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Modulation Instability and Solitons on Finite Background
  1. Wave Trains, Solitons and Modulation Theory in FPU Chains |
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The time of maximum at both the stations seems to be positively correlated with each other during the entire period. The time of maximum of semi-diurnal anisotropy f 2 significantly fluctuates during and significantly shifts towards an earlier time during solar activity maximum and then shifts towards later hours from onwards at Inuvik.

It is also noteworthy that the time of maximum significantly shifts towards an earlier time at Deep River station as compared to the time of maximum at Inuvik station throughout the period.

It is also observed that the time of maximum f 2 changes quite frequently from higher to lower values at Deep River throughout the period. As seen from the figure it is also noteworthy that the time of maximum for these two stations is found to positively correlated during and anti-correlated for the period Solar wind and interplanetary magnetic field IMF plays an important role in controlling the electrodynamics of the heliosphere Parker, Solar wind speed, V and IMF parameters, such as vector B , spiral angle and tilt are important for the transport of energetic cosmic ray particles in the heliosphere, for the modulation of cosmic ray and creation of cosmic ray anisotropy in the interplanetary space.

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The solar wind velocity determines two components of the cosmic ray modulation mechanism: the convection and the adiabatic energy changes. The high velocity solar wind fluxes associated with coronal holes give rise to both isotropic and anisotropic variations in cosmic ray intensity Iucci et al. Changes of the solar wind velocity near the Earth may have not only local but also the global character Sheeley et al. Kondoh et al. The IMF magnitude and fluctuations are responsible for the depression of cosmic ray intensity during high-speed solar wind events Sabbah, a.

The IMF magnitude reaches the highest value during declining phase of solar activity Sabbah, The correlation between cosmic ray intensity and solar wind velocity is statistically significant, especially in the period of the maximum solar activity. The relation of cosmic ray intensity to solar wind velocity is, in general, dependent on physical conditions in the interplanetary space varying with the solar activity. The year-to-year variation of the effect of solar wind upon cosmic ray intensity is dependent on solar activity and the decrement of cosmic ray intensity due to the variation of solar wind velocity is proportional to sunspot number Fujimoto et al.

As depicted in Fig.

Thus from the above investigations we may infer that neither the amplitude nor the direction of all the three harmonics have any significant trend associated with solar wind velocity on quiet days at Inuvik station with low cut off rigidity during Therefore, it may be deduced from these plots that the amplitude as well as direction of first three harmonics on quiet days do not depend on the HSSWS or by the sources on the Sun responsible for producing the HSSWS such as polar coronal holes PCH etc. Thus, we may infer that the amplitude and direction of the anisotropy on quiet days are weakly dependent on HSSWSs for two neutron monitoring station of mid and low cutoff rigidity threshold, which is in agreement with earlier findings Munakata et al.

According to Ahluwalia and Riker there is no relation between solar wind speed and diurnal variation in high rigidity region. The modulation of solar diurnal anisotropy is weakly or less dependent on the solar wind velocity Munakata et al. The other components amplitude and phase shows very weak correlation with Bz and V X Bz. While the remaining parameters i. Thus, from the above findings we may infer that the amplitude as well as direction of second harmonic have a good anti-correlation with IMF Bz and the product V x Bz on quiet days at Deep River station.

Sabbah obtained an inverse correlation between cosmic ray intensity and the geomagnetic activity and observed the enhancement in upper cut-off rigidity, Rc and the geomagnetic activity resulting from variation in the solar plasma parameters. Upper cut-off rigidity correlates well with the product VB rather than with magnetic field B since VB reflects both diffusion by the IMF and convection with solar wind. The product VB is more important for cosmic rays and geomagnetic activity modulation rather than IMF alone.

Burlaga and Ness argued that it is ultimately the strong magnetic field and their associated fluctuations that produce the modulation of cosmic rays. Coupling between the IMF strength B and the CR transport parameters leads to a simple modulation model in which the modulation process is linked to global variations of B. Belov suggested that the local value of the IMF place a significant role in controlling the GCR modulation at an observing site. On the basis of above investigations following important conclusions may be drawn:. Additional studies can aid in understanding the results reported here and help to exploit this information to constrain models of solar modulation.

