A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Evolution of linearly polarized electromagnetic pulses in laser plasmas

An analytical and numerical investigation is presented of the behavior of a linearly polarized electromagnetic pulse as it propagates through a plasma. Considering a weakly relativistic regime, the system of one-dimensional fluid-Maxwell equations is reduced to a generalized nonlinear Schrodinger type equation, which is solved numerically using a split step Fourier method. The spatio-temporal evolution of an electromagnetic pulse is investigated. The evolution of the envelope amplitude of density harmonics is also studied. An electromagnetic pulse propagating through the plasma tends to broaden due to dispersion, while the nonlinear frequency shift is observed to slow down the pulse at a speed lower than the group velocity. Such nonlinear effects are more important for higher density plasmas. The pulse broadening factor is calculated numerically, and is shown to be related to the background plasma density. In particular, the broadening effect appears to be stronger for dense plasmas. The relation to existing results on electromagnetic pulses in laser plasmas is discussed. (c) 2008 American Institute of Physics.

Low-frequency electrostatic defect mode in doped pair-ion plasmas

The nonlinear amplitude modulation dynamics of electrostatic oscillations of massive charged defects in a three-component pair plasma is investigated; i.e. doped pair-ion plasmas (anticipating the injection of a massive charged component in the background; e.g. in fullerene experiments). Ton-acoustic oscillations in electron-positron-ion (e-p-i) plasmas are also covered, in the appropriate limit. Linear and nonlinear effects (MI, envelope modes) are discussed. The role of the temperature and density ratio between the pair species is stressed.

Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality

All-optical signal processing enables modulation and transmission speeds not achievable using electronics alone(1,2). However, its practical applications are limited by the inherently weak nonlinear effects that govern photon-photon interactions in conventional materials, particularly at high switching rates(3). Here, we show that the recently discovered nonlocal optical behaviour of plasmonic nanorod metamaterials(4) enables an enhanced, ultrafast, nonlinear optical response. We observe a large (80%) change of transmission through a subwavelength thick slab of metamaterial subjected to a low control light fluence of 7 mJ cm(-2), with switching frequencies in the terahertz range. We show that both the response time and the nonlinearity can be engineered by appropriate design of the metamaterial nanostructure. The use of nonlocality to enhance the nonlinear optical response of metamaterials, demonstrated here in plasmonic nanorod composites, could lead to ultrafast, low-power all-optical information processing in subwavelength-scale devices.

On visco-elastic modelling of polyethylene terephthalate behaviour during multiaxial elongations slightly over the glass transition temperature

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature Tg, the stress-strain curve presents a strain softening effect vs strain rate but a strain hardening effect vs strain under conditions of large deformations. The main goal of this work is to propose a viscoelastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained trough a comparison with the experimental uniaxial and biaxial tests. The in?uence of the temperature on the viscous part is also modelled and an evaluation of the adiabatic self heating of the specimen is compared to experimental results.

Design and optimization next generation passive all-optical networks

Este trabalho investiga novas metodologias para as redes óticas de acesso de próxima geração (NG-OAN). O trabalho está dividido em quatro tópicos de investigação: projeto da rede, modelos numéricos para efeitos não lineares da fibra ótica, impacto dos efeitos não lineares da fibra ótica e otimização da rede. A rede ótica de acesso investigada nesse trabalho está projetado para suprir os requisitos de densidade de utilizadores e cobertura, isto é, suportar muitos utilizadores ( 1000) com altas velocidades de conexão dedicada ( 1 Gb/s) ocupando uma faixa estreita do espectro ( 25 nm) e comprimentos de fibra ótica até 100 km. Os cenários são baseados em redes óticas passivas com multiplexagem por divisão no comprimento de onda de alta densidade (UDWDM-PON) utilizando transmissores/receptores coerentes nos terminais da rede. A rede é avaliada para vários ritmos de transmissão usando formatos de modulação avançados, requisitos de largura de banda por utilizador e partilha de banda com tecnologias tradicionais de redes óticas passivas (PON). Modelos numéricos baseados em funções de transferência das séries de Volterra (VSTF) são demonstrados tanto para a análise dos efeitos não lineares da fibra ótica quanto para avaliação do desempenho total da rede. São apresentadas as faixas de potência e distância de transmissão nas quais as séries de Volterra apresentam resultados semelhantes ao modelo referência Split-Step Fourier (SSF) (validado experimentalmente) para o desempenho total da rede. Além disso, um algoritmo, que evita componentes espectrais com intensidade nulo, é proposto para realizar cálculos rápidos das séries. O modelo VSTF é estendido para identificar unicamente os efeitos não lineares da fibra ótica mais relevantes no cenário investigado: Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) e Four-Wave Mixing (FWM). Simulações numéricas são apresentadas para identificar o impacto isolado de cada efeito não linear da fibra ótica, SPM, XPM e FWM, no desempenho da rede com detecção coerente UDWDM-PON, transportando canais com modulação digital em fase (M-ária PSK) ou modulação digital em amplitude (M-ária QAM). A análise numérica é estendida para diferentes comprimentos de fibra ótica mono modo (SSMF), potência por canal e ritmo de transmissão por canal. Por conseguinte, expressões analíticas são extrapoladas para determinar a evolução do SPM, XPM e FWM em função da potência e distância de transmissão em cenários NG-OAN. O desempenho da rede é otimizada através da minimização parcial da interferência FWM (via espaçamento desigual dos canais), que nesse caso, é o efeito não linear da fibra ótica mais relevante. Direções para melhorias adicionas no desempenho da rede são apresentados para cenários em que o XPM é relevante, isto é, redes transportando formatos de modulação QAM. A solução, nesse caso, é baseada na utilização de técnicas de processamento digital do sinal.

