Search results for "Wave equation"
showing 10 items of 74 documents
Reflection and Refraction of Singularities for Wave Equations with Interface Conditions given by Fourier Integral Operators
1992
Cauchy problems for hyperbolic operators often have the property, that the singularities of the initial data propagate along the bicharacteristic strips of the operator (cf. e.g. [13]). We consider, in the linear case, the situation where the bicharacteristics hit transversally a spacelike interface, which is ‘active’ in the sense that the interface condition is given via certain Fourier integral operators. Taking the identity, we obtain classical transmission conditions. A suitable functional analytic setting is furnished by the interaction concept [3], [6], [7], which covers very general mutual influences of evolution phenomena on different domains.
Sound absorption prediction of linear damped acoustic resonators using a lightweight hybrid model
2019
International audience; A lightweight numerical method is developed to predict the sound absorption coefficient of resonators whose cross-section dimensions are significantly larger compared to the viscous and thermal boundary layer’s thicknesses. This method is based on the boundary layer theory and on the perturbations theory. According to the perturbations theory, in acoustical domains with large dimensions, the fluid viscosity and thermal conductivity only affect the boundary layers. The model proposed in this article combines the lossless Helmholtz wave equation derived from a perfect fluid hypothesis, with viscosity and thermal conductivity values of a real fluid to compute the sound …
What is the Right Theory for Anderson Localization of Light? An Experimental Test
2018
Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description, the random potential depends on the wavelength of the incident light. For transverse Anderson localization, this leads to the prediction that the distribution of localization lengths---and, hence, its average---strongly depends on the wavelength. In an alternative description, in terms of a spatially fluctuating electric modulus, this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using optical samples exhibiting transverse Anderson localization. We do not find any dependence of the …
Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases
2003
We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.
Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: exact results
2015
A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate (BEC) acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low frequency limit.
Condensation of classical nonlinear waves
2005
We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave tu…
Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover w…
2013
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-d…
Paraxial waves in the far-field region
2002
Summary By investigating the changes suffered by a paraxial beam propagating in the near-field and in the far-field regions, it has been found a set of wave equations valid for points gradually closer to the near field. A relevant expression for the validity of the far-field approximation is given from the paraxial Helmholtz equation. It is pointed out that the well-known Fresnel number associated with every transverse diffraction pattern can be interpreted as a magnitude that measures the relative standard deviation of the Fraunhofer pattern and a first-order field, thus reporting on an integral expression suitable for a general case. Finally, the Rayleigh range of the optical beam is dedu…
Dispersion-compensated beam-splitting of femtosecond light pulses: Wave optics analysis
2007
Recently, using parageometrical optics concepts, a hybrid, diffractive-refractive, lens triplet has been suggested to significantly improve the spatiotemporal resolution of light spots in multifocal processing with femtosecond laser pulses. Here, we carry out a rigorous wave-optics analysis, including the spatiotemporal nature of the wave equation, to elucidate both the spatial extent of the diffractive spots and the temporal duration of the pulse at the output plane. Specifically, we show nearly transform-limited behavior of diffraction maxima. Moreover, the temporal broadening of the pulse is related to the group velocity dispersion, which can be pre-compensated for in practical applicati…
A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms
2021
Abstract We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogeneous term depends only on the variable space, the Fujita critical exponent and the second critical exponent in the sense of Lee and Ni are derived.