How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Beta-sheet preferences from first principles

The natural amino acids have different preferences of occurring in specific types of secondary protein structure. Simulations are performed on periodic model beta-sheets of 14 different amino acids, at the level of density functional theory, employing the generalized gradient approximation. We find that the statistically observed beta-sheet propensities correlate very well with the calculated binding energies. Analysis of the calculations shows that the beta-sheet propensities are determined by the local flexibility of the individual polypeptide strands.     

Instability criteria for steady flows of a perfect fluid

An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.     

Boundary tangency for density interfaces in compressible viscous fluid flows

We prove that, for solutions of the Navier-Stokes equations of two-dimensional, viscous, compressible flow, curves which are initially transverse to the spatial boundary and across which the fluid density is discontinuous become tangent to the boundary instantaneously in time. This effect is seen to result from the strong pressure gradient force, which in this case includes a vector measure supported on the curve, together with the fact that singularities in this system are convected with the fluid velocity.     

Effective fields in laser-driven electron recollision and charge localization

We propose a model to describe correlated two-electron dynamics in strong laser fields during laser-induced recollision between an electron and its parent ion. We derive an effective interaction potential which describes the effect of the laser-driven electron collision with an ion while retaining the correlation between the colliding and the bound electron. Using dissociative ionization of molecular hydrogen as an example, we analyze the dynamics of correlation-driven electron localization in a dissociating hydrogen molecular ion.     

Suppression of decoherence in a wave packet via nonlinear resonance

We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.     

Flow properties of a dusty-gas point source in a supersonic free stream

By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of " mufti- layer structure" in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .     

Formation of vortices in a laminar jet under the action of acoustic field

Results on visual investigation of a structure of a round minijet under the action of an acoustic field are presented. Characteristic features of the laminar jet structure in the acoustic field were revealed from the data of video and photo records of a flow picture. In the flow we observed characteristic large-scale vortex structures and violent turbulent mixing zones.We revealed formation of vortex structures in a laminar jet under acoustic field and an oscillating jet flow regime at the outlet from the pipe 1.35 mm in diameter.     

Use of electron correlation to make attosecond measurements without attosecond pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.     

Optimal generation of single-dispersion precompensated 1-fs pulses by molecular phase modulation

We show how an optimal control approach can be combined with the pump-probe technique for pulse compression by molecular phase modulation in hollow-core fibers to generate single 1-fs pulses in the visible. Varying the intensity and duration of the Gaussian-shaped pump pulse at the input induces optimal rotational response of the molecules. The probe pulse, which scatters off of the resulting time variation of the refractive index, is shaped at the input for optimal compression at the output, including dispersion to all orders.