Large Values Of Amplitude Research Articles

Eddy surface properties and propagation at Southern Hemisphere western boundary current systems

Abstract. Oceanic eddies exist throughout the world oceans, but are more energetic when associated with western boundary currents (WBC) systems. In these regions, eddies play an important role in mixing and energy exchange. Therefore, it is important to quantify and qualify eddies associated with these systems. This is particularly true for the Southern Hemisphere WBC system where only few eddy censuses have been performed to date. In these systems, important aspects of the local eddy population are still unknown, like their spatial distribution and propagation patterns. Moreover, the understanding of these patterns helps to establish monitoring programs and to gain insight in how eddies would affect local mixing. Here, we use a global eddy data set to qualify eddies based on their surface characteristics in the Agulhas Current (AC), the Brazil Current (BC) and the East Australian Current (EAC) systems. The analyses reveal that eddy propagation within each system is highly forced by the local mean flow and bathymetry. Large values of eddy amplitude and temporal variability are associated with the BC and EAC retroflections, while small values occur in the centre of the Argentine Basin and in the Tasman Sea. In the AC system, eddy polarity dictates the propagation distance. BC system eddies do not propagate beyond the Argentine Basin, and are advected by the local ocean circulation. EAC system eddies from both polarities cross south of Tasmania but only the anticyclonic ones reach the Great Australian Bight. For all three WBC systems, both cyclonic and anticyclonic eddies present a geographical segregation according to radius size and amplitude. Regions of high eddy kinetic energy are associated with the eddies' mean amplitudes, and not with their densities.

Separation of source, site and near-surface attenuation effects in western Turkey

We analyzed 1764 records from 322 micro- and moderate-size local earthquakes in the central west Turkey to separate source, site and near-surface attenuation effects by utilizing a generalized inversion technique (GIT) to the spectra. GIT site transfer functions were compared with horizontal-to-vertical spectral ratio (HVSR) estimates by Akyol et al. (Pure Appl Geophys 170(12):2107–2125. doi: 10.1007/s00024-013-0661-2, 2013). Large amplitude values of vertical component GIT site transfer functions were obtained at different frequency bands for some of the sites. These results imply contaminations of HVSR estimates due to basin geometry induced waves caused by deep or shallow lateral heterogeneities. GIT source function estimates were interpreted as Brune source model. Weak epicentral dependence of near-surface attenuation parameter κ with large scattering could be attributed to the source and propagation path complexities along different paths arriving to the stations. Large fe values with large κ0 values emphasize near-surface weathered zones attenuation effect at high frequencies.

Facilitation of late Somatosensory evoked potentials by electrical train stimuli

Somatosensory evoked potentials (SSEP) may reflect synaptic events and could be suitable to characterise the short-time plasticity of synaptic potentials (SP). For this purpose, the left superficial radial nerve was stimulated in 7 subjects with single or trains of 3 stimuli (C4' against Fz, time interval 500 ms, 1 Hz or 0.4 Hz). The within train interstimulus intervals (ISI) were varied from 2 ms to 10 ms. N20, N1 and N2 displayed a significant gain in amplitude following train stimuli compared with single stimuli. Short ISIs of 2-4 ms led to higher amplitudes of N20, N1 and N2 compared with longer ISIs of 7-10 ms. In general, larger amplitude values were observed with 0.4 Hz stimulus repetition compared with 1.0 Hz. This data reflects synaptic facilitation and refractoriness/habituation. Our results could be helpful to non-invasevely investigate synaptic decay dynamics by late SSEP in diseases of the central nervous system such as migraine or epilepsy.

A method to determine optimal grid parameters based on characteristic analysis of discrete data distribution

We evaluated a method that determines the optimal grid parameters of potential-field data such as the intervals of grid nodes and the grid azimuth. Optimal grid parameters produced the best gridding results with the least amount of data distortions. We used spectral analysis of the data statistics on azimuth projections. The direction with the largest degree of periodicity was defined as the optimal azimuth of the grid. The grid line interval was determined according to the frequency point with the largest amplitude value. By spectral analysis of the data sequence projected in the direction normal to the survey lines, grid point spacing was also determined. Correlative analysis of the template matching method was used to determine the optimal grid range. Tests on simulated and field data proved that this method is rather robust and can be incorporated into gridding software packages.

