292 research outputs found

    Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-D\"onau-Frauendorf theory

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    We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong coupling limit so as to yield a completely equivalent formulation. It is emphasized that the conventional core-particle coupling calculation introduces a further approximation that avoids what has hitherto been the most time-consuming feature of the full theory, and that this approximation can be introduced either in the intrinsic system, the usual case, or in the laboratory system, our preference. A new algorithm is described for the full theory that largely removes the difference in complexity between the two types of calculation. Comparison of the full and approximate theories for some representative cases provides a basis for the assessment of the accuracy of the traditional approach. We find that for well-deformed nuclei, e.g. 157Gd and 157Tb, the core-coupling method and the full theory give similar results.Comment: revtex, 3 figures(postscript), submitted to Phys.Rev.

    Foundations of self-consistent particle-rotor models and of self-consistent cranking models

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    The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.Comment: 29 page

    Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

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    Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances (\approx10~μm\mu m) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

    High-order Harmonic Generation and Dynamic Localization in a driven two-level system, a non-perturbative solution using the Floquet-Green formalism

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    We apply the Floquet-Green operator formalism to the case of a harmonically-driven two-level system. We derive exact expressions for the quasi-energies and the components of the Floquet eigenstates with the use of continued fractions. We study the avoided crossings structure of the quasi-energies as a function of the strength of the driving field and give an interpretation in terms of resonant multi-photon processes. From the Floquet eigenstates we obtain the time-evolution operator. Using this operator we study Dynamic Localization and High-order Harmonic Generation in the non-perturbative regime

    Finding Anomalous Periodic Time Series: An Application to Catalogs of Periodic Variable Stars

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    Catalogs of periodic variable stars contain large numbers of periodic light-curves (photometric time series data from the astrophysics domain). Separating anomalous objects from well-known classes is an important step towards the discovery of new classes of astronomical objects. Most anomaly detection methods for time series data assume either a single continuous time series or a set of time series whose periods are aligned. Light-curve data precludes the use of these methods as the periods of any given pair of light-curves may be out of sync. One may use an existing anomaly detection method if, prior to similarity calculation, one performs the costly act of aligning two light-curves, an operation that scales poorly to massive data sets. This paper presents PCAD, an unsupervised anomaly detection method for large sets of unsynchronized periodic time-series data, that outputs a ranked list of both global and local anomalies. It calculates its anomaly score for each light-curve in relation to a set of centroids produced by a modified k-means clustering algorithm. Our method is able to scale to large data sets through the use of sampling. We validate our method on both light-curve data and other time series data sets. We demonstrate its effectiveness at finding known anomalies, and discuss the effect of sample size and number of centroids on our results. We compare our method to naive solutions and existing time series anomaly detection methods for unphased data, and show that PCAD's reported anomalies are comparable to or better than all other methods. Finally, astrophysicists on our team have verified that PCAD finds true anomalies that might be indicative of novel astrophysical phenomena

    Semiclassical description of multiphoton processes

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    We analyze strong field atomic dynamics semiclassically, based on a full time-dependent description with the Hermann-Kluk propagator. From the properties of the exact classical trajectories, in particular the accumulation of action in time, the prominent features of above threshold ionization (ATI) and higher harmonic generation (HHG) are proven to be interference phenomena. They are reproduced quantitatively in the semiclassical approximation. Moreover, the behavior of the action of the classical trajectories supports the so called strong field approximation which has been devised and postulated for strong field dynamics.Comment: 10 pages, 11 figure

    Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

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    We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei 155,157^{155,157}Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st
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