Dynamics of nonlinear excitations of helically confined charges

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behaviour of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behaviour using an effective discrete nonlinear Schr\"{o}dinger model, which allows us among others to identify a number of breather-like excitations.Comment: 11 pages, 7 figure

Finite temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles N and the box size L, implying non-extensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form whereas in the high temperature regime an exponential decay is observed. The high temperature behaviour shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the non-linear behaviour of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.Comment: 12 pages, 13 figure

Long non-coding RNA structure and function: Is there a link?

RNA has emerged as the prime target for diagnostics, therapeutics and the development of personalized medicine. In particular, the non-coding RNAs (ncRNAs) that do not encode proteins, display remarkable biochemical versatility. They can fold into complex structures and interact with proteins, DNA and other RNAs, modulating the activity, DNA targets or partners of multiprotein complexes. Thus, ncRNAs confer regulatory plasticity and represent a new layer of epigenetic control that is dysregulated in disease. Intriguingly, for long non-coding RNAs (lncRNAs, >200 nucleotides length) structural conservation rather than nucleotide sequence conservation seems to be crucial for maintaining their function. LncRNAs tend to acquire complex secondary and tertiary structures and their functions only impose very subtle sequence constraints. In the present review we will discuss the biochemical assays that can be employed to determine the lncRNA structural configurations. The implications and challenges of linking function and lncRNA structure to design novel RNA therapeutic approaches will also be analyzed

Classical scattering of charged particles confined on an inhomogeneous helix

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincar\'e surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.Comment: 15 pages, 18 figure

Exploring Rigidly Rotating Vortex Configurations and their Bifurcations in Atomic Bose-Einstein Condensates

In the present work, we consider the problem of a system of few vortices $N \leq 5$ as it emerges from its experimental realization in the field of atomic Bose-Einstein condensates. Starting from the corresponding equations of motion, we use a two-pronged approach in order to reveal the configuration space of the system's preferred dynamical states. On the one hand, we use a Monte-Carlo method parametrizing the vortex "particles" by means of hyperspherical coordinates and identifying the minimal energy ground states thereof for $N=2, ..., 5$ and different vortex particle angular momenta. We then complement this picture with a dynamical systems analysis of the possible rigidly rotating states. The latter reveals all the supercritical and subcritical pitchfork, as well as saddle-center bifurcations that arise exposing the full wealth of the problem even at such low dimensional cases. By corroborating the results of the two methods, it becomes fairly transparent which branch the Monte-Carlo approach selects for different values of the angular momentum which is used as a bifurcation parameter.Comment: 12 pages, 7 figures. New improved result

Long non-coding RNA structure and function: Is there a link?

RNA has emerged as the prime target for diagnostics, therapeutics and the development of personalized medicine. In particular, the non-coding RNAs (ncRNAs) that do not encode proteins, display remarkable biochemical versatility. They can fold into complex structures and interact with proteins, DNA and other RNAs, modulating the activity, DNA targets or partners of multiprotein complexes. Thus, ncRNAs confer regulatory plasticity and represent a new layer of epigenetic control that is dysregulated in disease. Intriguingly, for long non-coding RNAs (lncRNAs, >200 nucleotides length) structural conservation rather than nucleotide sequence conservation seems to be crucial for maintaining their function. LncRNAs tend to acquire complex secondary and tertiary structures and their functions only impose very subtle sequence constraints. In the present review we will discuss the biochemical assays that can be employed to determine the lncRNA structural configurations. The implications and challenges of linking function and lncRNA structure to design novel RNA therapeutic approaches will also be analyzed