70 research outputs found
Low Energy Nucleon-Nucleon Scattering with the Skyrme Model in the Geodetic Approximation
We calculate nucleon-nucleon scattering at low energies and large impact
parameter in the Skyrme model within the framework for soliton scattering
proposed by Manton. This corresponds to a truncation of the degrees of freedom
to the twelve collective coordinates which essentially describe the rigid body
motion of the pair of Skyrmions. We take to its logical conclusion the result
that the induced kinetic energy for these collective coordinates in the product
ansatz behaves as one over the separation and hence can dominate over the
potential. This behaviour implies to leading order that we can drop the
potential and the resulting motion reduces simply to geodesic motion on the
manifold parametrized by the variables of the product ansatz. We formulate the
semi-classical quantization of these variables to obtain the motion
corresponding to the nucleonic states of the Skyrme model. This is the
appropriate description for the nucleons in order to consider their scattering
within Manton's framework in the semi-classical approximation. We investigate
the implications for the scattering of nucleons with various initial
polarizations using the approximation method of ``variation of constants''.Comment: 18 pages, UDEM-LPN-TH-94-19
The Effect of low Momentum Quantum Fluctuations on a Coherent Field Structure
In the present work the evolution of a coherent field structure of the
Sine-Gordon equation under quantum fluctuations is studied. The basic equations
are derived from the coherent state approximation to the functional
Schr\"odinger equation for the field. These equations are solved asymptotically
and numerically for three physical situations. The first is the study of the
nonlinear mechanism responsible for the quantum stability of the soliton in the
presence of low momentum fluctuations. The second considers the scattering of a
wave by the Soliton. Finally the third problem considered is the collision of
Solitons and the stability of a breather.
It is shown that the complete integrability of the Sine-Gordon equation
precludes fusion and splitting processes in this simplified model.
The approximate results obtained are non-perturbative in nature, and are
valid for the full nonlinear interaction in the limit of low momentum
fluctuations. It is also found that these approximate results are in good
agreement with full numerical solutions of the governing equations. This
suggests that a similar approach could be used for the baby Skyrme model, which
is not completely integrable. In this case the higher space dimensionality and
the internal degrees of freedom which prevent the integrability will be
responsable for fusion and splitting processes. This work provides a starting
point in the numerical solution of the full quantum problem of the interaction
of the field with a fluctuation.Comment: 15 pages, 9 (ps) figures, Revtex file. Some discussion expanded but
conclusions unchanged. Final version to appear in PR
Stable spinning optical solitons in three dimensions
We introduce spatiotemporal spinning solitons (vortex tori) of the
three-dimensional nonlinear Schrodinger equation with focusing cubic and
defocusing quintic nonlinearities. The first ever found completely stable
spatiotemporal vortex solitons are demonstrated. A general conclusion is that
stable spinning solitons are possible as a result of competition between
focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let
Nucleon-nucleon interaction in the Skyrme model
We consider the interaction of two skyrmions in the framework of the sudden
approximation. The widely used product ansatz is investigated. Its failure in
reproducing an attractive central potential is associated with terms that
violate G-parity. We discuss the construction of alternative ans\"atze and
identify a plausible solution to the problem.Comment: 18 pages, 9 figure
Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions
We compute the finite temperature induced fermion number for fermions coupled
to a static nonlinear sigma model background in (2+1) dimensions, in the
derivative expansion limit. While the zero temperature induced fermion number
is well known to be topological (it is the winding number of the background),
at finite temperature there is a temperature dependent correction that is
nontopological -- this finite T correction is sensitive to the detailed shape
of the background. At low temperature we resum the derivative expansion to all
orders, and we consider explicit forms of the background as a CP^1 instanton or
as a baby skyrmion.Comment: 10 pp, revtex
Subsampling effects in neuronal avalanche distributions recorded in vivo
Background Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma=1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task. Results Neither the LFP nor the subsampled SOC models showed a power law for f(s). Both, f(s) and sigma, depended sensitively on the subsampling geometry and the dynamics of the model. Only one of the SOC models, the Abelian Sandpile Model, exhibited f(s) and sigma similar to those calculated from LFP activity. Conclusions Since subsampling can prevent the observation of the characteristic power law and sigma in SOC systems, misclassifications of critical systems as sub- or supercritical are possible. Nevertheless, the system specific scaling of f(s) and sigma under subsampling conditions may prove useful to select physiologically motivated models of brain function. Models that better reproduce f(s) and sigma calculated from the physiological recordings may be selected over alternatives
Self-organization of developing embryo using scale-invariant approach
<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p
Complex systems and the technology of variability analysis
Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients
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