on a conceptually designed preliminary flight trainer. The Triton 2 (1B) must meet the current regulations in FAR Part 23. The detailed design process included the tasks of sizing load carrying members, pulleys, bolts, rivets, and fuselage skin for the safety cage, empennage, and control systems. In addition to the regulations in FAR Part 23, the detail design had to meet established minimums for environmental operating conditions and material corrosion resistance

Quantum Poincar\'e Recurrences

We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal value p=1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.Comment: revtex, 4 pages, 4 figure

Structural basis for stable DNA complex formation by the caspase-activated DNase

We describe a structural model for DNA binding by the caspase-activated DNase (CAD). Results of a mutational analysis and computational modeling suggest that DNA is bound via a positively charged surface with two functionally distinct regions, one being the active site facing the DNA minor groove and the other comprising distal residues close to or directly from helix α4, which binds DNA in the major groove. This bipartite protein-DNA interaction is present once in the CAD/inhibitor of CAD heterodimer and repeated twice in the active CAD dimer. © 2005 by The American Society for Biochemistry and Molecular Biology, Inc

Mechanism of DNA cleavage by the DNA/RNA-non-specific Anabaena sp. PCC 7120 endonuclease NucA and its inhibition by NuiA

A structural model of the DNA/RNA non-specific endonuclease NucA from Anabaena sp. PCC7120 that has been obtained on the basis of the three-dimensional structure of the related Serratia nuclease, suggests that the overall architecture of the active site including amino acid residues H124, N155 and E163 (corresponding to H89, N119 and E127 in Serratia nuclease) is similar in both nucleases. Substitution of these residues by alanine leads to a large reduction in activity (<0.1%), similarly as observed for Serratia nuclease demonstrating that both enzymes share a similar mechanism of catalysis with differences only in detail. NucA is inhibited by its specific polypeptide inhibitor with a K1 value in the subpicomolar range, while the related Serratia nuclease at nanomolar concentrations is only inhibited at an approximately 1000-fold molar excess of NuiA. The artificial chromophoric substrate deoxythymidine 3',5'-bis-(p-nitrophenyl phosphate) is cleaved by NucA as well as by Serratia nuclease. Cleavage of this analogue by NucA, however, is not inhibited by NuiA, suggesting that small molecules gain access to the active site of NucA in the enzyme-inhibitor complex under conditions where cleavage of DNA substrates is completely inhibited. The active site residue E163 seems to be the main target amino acid for inhibition of NucA by NuiA, but R93, R122 and R167 (corresponding to K55, R87, R131 in Serratia nuclease) are also involved in the NucA/NuiA interaction. NuiA deletion mutants show that the structural integrity of the N and C-terminal region of the inhibitor is important for complex formation with NucA and inhibition of nuclease activity. Based on these results a mechanism of DNA cleavage by NucA and its inhibition by NuiA is proposed. (C) 2000 Academic Press

Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.Comment: revtex, 4 pages, 3 ps-figure