Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.

Coral reef development in response to large amplitude internal waves and monsoon impact

The Andaman Sea and other macrotidal semi-enclosed tropical seas feature large amplitude internal waves (LAIW). Although LAIW induce strong fluctuations i.e. of temperature, pH, and nutrients, their influence on reef development is so far unknown. A better-known source of disturbance is the monsoon affecting corals due to turbulent mixing and sedimentation. Because in the Andaman Sea both, LAIW and monsoon, act from the same westerly direction their relative contribution to reef development is difficult to discern. Here, we explore the framework development in a number of offshore island locations subjected to differential LAIW- and SW-monsoon impact to address this open question. Cumulative negative temperature anomalies - a proxy for LAIW impact - explained a higher percentage of the variability in coral reef framework height, than sedimentation rates which resulted mainly from the monsoon. Temperature anomalies and sediment grain size provided the best correlation with framework height suggesting that so far neglected subsurface processes (LAIW) play a significant role in shaping coral reefs.

Coral communities exposed to differential large amplitude internal waves cooling and a severe heat stress in 2010 in the Andaman Sea

Tropical scleractinian corals are particularly vulnerable to global warming as elevated sea surface temperatures (SST) disrupt the delicate balance between the coral host and their algal endosymbionts, leading to symbiont expulsion, mass bleaching and mortality. While satellite sensing of SST has proven a good predictor of coral bleaching at the regional scale, there are large deviations in bleaching severity and mortality on the local scale, which are only poorly understood. Here, we show that internal waves play a major role in explaining local coral bleaching and mortality patterns in the Andaman Sea. In spite of a severe region-wide SST anomaly in May 2010, frequent upslope intrusions of cold sub-pycnocline waters due to breaking large amplitude internal waves (LAIW) alleviated heating and mitigated coral bleaching and mortality in shallow LAIW-exposed waters. In LAIW-sheltered waters, by contrast, bleaching susceptible species suffered severe bleaching and total mortality. These findings suggest that LAIW, which are ubiquitous in tropical stratified waters, benefit coral reefs during thermal stress and provide local refugia for bleaching susceptible corals. The swash zones of LAIW may thus be important, so far overlooked, conservation areas for the maintainance of coral diversity in a warming climate. The consideration of LAIW can significantly improve coral bleaching predictions and can provide a valuable tool for coral reef conservation and management.

Molecular Origins of Higher Harmonics in Large-Amplitude Oscillatory Shear Flow: Shear Stress Response

Recent work has focused on deepening our understanding of the molecular origins of the higher harmonics that arise in the shear stress response of polymeric liquids in large-amplitude oscillatory shear flow. For instance, these higher harmonics have been explained by just considering the orientation distribution of rigid dumbbells suspended in a Newtonian solvent. These dumbbells, when in dilute suspension, form the simplest relevant molecular model of polymer viscoelasticity, and this model specifically neglects interactions between the polymer molecules [R.B. Bird et al., J Chem Phys, 140, 074904 (2014)]. In this paper, we explore these interactions by examining the Curtiss-Bird model, a kinetic molecular theory designed specifically to account for the restricted motions that arise when polymer chains are concentrated, thus interacting and specifically, entangled. We begin our comparison using a heretofore ignored explicit analytical solution [Fan and Bird, JNNFM, 15, 341 (1984)]. For concentrated systems, the chain motion transverse to the chain axis is more restricted than along the axis. This anisotropy is described by the link tension coefficient, ε, for which several special cases arise: ε = 0 corresponds to reptation, ε > 1/8 to rod-climbing, 1/2 ≥ ε ≥ 3/4 to reasonable predictions for shear-thinning in steady simple shear flow, and ε = 1 to the dilute solution without hydrodynamic interaction. In this paper, we examine the shapes of the shear stress versus shear rate loops for the special cases ε = (0,1/8, 3/8,1) , and we compare these with those of rigid dumbbell and reptation model predictions.

Potential surfaces from vibration-rotation data

The problems of inverting experimental information obtained from vibration-rotation spectroscopy to determine the potential energy surface of a molecule are discussed, both in relation to semi-rigid molecules like HCN, NO2, H2CO, etc., and in relation to non-rigid or floppy molecules with large amplitude vibrations like HCNO, C3O2, and small ring molecules. Although standard methods exist for making the necessary calculations in the former case, they are complex, and they require an abundance of precise data on the spectrum that is rarely available. In the case of floppy molecules there are often data available over many excited states of the large amplitude vibration, but there are difficulties in knowing the precise form of the large amplitude coordinate(s), and in allowing for the vibrational averaging effects of the other modes. In both cases difficulties arise from the curvilinear nature of the vibrational paths which are not adequately handled by our present theories.