Facilitation of late somatosensory evoked potentials by electrical train stimuli

Somatosensory evoked potentials (SSEP) may reflect synaptic events and could be suitable to characterise the short-time plasticity of synaptic potentials (SP). For this purpose, the left superficial radial nerve was stimulated in 7 subjects with single or trains of 3 stimuli (C4′ against Fz, time interval 500ms, 1Hz or 0.4Hz). The within train interstimulus intervals (ISI) were varied from 2ms to 10ms. N20, N1 and N2 displayed a significant gain in amplitude following train stimuli compared with single stimuli. Short ISIs of 2–4ms led to higher amplitudes of N20, N1 and N2 compared with longer ISIs of 7–10ms. In general, larger amplitude values were observed with 0.4Hz stimulus repetition compared with 1.0Hz. This data reflects synaptic facilitation and refractoriness/habituation. Our results could be helpful to non-invasevely investigate synaptic decay dynamics by late SSEP in diseases of the central nervous system such as migraine or epilepsy.

Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators

In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion equation of nonlinear oscillators by the iteration method to obtain the relationship between amplitude and angular frequency. We compare the approximate periods obtained by our procedure with the numerical solution and with other methods like energy balance method and variational iteration method. The results show that the approximations are of extreme accuracy.

Quantum Monte Carlo Study of Hard-Core Bosons on the Shastry–Sutherland Lattice

We study the ground state properties of the extended hard-core Bose–Hubbard model in a two-dimensional Shastry–Sutherland lattice by quantum Monte Carlo simulations. The effects of the geometric frustration, described by the ratio t ′ / t between hopping integrals along the nearest-neighbor links and the diagonal links, are studied. We find that for small values of frustration amplitude t ′ / t , a checkerboard solid state emerges at ρ= 1/2; for large values of frustration amplitude t ′ / t , a solid state emerges at ρ= 1/2 with one boson per dimer (dimers on diagonal links); for intermediate values of frustration amplitude t ′ / t , besides the ρ= 1/2 solid state, the ρ= 1/3,2/3 solid states emerge. No stable supersolid state is observed in our calculations. At half filling, we find solid-superfluid-solid phase transition as the frustration amplitude t ′ / t is increased.

Homotopy perturbation method for a conservative x1/3 force nonlinear oscillator

The homotopy perturbation method is used to obtain the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x 1 / 3 . We find this method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.60% for small and large values of oscillation amplitude, while this relative error is as low as 0.050% for the second iteration. Comparison of the results obtained using this method with those obtained by different harmonic balance methods reveals that the former is more effective and convenient for these types of nonlinear oscillators.

Planetary waves in ozone and temperature in the Northern Hemisphere winters of 2002/2003 and early 2005

Abstract. Temperature and ozone data from the sub-millimetre radiometer (SMR) installed aboard the Odin satellite have been examined to study the relationship between temperature and ozone concentration in the lower and upper stratosphere in winter time. The retrieved ozone and temperature profiles have been considered between the range of 24–46 km during the Northern Hemisphere (NH) winter of December 2002 to March 2003 and January to March 2005. A comparison between the ozone mixing ratio and temperature fields has been made for the zonal means, wavenumber one variations and 5-day planetary waves. The amplitude values in temperature variations are ~5 K in the wavenumber one and 0.5–1 K in the 5-day wave. In ozone mixing ratio, the amplitudes reach ~0.5 ppmv in the wavenumber one and 0.05–0.1 ppmv in the 5-day wave. Several stratospheric warming events were observed during the NH winters of 2002/2003 and early 2005. Along with these warming events, amplification of the amplitude has been detected in wavenumber one (up to 30 K in temperature and 1.25 ppmv in ozone) and partly in the 5-day perturbation (up to 2 K in temperature and 0.2 ppmv in ozone). In general, the results show the expected in-phase behavior between the temperature and ozone fields in the lower stratosphere due to dynamic effects, and an out-of-phase pattern in the upper stratosphere, which is expected as a result of photochemical effects. However, these relationships are not valid for zonal means and wavenumber one components when the wave amplitudes are changing dramatically during the strongest stratospheric warming event (at the end of December 2002/beginning of January 2003). Also, for several shorter intervals, the 5-day perturbations in ozone and temperature are not well-correlated at lower heights, particularly when conditions change rapidly. Odin's basic observation schedule provides stratosphere mode data every third day and to validate the reliability of the 5-day waves extracted from the Odin measurements, additional independent data have been analysed in this study: temperature assimilation data by the European Centre for Medium-range Weather Forecasts (ECMWF) for the NH winter of 2002/2003, and satellite measurements of temperature and ozone by the Microwave Limb Sounder (MLS) on board the Aura satellite for the NH winter in early 2005. Good agreement between the temperature fields from Odin and ECMWF data is found at middle latitude where, in general, the 5-day perturbations from the two data sets coincide in both phase and amplitude throughout the examined interval. Analysis of the wavenumber one and the 5-day wave perturbations in temperature and ozone fields from Odin and from Aura demonstrates that, for the largest part of the examined period, quite similar characteristics are found in the spatial and temporal domain, with slightly larger amplitude values seen by Aura. Hence, the comparison between the Odin data, sampled each third day, and daily data from Aura and the ECMWF shows that the Odin data are sufficiently reliable to estimate the properties of the 5-day oscillations, at least for the locations and time intervals with strong wave activity.