It will also be of interest to determine how the correlation slopes depend on the time scale over which the data are averaged since the spatial extent of the structures in the heliosphere that control the modulation on short time scales must be smaller than those that produce long term effects. The authors are indebted to various experimental groups, in particular, Prof.

Margret D. Wilson, Prof. Nagashima, Miss. Aoi Inoue and Prof. King for providing the data. Agrawal, S. High-energy cosmic ray intensity increase of non-solar origin and the unusual Forbush decrease of August Journal of Geophysical Research. Is there a twenty year wave in the diurnal anisotropy of cosmic rays. Geophysical Research Letters. Secular changes in the upper cut-off rigidity of the solar diurnal anisotropy. Planetary and Space Science. Edited by B.

Sripathi Acharya, Sunil Gupta, P. Jagadeesan, Atul Jain, S. Karthikeyan, Samuel Morris, and Suresh Tonwar. Mumbai: Tata Institute of Fundamental Research.

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The modulation of galactic cosmic rays in the interplanetary medium. Anisotropic diffusion of solar cosmic rays. Further evidence on the correlation between transverse fluctuations in the interplanetary magnetic field and Kp. Edited by D. Kieda, M. Salamon, and B.

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  • Inactivation of these channels, and the current associated with them the M-current , changes the intrinsic excitability of neurons. Experiments have shown that ACh modulates neural excitability in two ways: 1 ACh reduces spike frequency adaptation SFA mediated by the M-current and increases the slope of the neural spike frequency-current f-I curve [ 9 , 10 ], and 2 it induces changes in the synchronization properties of neurons via the phase response curve PRC [ 11 , 12 ].

    It has been previously shown that networks of type 1 neurons are asynchronous while those of type 2 neurons are highly synchronous [ 12 ]. Our network model consists of a square lattice split into an excitatory and an inhibitory layer. A connectivity scheme balancing short-range excitation and global inhibition was used to mimic the lateral inhibition motif seen in many areas of the cerebral cortex.

    Breaking of modulated wave groups: Kinematics and energy dissipation processes

    The red dots indicate the spike times of the neuron in question and illustrate the the offset of an upstate corresponds to the maximal level of. The phase response curve of individual neurons shifts from type 1 to type 2 as increases. Key: 1 quiescent 2 mixed dynamics, 3 stationary bump 4 traveling bump 5 global high frequency activity 6 multiple interacting bumps 7 planar wave 8 global burst. The aim of this paper is to elucidate how cholinergic modulation interacts with network connectivity structure to form various patterns of network activation obtained experimentally.

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    To do so we use simulations of a conductance-based Hodgkin-Huxley cortical network model including cholinergic modulation [ 13 ] and a mexican hat type of connectivity scheme that was experimentally observed in various cortical areas [ 14 , 15 ]. We demonstrate how regulation of SFA in conjunction with the balance between excitation and inhibition leads to various network dynamics. We then study the properties of the two states and their transition. Functionally, the high ACh state is far more sensitive to heterogeneities in network structure than the traveling wave state.

    We use a conductance-based model of cholinergic modulation in pyramidal cells using Hodgkin-Huxley type gating dynamics for active conductances [ 13 ]. The membrane voltage dynamics are described by: 1 The gating variables m , h , n , and s represent the sodium conductance, the effective blockage of sodium current and potassium conductances respectively. The s variable corresponds to the slow potassium current which is ultimately responsible for the shift in neural excitability mediated by ACh. Adjusting the magnitude of this current i. For low values neurons have a minimal level of SFA.

    As increases the neurons display high levels of SFA. The direct input current, I tune , was adjusted so that all cells fired at 10 Hz in the absence of any synaptic input, independent of. Values of the neural parameters were adopted from [ 12 ] and are listed in 1.