Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region

In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.

Self-assembly of highly ordered DNA origami lattices at solid-liquid interfaces by controlling cation binding and exchange

The surface-assisted hierarchical self-assembly of DNA origami lattices represents a versatile and straightforward method for the organization of functional nanoscale objects such as proteins and nanoparticles.Here,we demonstrate that controlling the binding and exchange of different monovalent and divalent cation species at the DNA-mica interface enables the self-assembly of highly ordered DNA origami lattices on mica surfaces.The development of lattice quality and order is quantified by a detailed topological analysis of high-speed atomic force microscopy(HS-AFM)images.We find that lattice formation and quality strongly depend on the monovalent cation species.Na^(+)is more effective than Li^(+)and K^(+)in facilitating the assembly of high-quality DNA origami lattices,because it is replacing the divalent cations at their binding sites in the DNA backbone more efficiently.With regard to divalent cations,Ca^(2+)can be displaced more easily from the backbone phosphates than Mg^(2+)and is thus superior in guiding lattice assembly.By independently adjusting incubation time,DNA origami concentration,and cation species,we thus obtain a highly ordered DNA origami lattice with an unprecedented normalized correlation length of 8.2.Beyond the correlation length,we use computer vision algorithms to compute the time course of different topological observables that,overall,demonstrate that replacing MgCl_(2) by CaCl_(2) enables the synthesis of DNA origami lattices with drastically increased lattice order.

Laws of Zipf and Benford, intermittency, and critical fluctuations

We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluctuations at criticality. The equivalences stem from a common statistical-mechanical structure that departs from the usual via a one-parameter deformation of the exponential and logarithmic functions. The generalized structure arises when configurational phase space is incompletely visited such that the accessible fraction has fractal properties. Thermodynamically, the common focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials. The theory is in quantitative agreement with real size-rank data and it naturally includes the bends or tails observed for small and large rank.