Superposition states of light in a three-photon absorbing dissipative medium

We consider the process of simultaneous absorption of three photons in a medium in the presence of weak one-photon absorption. We show that in such a system stationary three-component superposition states of light may be formed in the range of small values of state amplitude (weak perturbation). This circumstance is associated with the fact that in this range of interaction the field spends more time in one of the three types of superposition states of light (constituting an ensemble of quantum trajectories of the system) than in two other types. We also show that in the range of large values of state amplitude it is possible to obtain three types of non-stationary superposition states of light. By using numerical simulation of quantum trajectories of the system we study the dynamics of the quantum entropy of the field. We calculate the Wigner functions of the field states. We also obtain analytical results for the density matrix of the steady state of the system.

Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.

Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ⩽ λ ⩽ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.

Ion-acoustic waves triggered by left-hand polarized finite-amplitude waves propagating in the beam direction

[1] Nonlinear ion-acoustic like waves triggered by large-amplitude circularly polarized waves propagating in the direction of a proton beam are studied. The properties are strongly dependent on the nature of the large-amplitude wave. Waves belonging to the Alfven branch of the dispersion relation require much larger amplitude values to excite the ion-acoustic waves than those belonging to the beam branch of the dispersion relation. The former can trigger only forward propagating waves and always above a wave number threshold, while the latter can destabilize forward as well as backward propagating waves with a zero wave number threshold. It is shown that in some cases the unstable frequency spectrum is very narrow, and damping rates are very small even under conditions where the linear theory predicts strong Landau damping. It is conjectured that these type of waves might be of common occurrence in the fast solar wind, preferably closer to the Sun. These results are consistent with observation of electrostatic ion-acoustic like emissions in the solar wind.

Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire

Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire are presented. The approximation is based on combining Newton's method with the harmonic balance method. One iteration step can provide very accurate analytical approximate solutions for both small and large values of oscillation amplitude and parameter.

A modified iteration perturbation method for some nonlinear oscillation problems

In this paper, we apply a new perturbation technique coupled with the iteration method. This procedure is obtained by combining the iteration methods of J. H. He and Mickens into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of oscillation amplitude, can be determined for nonlinear oscillations with a single degree of freedom. Four examples are given to illustrate the validity and accuracy of this procedure. We compare the approximate periods obtained by our procedure with the exact known periods. The results show that the approximations are of extreme accuracy.

Superposition of phase-space hole streets in Vlasov plasmas

We present a study of a collision-less plasma governed by the Vlasov- Poisson system of equations in one space and one velocity dimension; the plasma is subject to initial density perturbations and to both periodic and non-periodic space boundary conditions. For sufficiently large values of the perturbation's amplitude and sufficiently small values of the Landau damping rate, we observe the develop- ment of two streets of phase-space holes each consisting of two counter-streaming families of holes. The two streets move in the phase space at different speeds and they may consist of a different number of holes. The fast moving street develops faster when periodic boundary conditions are used, but it appears to be more prom- inent and robust under non-periodic boundary conditions. In two instances, the distribution function decays within the slow moving street; it remains unaffected within the fast moving street, but it has much smaller values there.

Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos.

The quantum-mechanical investigation of nonlinear resonance in terms of approximation to moderate nonlinearity is reduced to the investigation of eigenfunctions and eigenvalues of the Mathieu-Schrodinger equation. The eigenstates of the Mathieu-Schrodinger equation are nondegenerate in a certain area of pumping amplitude values in the neighborhood of the classical separatrix. Outside this area, the system finds itself in a degenerate state for both small and large pumping amplitude values. Degenerate energy terms arise as a result of merging and branching of pairs of nondegenerate energy terms. Equations are obtained for finding the merging points of energy terms. These equations are solved by numerical methods. The main objective of this paper is to establish a quantum analog of the classical stochastic layer formed in the separatrix area. With this end in view, we consider a nonstationary quantum-mechanical problem of perturbation of the state of the Mathieu-Schrodinger equation. It is shown that in passing through the branching point the system may pass from the pure state to the mixed one. At multiple passages through branching points there develops the irreversible process of "creeping" of the system to quantum states. In that case, the observed population of a certain number of levels can be considered, in our opinion, to be a quantum analog of the stochastic layer. The number of populated levels is defined by a perturbation amplitude.

Chaotic Motion in a Spinning Spacecraft with Circumferential Nutational Damper

The dynamics of a simplified model of a spinning spacecraft with a circumferential nutational damper is investigated using numerical simulations for nonlinear phenomena. A realistic spacecraft parameter configuration is investigated and is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. The equations of motion of the model are derived with Lagrange's equations using a generalisation of the kinetic energy equation and a linear stability analysis is given. Numerical simulations for satellite parameters are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. The motion is studied by means of time history, phase space, frequency spectrum, Poincare map, Lyapunov characteristic exponents and Correlation Dimension. For sufficiently large values of torque amplitude, the behaviour of the system was found to have much in common with a two well potential problem such as a Duffing oscillator. Evidence is also presented, indicating that the onset of chaotic motion was characterised by period doubling as well as intermittency.

Hysteretic ac losses and susceptibility of thin superconducting disks.

We calculate hysteretic magnetization curves and ac-susceptibility components ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\ensuremath{'}}$ and ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\mathrm{\ensuremath{''}}}$ for n=1, 3, and 5 for a type-II superconducting thin circular disk subjected to a low-frequency oscillating applied field, extending previous approaches for calculating hysteretic current-density and magnetic flux-density profiles in the critical state. We also present limiting expressions for \ensuremath{\chi}\ensuremath{'}=${\mathrm{\ensuremath{\chi}}}_{1}^{\ensuremath{'}}$ and \ensuremath{\chi}\ensuremath{''}=${\mathrm{\ensuremath{\chi}}}_{1}^{\mathrm{\ensuremath{''}}}$ for both small and large values of the ac field amplitude, and we show how \ensuremath{\chi}\ensuremath{''} is simply related to the ac loss per cycle per unit volume. Finally, a comparison is made between our results and those obtained for slab and strip geometries.

Tropospheric rivers: A one‐year record and a possible application to ice core data

The morphology of tropospheric rivers has been examined for the period June 1991–May 1992 from atmospheric specific humidity and wind velocity data. Vertically integrated water vapor flux vectors are subjected to harmonic analysis and the high frequency components (periods less than 3 days) show large amplitude values in the North Atlantic, North Pacific, South Atlantic, South Indian Ocean and South Pacific plus small amplitude occurrences in the Red Sea‐Arabian Sea region in the December–February season. In June–August the latter is replaced with a large amplitude monsoon‐related region over South‐East Asia. Maximum intensities increase slightly in altitude with latitude. The correspondence between rivers, frontal boundaries and storm tracks is noted.Sometimes rivers originating over the North Pacific cross North America and reach Greenland while at other times they pass polewards over the North Atlantic, raising the possibility that water vapor involved in ice core formation may have evaporated from surface water bodies with different temperature and salinity characteristics. Changes in oxygen isotope variations at a point may therefore reflect changes in the dynamics of tropospheric rivers in addition to local temperature changes.