On an Non-Ideal Global and Local Energy Transfer, Using an Electro-Magneto and Magneto-Rheological Dampers

In this paper, we investigated the nonlinear vibrations of a Non-ideal (NIS) electromechanical absorber (NEVA), taking into account a modified mathematical model of (MR) Damper. We observed the presence of the Sornmerfeld effect (it is the steady state frequencies of the DC motor, which it will usually increasing as more power (Voltage) is given to it, in a step-by-step fashion. When a resonance condition it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation, without sensible change of the motor frequency). The obtained results, by using numerical and analytical simulations, were discussed, in details.

A structure excited by a DC motor of limited power supply and controlled by a pendulum like device

In this paper, a mathematical model is derived via Lagrange's Equation for a shear building structure that acts as a foundation of a non-ideal direct current electric motor, controlled by a mass loose inside a circular carving. Non-ideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure, not being a function of time only as in the ideal case. Thus, in this case, an additional equation of motion is written, related to the motor rotation, coupled to the equation describing the horizontal motion of the shear building. This kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure is reached, the better part of this energy is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. If additional increase steps in voltage are made, one may reach a situation where the rotor will jump to higher rotation regimes, no steady states being stable in between. As a device of passive control of both large amplitude vibrations and the Sommerfeld effect, a scheme is proposed using a point mass free to bounce back and forth inside a circular carving in the suspended mass of the structure. Numerical simulations of the model are also presented Copyright © 2007 by ASME.

An investigations on local and global behavior of a (SMA) oscillator of 3 - DOF driven by a limited power supply

SMART material systems offer great possibilities in terms of providing novel and economical solutions to engineering problems. The technological advantages of these materials over traditional ones are due to their unique microstructure and molecular properties. Smart materials such as shape memory alloys (SMA), has been used in such diverse areas of engineering science, nowadays. In this paper, we present a numerical investigation of the dynamics interaction of a nonideal structure (NIS). We analyze the phenomenon of the passage through resonance region in the steady state processes. We remarked that this kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the DC motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. The results obtained by using numerical simulations are discussed in details. Copyright © 2009 by ASME.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Born-Oppenheimer failure in the separation of low frequency vibrations

Changes in the effective potential function of a low-frequency large-amplitude molecular vibration, resulting from excitation of a high-frequency vibration, are discussed. It is shown that in some situations a significant contribution to such changes may arise from failure of the Born-Oppenheimer separation of the low-frequency mode. In the particular example of the HF dimer, recent evidence that the tunneling barrier increases on exciting either of the H-stretching vibrations is probably due to this effect.

The vibrations and tunnelling of malonaldehyde on a Moller-Plesset surface

The vibrations and tunnelling motion of malonaldehyde have been studied in their full dimensionality using an internal coordinate path Hamiltonian. In this representation there is one large amplitude internal coordinate s and 3N - 7 (=20) normal coordinates Q which are orthogonal to the large amplitude motion at all points. It is crucial that a high accuracy potential energy surface is used in order to obtain a good representation for the tunneling motion; we use a Moller-Plesset (MP2) surface. Our methodology is variational, that is we diagonalize a sufficiently large matrix in order to obtain the required vibrational levels, so an exact representation for the kinetic energy operator is used. In a harmonic valley representation (s, Q) complete convergence of the normal coordinate motions and the internal coordinate motions has been obtained; for the anharmonic valley in which we use two- and three-body terms in the surface (s, Q(1), Q(2)), we also obtain complete convergence. Our final computed stretching fundamentals are deficient because our potential energy surface is truncated at quartic terms in the normal coordinates, but our lower fundamentals are good.

Reorientation of Water Inside Carbon Nanorings by Large Angular Jumps

Molecular dynamics simulations of the orientational dynamics of water molecules confined inside narrow carbon nanorings reveal that reorientational relaxation is mediated by large amplitude angular jumps. The distribution of waiting time between jumps peaks at about 60 fs, and has a slowly decaying exponential tail with a timescale of about 440 fs. These time scales are much faster than the mean waiting time between jumps of the water molecules in bulk.

Finite amplitude envelope solitons in pair-ion plasmas

The nonlinear coupling between finite amplitude ion thermal waves (ITWs) and quasistationary density perturbations in a pair-ion plasma is considered. A generalized nonlinear Schrödinger equation is derived for the ITW electric field envelope, accounting for large amplitude quasistationary plasma slow motion describing the ITW ponderomotive force. The present theory accounts for the trapping of ITWs in a large amplitude ion density hole. The small amplitude limit is considered and exact analytical solutions are obtained. Finite amplitude solutions are obtained numerically and their characteristics are discussed.

Oblique propagation of arbitrary amplitude electron acoustic solitary waves in magnetized kappa-distributed plasmas

The linear and nonlinear properties of large-amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modeled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential-type analysis reveals the existence of large-amplitude electrostatic solitary waves and allows for an investigation of their propagation characteristics and existence domain, in terms of the soliton speed (Mach number). The effects of the key plasma configuration parameters, namely the superthermality index and the cold electron density, on the soliton characteristics and existence domain, are studied. The role of obliqueness and magnetic field is discussed.