Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

In this work, a new theoretical mechanism is presented in which equatorial Rossby and inertio-gravity wave modes may interact with each other through resonance with the diurnal cycle of tropical deep convection. We have adopted the two-layer incompressible equatorial primitive equations forced by a parametric heating that roughly represents deep convection activity in the tropical atmosphere. The heat source was parametrized in the simplest way according to the hypothesis that it is proportional to the lower-troposphere moisture convergence, with the background moisture state function mimicking the structure of the ITCZ. In this context, we have investigated the possibility of resonant interaction between equatorially trapped Rossby and inertio-gravity modes through the diurnal cycle of the background moisture state function. The reduced dynamics of a single resonant duo shows that when this diurnal variation is considered, a Rossby wave mode can undergo significant amplitude modulations when interacting with an inertio-gravity wave mode, which is not possible in the context of the resonant triad non-linear interaction. Therefore, the results suggest that the diurnal variation of the ITCZ can be a possible dynamical mechanism that leads the Rossby waves to be significantly affected by high frequency modes.

A path integral approach to the full Dicke model with dipole-dipole interaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Wind plant interaction with series-compensated power systems

Wind power based generation has been rapidly growing world-wide during the recent past. In order to transmit large amounts of wind power over long distances, system planners may often add series compensation to existing transmission lines owing to several benefits such as improved steady-state power transfer limit, improved transient stability, and efficient utilization of transmission infrastructure. Application of series capacitors has posed resonant interaction concerns such as through subsynchronous resonance (SSR) with conventional turbine-generators. Wind turbine-generators may also be susceptible to such resonant interactions. However, not much information is available in literature and even engineering standards are yet to address these issues. The motivation problem for this research is based on an actual system switching event that resulted in undamped oscillations in a 345-kV series-compensated, typical ring-bus power system configuration. Based on time-domain ATP (Alternative Transients Program) modeling, simulations and analysis of system event records, the occurrence of subsynchronous interactions within the existing 345-kV series-compensated power system has been investigated. Effects of various small-signal and large-signal power system disturbances with both identical and non-identical wind turbine parameters (such as with a statistical-spread) has been evaluated. Effect of parameter variations on subsynchronous oscillations has been quantified using 3D-DFT plots and the oscillations have been identified as due to electrical self-excitation effects, rather than torsional interaction. Further, the generator no-load reactance and the rotor-side converter inner-loop controller gains have been identified as bearing maximum sensitivity to either damping or exacerbating the self-excited oscillations. A higher-order spectral analysis method based on modified Prony estimation has been successfully applied to the field records identifying dominant 9.79 Hz subsynchronous oscillations. Recommendations have been made for exploring countermeasures.

Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

Ejection of energetic photoelectrons in laser-induced autoionisation: effects of high-order ionisation processes

Resonant interaction of an autoionising state with a strong laser field is considered and effects of second-order ionisation processes are investigated. The authors show that these processes play a very important role in laser-induced autoionisation (LIA). They drastically affect the lowest-order peaks in the photoelectron spectrum. In addition to these peaks, high-order peaks due to ejection of energetic photoelectrons appear. For the laser intensities of current interest, second-order peaks are much stronger than the original ones, an important result that, they believe, can be observed experimentally. Moreover, `peak switching', a general feature of above-threshold ionisation, is also manifest in the electron spectrum of LIA.

Global oscillations in a magnetic solar model : II Oblique propagation

Pint?r, B.; Erd?lyi, R.; Goossens, M., Global oscillations in a magnetic solar model. II. Oblique propagation, Astronomy and Astrophysics, Volume 466, Issue 1, April IV 2007, pp.377-388 Pint?r, B.; Erd?lyi, R.; Goossens, M., (2007) 'Global oscillations in a magnetic solar model II. Oblique propagation', Astronomy and Astrophysics 466(1) pp.377-388 RAE2008

Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions

Li, Xing; Habbal, S.R., (2005) 'Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions', Journal of Geophysical Research 110(A10) pp.A10109 RAE2008

Uma análise da dinâmica do pêndulo eletromecânico utilizando a teoria de pertubações

Pós-graduação em Matemática - IBILCE

Turbulence driven particle transport in Texas Helimak

We analyze the turbulence driven particle transport in Texas Helimak [K. W. Gentle and H. He, Plasma Sci. Technol. 10, 284 (2008)], a toroidal plasma device with a one-dimensional equilibrium with magnetic curvature and shear. Alterations on the radial electric field, through an external voltage bias, change the spectral plasma characteristics inducing a dominant frequency for negative bias values and a broad band frequency spectrum for positive bias values. When applying a negative bias, the transport is high where the waves propagate with phase velocities near the plasma flow velocity, an indication that the transport is strongly affected by a wave particle resonant interaction. On the other hand, for positive bias values, the plasma has a reversed shear flow, and we observe that the transport is almost zero in the shearless radial region, an evidence of a transport barrier in this region. (c) 2012 American Institute of Physics. [doi:10.1063/1.3676607]

Analysis of Electrostatic Turbulence Drive in Texas Helimak.

Plasma turbulence and particle transport in Texas Helimak change with the radial electric field profile modified by an external voltage bias. When the bias is positive, the turbulence shows enhanced level and broadband spectra with extreme events, similar to the turbulence in tokamak scrape-‐off layer. However, negative bias reduces the turbulence level and decreases the spectrum widths. Moreover, for negative biased shots, the particle transport is strongly affected by a wave particle resonant interaction. On the other hand, for positive bias values, the plasma presents a transport barrier in the reversed shear flow region.

Thalamocortical dysrhythmia: A neurological and neuropsychiatric syndrome characterized by magnetoencephalography

Spontaneous magnetoencephalographic activity was recorded in awake, healthy human controls and in patients suffering from neurogenic pain, tinnitus, Parkinson's disease, or depression. Compared with controls, patients showed increased low-frequency θ rhythmicity, in conjunction with a widespread and marked increase of coherence among high- and low-frequency oscillations. These data indicate the presence of a thalamocortical dysrhythmia, which we propose is responsible for all the above mentioned conditions. This coherent θ activity, the result of a resonant interaction between thalamus and cortex, is due to the generation of low-threshold calcium spike bursts by thalamic cells. The presence of these bursts is directly related to thalamic cell hyperpolarization, brought about by either excess inhibition or disfacilitation. The emergence of positive clinical symptoms is viewed as resulting from ectopic γ-band activation, which we refer to as the “edge effect.” This effect is observable as increased coherence between low- and high-frequency oscillations, probably resulting from inhibitory asymmetry between high- and low-frequency thalamocortical modules at the cortical level.

On the 3-Wave Equations with Constant Boundary Conditions

2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).