scholarly journals Nonlinear Classical Elasticity Model for Materials with Fluid and Matrix Phases

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Rafael Muñoz ◽  
Juan Melchor
Keyword(s):  
Constitutive Equation ◽  
Nonlinear Model ◽  
Shear Waves ◽  
Nonlinear Effects ◽  
Nonlinear Propagation ◽  
Solid Matrix ◽  
Classical Elasticity ◽  
Third Order ◽  
Longitudinal Waves ◽  
Acoustic Responses

Materials with fluid and matrix phases present different acoustic responses in each phase. While longitudinal waves propagate in both phases, shear waves do it only through the solid matrix. Longitudinal waves are mainly described by volumetric propagation and shear waves by deviatoric processes. In the case of nonlinear propagation cross effects occur between both components. This paper presents a new classical nonlinear model proposing a constitutive equation that separates volumetric and deviatoric effects. Four nonlinear constants of third order are defined. The formulation is compared to constitutive equations with Landau constants for weakly elasticity and both types of nonlinear constants related. Some reinterpretation of the Landau’s constants arises in terms of parallel or cross nonlinear effects between volumetric and deviatoric components.

scholarly journals The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

Third Order Nonlinear Optical Responses of Metallophthalocyanines in Films and Solutions

1992 ◽  
Vol 247 ◽  
Author(s):  
Roger J. Reeves ◽  
Richard C. Powell ◽  
Warren T. Ford ◽  
Young H. Chang ◽  
Weiming Zhu
Keyword(s):  
Excited State Absorption ◽  
Third Order ◽  
Incident Intensity ◽  
Optical Responses ◽  
A Value ◽  
Fast Electronic ◽  
Probe Spectroscopy ◽  
Acoustic Responses ◽  
532 Nm ◽  
Pulse Probe

ABSTRACTDihydrogen, copper, platinum, and lead octakis(2-ethylhexyloxy)phthalocyanines (Pc's) were studied in polystyrene films at 532 nm and in chloroform solutions at 1064 nm by picosecond degenerate four wave mixing. Resonant χ(3) values of Pc's at 532 nm (a local minimum in the absorption spectrum) at a time coincident with the 20 psec pump pulses were as high as 104 times that of CS2 by extrapolation of the response from 1 wt % PtPc in polystyrene film to a value for pure PtPc. Delay of the probe pulse as long as 3 nsec revealed acoustic responses stronger than the fast electronic responses. The films showed the expected quadratic dependence of the instantaneous reflectivity on incident intensity only for a decade of magnitude of intensity, 100–1000 MW/cm2, with the output saturating at higher intensities. Excited state absorption at 532 nm was detected in the film samples by pulse-probe spectroscopy and was shown to be a factor in the saturation observed in the NLO signals. Nonresonant χ(3) values at 1064 nm were as high as 120 times that of CS2 from measured responses of 1 wt % chloroform solutions of Pc's. Time delay of the probe revealed both fast electronic and slower acoustic responses at 1064 nm too.

scholarly journals Large enhancement of third-order nonlinear effects with a resonant all-dielectric metasurface

AIP Advances ◽  
2016 ◽  
Vol 6 (11) ◽  
pp. 115213 ◽  
Author(s):  
Samad Jafar-Zanjani ◽  
Jierong Cheng ◽  
Vladimir Liberman ◽  
Jeffrey B. Chou ◽  
Hossein Mosallaei
Keyword(s):  
Nonlinear Effects ◽  
Third Order ◽  
Large Enhancement ◽  
Dielectric Metasurface

SIMULATION OF NONLINEAR ULTRASONIC PULSES PROPAGATING THROUGH BUBBLY LAYERS IN A LIQUID: FILTERING AND CHARACTERIZATION

2010 ◽  
Vol 18 (01) ◽  
pp. 47-68 ◽  
Author(s):  
CHRISTIAN VANHILLE ◽  
CLEOFÉ CAMPOS-POZUELO
Keyword(s):  
Homogeneous Medium ◽  
Nonlinear Effects ◽  
Nonlinear Propagation ◽  
Pressure Amplitude ◽  
Screen Effect ◽  
Nonlinear Characterization ◽  
Bubble Sizes ◽  
The Time Domain ◽  
Filter Effects

This paper deals with the nonlinear propagation of ultrasonic pulses in a homogeneous medium in which a bubbly layer is placed. The medium we use is air bubbles in water. During the propagation of a pulse, the interaction of the acoustic field and bubbles vibration is assured via the coupling of a nonlinear differential system. The solution is tracked in the time domain by means of the SNOW-BL code. In the biphasic fluid, attenuation and nonlinear effects are due to the bubbles only. The study addresses to two applications: filter effects of the layer and nonlinear characterization of liquid–gas mixtures. We study the filter effects (screen effect) a layer has for some frequency ranges present in the initial ultrasonic pulses, in the linear and nonlinear regimes, i.e. for low and high pressure amplitude. One (or several) simple layer is contemplated in numerical experiments with different bubble densities, bubble sizes, layer thicknesses, for different kinds of pulse.

Competing second and third order nonlinear effects in plasmonic nanoantennas (Conference Presentation)

2018 ◽  
Author(s):  
Costantino De Angelis ◽  
Michele Celebrano ◽  
Lavinia Ghirardini ◽  
Giovanni Pellegrini ◽  
Paolo Biagioni ◽  
...  
Keyword(s):  
Nonlinear Effects ◽  
Third Order ◽  
Plasmonic Nanoantennas

scholarly journals On the Jordan–Moore–Gibson–Thompson Wave Equation in Hereditary Fluids with Quadratic Gradient Nonlinearity

2020 ◽  
Vol 23 (1) ◽  
Author(s):  
Vanja Nikolić ◽  
Belkacem Said-Houari
Keyword(s):  
Wave Equation ◽  
Nonlinear Effects ◽  
Global Solvability ◽  
Acoustic Wave Equation ◽  
Third Order ◽  
Memory Kernel ◽  
Energy Bounds ◽  
Ultrasonic Propagation ◽  
Gradient Nonlinearity ◽  
With Memory

AbstractWe prove global solvability of the third-order in time Jordan–More–Gibson–Thompson acoustic wave equation with memory in $${\mathbb {R}}^n$$ R n , where $$n \ge 3$$ n ≥ 3 . This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global existence is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data.

Large Third-Order Optical Nonlinear Effects of Gold Nanoparticles with Unusual Fluorescence Enhancement

Langmuir ◽  
2008 ◽  
Vol 24 (15) ◽  
pp. 8297-8302 ◽  
Author(s):  
Jing Lv ◽  
Li Jiang ◽  
Cuihong Li ◽  
Xiaofeng Liu ◽  
Mingjian Yuan ◽  
...  
Keyword(s):  
Gold Nanoparticles ◽  
Fluorescence Enhancement ◽  
Nonlinear Effects ◽  
Third Order
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