Search Results (4 total)

A method to reconstruct the energy landscape of small peptides is presented with reference to a two-dimensional off-lattice model. The starting point is a statistical analysis of the configurational distances between generic minima and directly connected pairs (DCP). As the mutual distance of DCP is typically much smaller than that of generic pairs, a metric criterion can be established to identify the great majority of DCP. Advantages and limits of this approach are thoroughly analyzed for three different heteropolymeric chains. A funnel-like structure of the energy landscape is found in all of the three cases, but the escape rates clearly reveal that the native configuration is more easily accessible (and is significantly more stable) for the sequence that is expected to behave as a real protein.

Jumps between neighboring minima in the energy landscape of both homopolymeric and heteropolymeric chains are numerically investigated by determining the average escape time from different valleys. The numerical results are compared to the theoretical expression derived by Langer [J.S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969)] with reference to a 2N-dimensional space. Our simulations indicate that the dynamics within the native valley is well described by a sequence of thermally activated process up to temperatures well above the folding temperature. At larger temperatures, systematic deviations from the Langer’s estimate are instead observed. Several sources for such discrepancies are thoroughly discussed.

A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the 1/3 betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model.

The network of resonances in the action plane for a four-dimensional map is obtained by computing the actions from the Fourier coefficients of the orbits, and it is compared with the results of Birkhoff normal forms. This method, which combines the positive features of standard frequency analysis and normal forms, is suitable to study the one turn map of a particle accelerator.