Abstract: Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.
Abstract: Fractal analyses of successive event of explosion
earthquake and harmonic tremor recorded at Semeru volcano were
carried out to investigate the dynamical system regarding to their
generating mechanism. The explosive eruptions accompanied by
explosion earthquakes and following volcanic tremor which are
generated by continuous emission of volcanic ash. The fractal
dimension of successive event of explosion and harmonic tremor was
estimated by Critical Exponent Method (CEM). It was found that the
method yield a higher fractal dimension of explosion earthquakes and
gradually decrease during the occurrence of harmonic tremor, and can
be considerably as correlated complexity of the source mechanism
from the variance of fractal dimension.
Abstract: The colonic tissue is a complicated dynamic system
and the colonic activities it generates are composed of irregular
segmental waves, which are referred to as erratic fluctuations or spikes.
They are also highly irregular with subunit fractal structure. The
traditional time-frequency domain statistics like the averaged
amplitude, the motility index and the power spectrum, etc. are
insufficient to describe such fluctuations. Thus the fractal
box-counting dimension is proposed and the fractal scaling behaviors
of the human colonic pressure activities under the physiological
conditions are studied. It is shown that the dimension of the resting
activity is smaller than that of the normal one, whereas the clipped
version, which corresponds to the activity of the constipation patient,
shows with higher fractal dimension. It may indicate a practical
application to assess the colonic motility, which is often indicated by
the colonic pressure activity.
Abstract: The dispersion of heavy particles line in an isotropic
and incompressible three-dimensional turbulent flow has been
studied using the Kinematic Simulation techniques to find out the
evolution of the line fractal dimension. In this study, the fractal
dimension of the line is found for different cases of heavy particles
inertia (different Stokes numbers) in the absence of the particle
gravity with a comparison with the fractal dimension obtained in the
diffusion case of material line at the same Reynolds number. It can
be concluded for the dispersion of heavy particles line in turbulent
flow that the particle inertia affect the fractal dimension of a line
released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the
beginning for small times, most of the different cases are not affected
by the inertia until a certain time, the particle response time τa, with
larger time as the particles inertia increases, the fractal dimension of
the line increases owing to the particles becoming more sensitive to
the small scales which cause the change in the line shape during its
journey.
Abstract: In this study, the dispersion of heavy particles line in
an isotropic and incompressible three-dimensional turbulent flow has
been studied using the Kinematic Simulation techniques to find out
the evolution of the line fractal dimension. The fractal dimension of
the line is found in the case of different particle gravity (in practice,
different values of particle drift velocity) in the presence of small
particle inertia with a comparison with that obtained in the diffusion
case of material line at the same Reynolds number. It can be
concluded for the dispersion of heavy particles line in turbulent flow
that the particle gravity affect the fractal dimension of the line for
different particle gravity velocities in the range 0.2 < W < 2. With
the increase of the particle drift velocity, the fractal dimension of the
line decreases which may be explained as the particles pass many
scales in their journey in the direction of the gravity and the particles
trajectories do not affect by these scales at high particle drift
velocities.