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We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
We present results of theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of microscopical, i.e., statistical-mechanical framework capable to explain the long living…
Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three…
We derive analytical expressions to describe how light is frequency-shifted when interacting with ultrasound within scattering media, due to the modulation of the refractive index induced by the ultrasound pressure waves. The model is…
We have investigated some statistical properties of integrated spectra of galaxies with principal component analysis. The projection of the spectra onto the plane defined by the first two principal components shows that normal galaxies are…
Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is considered. The resonances for the corresponding acoustic propagator are studied. It is shown that the distribution of the resonances depends on…
Classification of galaxy spectral energy distributions in terms of orthogonal basis functions provides an objective means of estimating the number of significant spectral components that comprise a particular galaxy type. We apply the…
We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
In a disordered medium with Kerr-type nonlinearity, the transmitted speckle pattern was predicted to become unstable, as a result of the positive feedback between the intensity fluctuations and the nonlinear dependence of the local…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
In this paper, we present a mathematical model and analysis for a new experimental method [Bureau and al., arXiv:2409.13901, 2024] for effective sound velocity estimation in medical ultrasound imaging. We perform a detailed analysis of the…
Recent analysis of the distribution of clusters of galaxies is reviewed. Clusters of galaxies located in rich superclusters form a quasiregular lattice. The mean power spectrum of galaxies and clusters has been found, it has a peak at…
While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations.…
The power-law dependence of the angle in the angular projection of galaxy distribution is explained by assuming that in the spherical shells within a small angle the distributions are also fractal. If this local angular fractal is…
L-shape probability distributions are extremely non-Gaussian distributions that have been surprisingly successful in describing the frequency of occurrence of extreme events, ranging from stock market crashes and natural disasters, the…