3,006 research outputs found

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

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    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

    Chaos and the continuum limit in nonneutral plasmas and charged particle beams

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    This paper examines discreteness effects in nearly collisionless N-body systems of charged particles interacting via an unscreened r^-2 force, allowing for bulk potentials admitting both regular and chaotic orbits. Both for ensembles and individual orbits, as N increases there is a smooth convergence towards a continuum limit. Discreteness effects are well modeled by Gaussian white noise with relaxation time t_R = const * (N/log L)t_D, with L the Coulomb logarithm and t_D the dynamical time scale. Discreteness effects accelerate emittance growth for initially localised clumps. However, even allowing for discreteness effects one can distinguish between orbits which, in the continuum limit, feel a regular potential, so that emittance grows as a power law in time, and chaotic orbits, where emittance grows exponentially. For sufficiently large N, one can distinguish two different `kinds' of chaos. Short range microchaos, associated with close encounters between charges, is a generic feature, yielding large positive Lyapunov exponents X_N which do not decrease with increasing N even if the bulk potential is integrable. Alternatively, there is the possibility of larger scale macrochaos, characterised by smaller Lyapunov exponents X_S, which is present only if the bulk potential is chaotic. Conventional computations of Lyapunov exponents probe X_N, leading to the oxymoronic conclusion that N-body orbits which look nearly regular and have sharply peaked Fourier spectra are `very chaotic.' However, the `range' of the microchaos, set by the typical interparticle spacing, decreases as N increases, so that, for large N, this microchaos, albeit very strong, is largely irrelevant macroscopically. A more careful numerical analysis allows one to estimate both X_N and X_S.Comment: 13 pages plus 17 figure

    Correlation of mRNA delivery timing and protein expression in lipid-based transfection

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    Non-viral gene delivery is constrained by the dwell time that most synthetic nucleic acid nanocarriers spend inside endosomal compartments. In order to overcome this endosomal-release bottleneck, methods are required that measure nanocarrier uptake kinetics and transfection efficiency simultaneously. Here, we employ live-cell imaging on single-cell arrays (LISCA) to study the delivery-time distribution of lipid-based mRNA complexes under varied serum conditions. By fitting a translation-maturation model to hundreds of individual eGFP reporter fluorescence time courses, the protein expression onset times and the expression rates after transfection are determined. Using this approach, we find that delivery timing and protein expression rates are not intrinsically correlated at the single-cell level, even though population-averaged values of both parameters conjointly change as a function of increasing external serum protein fraction. Lipofectamine-mediated delivery showed decreased transfection efficiency and longer delivery times with increasing serum protein concentration. This is in contrast to ionizable lipid nanoparticle (i-LNP)-mediated transfer, which showed increased efficiency and faster uptake in the presence of serum. In conclusion, the interdependences of single-cell expression rates and onset timing provide additional clues on uptake and release mechanisms, which are useful for improving nucleic acid delivery

    Bosonization of current-current interactions

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    We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of WW_\infty on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.Comment: 15 pages, TeX, C Version 3.0, Princeton preprin

    Correlation length scalings in fusion edge plasma turbulence computations

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    The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence computations. Scalings by density gradient length, collisionality, plasma beta, and by an imposed shear flow are considered. It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.Comment: Submitted to "Plasma Physics and Controlled Fusion
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