The asymptotic quasi-stationary states of the two-dimensional magnetically confined plasma and of the planetary atmosphere

We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is related to the system consisting of a discrete set of point-like vortices interacting in plane by a short range potential. A field-theoretical formalism is developed for describing the continuous version of this system. The action functional can be written in the Bogomolnyi form (emphasizing the role of Self-Duality of the asymptotic states) but the minimum energy is no more topological and the asymptotic structures appear to be non-stationary, which is a major difference with respect to traditional topological vortex solutions. Versions of this field theory are discussed and we find arguments in favor of a particular form of the equation. We comment upon the significant difference between the CHM fluid/plasma and the Euler fluid and respectively the Abelian-Higgs vortex models.Comment: Latex 126 pages, 7 eps figures included. Discussion on various forms of the equatio

Long-range sound-mediated dark soliton interactions in trapped atomic condensates

A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An idealized double well geometry is shown to yield perfect energy transfer and complete periodic identity reversal of the two solitons. Two experimentally relevant geometries are analyzed which should enable the observation of this long-range interaction

User needs, benefits and integration of robotic systems in a space station laboratory

The methodology, results and conclusions of the User Needs, Benefits, and Integration Study (UNBIS) of Robotic Systems in the Space Station Microgravity and Materials Processing Facility are summarized. Study goals include the determination of user requirements for robotics within the Space Station, United States Laboratory. Three experiments were selected to determine user needs and to allow detailed investigation of microgravity requirements. A NASTRAN analysis of Space Station response to robotic disturbances, and acceleration measurement of a standard industrial robot (Intelledex Model 660) resulted in selection of two ranges of low gravity manipulation: Level 1 (10-3 to 10-5 G at greater than 1 Hz.) and Level 2 (less than = 10-6 G at 0.1 Hz). This included an evaluation of microstepping methods for controlling stepper motors and concluded that an industrial robot actuator can perform milli-G motion without modification. Relative merits of end-effectors and manipulators were studied in order to determine their ability to perform a range of tasks related to the three low gravity experiments. An Effectivity Rating was established for evaluating these robotic system capabilities. Preliminary interface requirements were determined such that definition of requirements for an orbital flight demonstration experiment may be established

Gapless finite-TT theory of collective modes of a trapped gas

We present predictions for the frequencies of collective modes of trapped Bose-condensed $^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.Comment: 4 pages Latex and 2 postscript figure

Kink Dynamics in a Topological Phi^4 Lattice

It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was then suggested that these ``topological discrete systems'' are a natural choice for the numerical study of continuum kink dynamics. Giving particular emphasis to the phi^4 theory, we numerically investigate kink-antikink scattering and breather formation in these topological lattices. Our results indicate that, even though these systems are quite accurate for studying free kinks in coarse lattices, for legitimate dynamical kink problems the accuracy is rather restricted to fine lattices (h~0.1). We suggest that this fact is related to the breaking of the Bogomol'nyi bound during the kink-antikink interaction, where the field profile loses its static property as required by the Bogomol'nyi argument. We conclude, therefore, that these lattices are not suitable for the study of more general kink dynamics, since a standard discretization is simpler and has effectively the same accuracy for such resolutions.Comment: RevTeX, 4 pages, 4 figures; Revised version, accepted to Physical Review E (Brief Reports

Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases

In this paper we use microscopic arguments to derive a nonlinear Schr\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body T-matrix approximation in a trap. In addition, we discuss how the bare particle many-body T-matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body T-matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e. Hartree-Fock-Bogoliubov (HFB), theory.Comment: Resolved some problems with printing of figure

Scattering and leapfrogging of vortex rings in a superfluid

The dynamics of vortex ring pairs in the homogeneous nonlinear Schr\"odinger equation is studied. The generation of numerically-exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the Biot-Savart law.Comment: 12 pages, 11 figure

DNA methylation in human epigenomes depends on local topology of CpG sites

In vertebrates, methylation of cytosine at CpG sequences is implicated in stable and heritable patterns of gene expression. The classical model for inheritance, in which individual CpG sites are independent, provides no explanation for the observed non-random patterns of methylation. We first investigate the exact topology of CpG clustering in the human genome associated to CpG islands. Then, by pooling genomic CpG clusters on the basis of short distances between CpGs within and long distances outside clusters, we show a strong dependence of methylation on the number and density of CpG organization. CpG clusters with fewer, or less densely spaced, CpGs are predominantly hyper-methylated, while larger clusters are predominantly hypo-methylated. Intermediate clusters, however, are either hyper- or hypo-methylated but are rarely found in intermediate methylation states. We develop a model for spatially-dependent collaboration between CpGs, where methylated CpGs recruit methylation enzymes that can act on CpGs over an extended local region, while unmethylated CpGs recruit demethylation enzymes that act more strongly on nearby CpGs. This model can reproduce the effects of CpG clustering on methylation and produces stable and heritable alternative methylation states of CpG clusters, thus providing a coherent model for methylation inheritance and methylation patterning.Cecilia Lövkvist, Ian B. Dodd, Kim Sneppen and Jan O. Haerte

Simulation of the behavior of biologically-inspired swarm robots for the autonomous inspection of buried pipes

The use of robots for the inspection of buried pipelines has gained popularity over the past decade. In this paper we move the vision forward by examining what behavior and attributes would be required for these robots to become autonomous and pervasive within buried water pipe infrastructure. We present the results from novel simulations to evidence the inspection capability of autonomous robots, investigating operation, cooperation and communication attributes. The simulation uses a biologically-inspired behavior that provides complete and consistent coverage of real life example clean water distribution management areas. We show that autonomous robots could operate without a centralized controller and benefit from having some degree of in-pipe communication. We evidence the ability to adapt to changes in communication, speed, and flow conditions. The mathematical model that we derive through the simulation is scalable with the change of network length, topology, robots’ speed and number. This work paves the way and sets the specifications for practical development of autonomous pervasive robots for the inspection of complex pipe networks

Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length

Using the explicit numerical solution of the axially-symmetric Gross-Pitaevskii equation we study the oscillation of the Bose-Einstein condensate induced by a periodic variation in the atomic scattering length $a$. When the frequency of oscillation of $a$ is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through maximum and minimum. Such growth and decay cycle of the amplitude may keep on repeating. Similar behavior is also observed in a rotating Bose-Einstein condensate.Comment: 14 REVTEX4 pages, 18 PS figures, final version Accepted in Journal of Physics