Intermodulation in active reconfigurable antennas

Due to the application of active components into antennas these became a source of distortion on wireless communication systems. In this paper we explore the nonlinear effects occurring in a frequency reconfigurable antenna operating with a PIN Diode. We describe the measurement setup used to check the antenna intermodulation products and the measured compression and third order intermodulation limitations of a frequency reconfigurable antenna, operating at the UMTS and WLAN frequencies.

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

The relationship between body mass index and breast cancer recurrence/progression and breast cancer-specific death

The aim of this study was to describe the nonlinear association between body mass index (BMI) and breast cancer outcomes and to determine whether BMI improves prediction of outcomes. A cohort of906 breast cancer patients diagnosed at Henry Ford Health System, Detroit (1985-1990) were studied. The median follow-up was 10 years. Multivariate logistic regression was used to model breast cancer recurrence/progression and breast cancer-specific death. Restricted cubic splines were used to model nonlinear effects. Receiver operator characteristic areas under the curves (ROC AUC) were used to evaluate prediction. BMI was nonlinearly associated with recurrence/progression and death (p= 0.0230 and 0.0101). Probability of outcomes increased with increase or decrease ofBMI away from 25. BMI splines were suggestive of improved prediction of death. The ROC AUCs for nested models with and without BMI were 0.8424 and 0.8331 (p= 0.08). I f causally associated, modifying patients BMI towards 25 may improve outcomes.

Time resolved study of CN band emission from plasma generated by laser irradiation of graphite

Time and space resolved studies of emission from CN molecules have been carried out in the plasma produced from graphite target by 1.06 urn pulses from a Q-switched Nd:YAG laser. Depending on the laser pulse energy, time of observation and position of the sampled volume of the plasma, the features of the emission spectrum are found to change drastically. The vibrational temperature and population distribution in the different vibrational levels have been studied as functions of distance, time, laser energy and ambient gas pressure. Evidence for nonlinear effects of the plasma medium such as self focusing which exhibits threshold-like behaviour are also obtained. Temperature and electron density of the plasma have been evaluated using the relative line intensities of successive ionization stages of carbon atom. These electron density measurements are verified by using Stark broadening method.

" Studies on Laser induced Phatothermal Phenomena in Selected Organic Compounds and Fullerenes"

In the pre—laser era it was difficult to believe that the optical properties of a medium depend upon the intensity of the radiation incident on it. The basis for this conclusion is that the electric field strength associated with the conventional light sources used before the advent of lasers was much smaller than (103 V/cm) the field sttrengths of atomic or interatomic fields (2 107 —- 10” V/cm). The radiation with such low intensity is not able to affect atomic fields to the extent of changing optical parameters. The invention of laser in 1960 was a turning point. The high degree of coherence of the laser radiation provides high spatial concentration of optical power. With the availability of the femtosecond lasers it has become possible to get extremely high peak powers 2 1013 W/cmz). At such high fields, the relationship between electric ‘polarization P and the electric field strength E ceases to be linear and several nonlinear effects begin to occur. Nonlinear absorption, a branch of nonlinear optics, refers to the interaction between radiation and matter accompanied by absorption of more than one photon. Nonlinear absorption has acquired great importance after the invention of high power lasers. One of the objectives of the present work is to investigate the nonlinear absorption processes occurring in fullerene, selected organic solvents and laser dyes. Fullerenes and laser dyes were chosen because of their highly nonlinear behaviour. Fullerenes, the most beautiful among molecules, offer fascinating field of research owinglto their significant structural properties. As toluene, benzene and carbon disulphide are themost widely used solvents for fullerenes, it seems important to study the nonlinear properties of these liquids as well. Like fullerenes, laser dyes also possess highly delocalized 7r electrons which are responsible for their nonlinear absorption. Dye lasers were the fulfillment of an experimenter’s pipe dream - to have a laser that is easily tunable over a wide range of wavelengths. A better understandingof the photophysical properties of laser dyes can significantly enhance the development and technology of dye lasers. We studied the nonlinear absorption properties of two rhodamine dyes to have some insight into their nonlinear optical properties.

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Umami: a delicious flavor formed by convergence of taste and olfactory pathways in the human brain

Umami taste is produced by glutamate acting on a fifth taste system. However, glutamate presented alone as a taste stimulus is not highly pleasant, and does not act synergistically with other tastes (sweet, salt, bitter and sour). We show here that when glutamate is given in combination with a consonant, savory, odour (vegetable), the resulting flavor can be much more pleasant. Moreover, we showed using functional brain imaging with fMRI that the glutamate taste and savory odour combination produced much greater activation of the medial orbitofrontal cortex and pregenual cingulate cortex than the sum of the activations by the taste and olfactory components presented separately. Supralinear effects were much less (and significantly less) evident for sodium chloride and vegetable odour. Further, activations in these brain regions were correlated with the pleasantness and fullness of the flavor, and with the consonance of the taste and olfactory components. Supralinear effects of glutamate taste and savory odour were not found in the insular primary taste cortex. We thus propose that glutamate acts by the nonlinear effects it can produce when combined with a consonant odour in multimodal cortical taste-olfactory convergence regions. We propose the concept that umami can be thought of as a rich and delicious flavor that is produced by a combination of glutamate taste and a consonant savory odour. Glutamate is thus a flavor enhancer because of the way that it can combine supralinearly with consonant odours in cortical areas where the taste and olfactory pathways converge far beyond the receptors.