Topological interactions between ring polymers: Implications for chromatin loops

Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.Comment: 12 pages, 11 figures. The article has been accepted by The Journal Of Chemical Physics. After it is published, it will be found at http://jcp.aip.or

Harmonically Trapped Four-Boson System

Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply-bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body $s$-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasi-universal, or strongly non-universal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body $s$-wave scattering length $a_s$, $a_s>0$. In the weakly- to medium-strongly-interacting regime, one of the states approaches the energy obtained for a hard core interaction model. This state is identified as the energetically lowest-lying "BEC state". Structural properties are also presented.Comment: 6 figure

Emergent structure in a dipolar Bose gas in a one-dimensional lattice

We consider an ultracold dipolar Bose gas in a one-dimensional lattice. For a sufficiently large lattice recoil energy, such a system becomes a series of non-overlapping Bose-Einstein condensates that interact via the long-range dipole-dipole interaction (ddi). We model this system via a coupled set of non-local Gross-Pitaevskii equations (GPEs) for lattices of both infinite and finite extent. We find significantly modified stability properties in the lattice due to the softening of a discrete roton-like mode, as well as "islands" in parameter space where biconcave densities are predicted to exist that only exist in the presence of the other condensates on the lattice. We solve for the elementary excitations of the system to check the dynamical stability of these solutions and to uncover the nature of their collapse. By solving a coupled set of GPEs exactly on a full numeric grid, we show that this emergent biconcave structure can be realized in a finite lattice with atomic $^{52}$Cr.Comment: 7+ pages, 2 column format, 7 figure

Dynamics of ultracold molecules in confined geometry and electric field

We present a time-independent quantum formalism to describe the dynamics of molecules with permanent electric dipole moments in a two-dimensional confined geometry such as a one-dimensional optical lattice, in the presence of an electric field. Bose/Fermi statistics and selection rules play a crucial role in the dynamics. As examples, we compare the dynamics of confined fermionic and bosonic polar KRb molecules under different confinements and electric fields. We show how chemical reactions can be suppressed, either by a "statistical suppression" which applies for fermions at small electric fields and confinements, or by a "potential energy suppression", which applies for both fermions and bosons at high electric fields and confinements. We also explore collisions that transfer molecules from one state of the confining potential to another. Although these collisions can be significant, we show that they do not play a role in the loss of the total number of molecules in the gas.Comment: 13 pages, 6 figure

Critical superfluid velocity in a trapped dipolar gas

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system.Comment: 5 pages, 4 figures, version accepted to PR

Effect of flow on the acoustic reflection coefficient at a duct inlet

The effect of duct Mach number upon the acoustic reflection coefficient at the inlet of a duct with mean flow is investigated. An analysis, which models the duct inlet as a very short, one-dimensional nozzle over which the mean flow is accelerated from rest, gives good agreement with some recent experimental results. Discrepancies between the analysis and the experimental results are discussed in terms of radiation losses at the inlet and real fluid-flow effects within the duct

Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.Comment: 39 pages, including 14 figure