195 research outputs found
Finite-velocity diffusion on a comb
A Cattaneo equation for a comb structure is considered. We present a rigorous
analysis of the obtained fractional diffusion equation, and corresponding
solutions for the probability distribution function are obtained in the form of
the Fox -function and its infinite series. The mean square displacement
along the backbone is obtained as well in terms of the infinite series of the
Fox -function. The obtained solutions describe the transition from normal
diffusion to subdiffusion, which results from the comb geometry.Comment: 7 page
Anomalous diffusion on a fractal mesh
An exact analytical analysis of anomalous diffusion on a fractal mesh is
presented. The fractal mesh structure is a direct product of two fractal sets
which belong to a main branch of backbones and side branch of fingers. The
fractal sets of both backbones and fingers are constructed on the entire
(infinite) and axises. To this end we suggested a special algorithm of
this special construction. The transport properties of the fractal mesh is
studied, in particular, subdiffusion along the backbones is obtained with the
dispersion relation , where the transport
exponent is determined by the fractal dimensions of both backbone and
fingers. Superdiffusion with has been observed as well when the
environment is controlled by means of a memory kernel
Plethora of plants – collections of the Botanical Garden, Faculty of Science, University of Zagreb (6): subfamily Tillandsioideae (Bromeliaceae)
In this paper, the plant lists of Tillandsioideae, subfamily of plants from 9 genera in the bromeliad family (Bromeliaceae), grown in the Zagreb Botanical Garden of the Faculty of Science from 1892 until 2021 are studied. Synonymy, nomenclature and origin of plant material were sorted. Lists of species, grown in the last 129 years have been constructed to show that during that period at least 82 taxa from the Tillandsioideae subfamily (3 from Catopsis, 6 from Guzmania, 63 from Tillandsia and 10 from Vriesea) inhabited the Garden’s collections. Today we have 73 species and cultivars from 4 genera in Tillandsioideae subfamily: 3 from Catopsis, 5 from Guzmania, 57 from Tillandsia and 8 from Vriesea
Heterogeneous diffusion in comb and fractal grid structures
We give an exact analytical results for diffusion with a power-law position
dependent diffusion coefficient along the main channel (backbone) on a comb and
grid comb structures. For the mean square displacement along the backbone of
the comb we obtain behavior , where
is the power-law exponent of the position dependent diffusion
coefficient . Depending on the value of we
observe different regimes, from anomalous subdiffusion, superdiffusion, and
hyperdiffusion. For the case of the fractal grid we observe the mean square
displacement, which depends on the fractal dimension of the structure of the
backbones, i.e., , where
is the fractal dimension of the backbones structure. The reduced
probability distribution functions for both cases are obtained by help of the
Fox -functions
Effects of a fractional friction with power-law memory kernel on string vibrations
AbstractIn this paper we give an analytical treatment of a wave equation for a vibrating string in the presence of a fractional friction with power-law memory kernel. The exact solution is obtained in terms of the Mittag-Leffler type functions and a generalized integral operator containing a four parameter Mittag-Leffler function in the kernel. The method of separation of the variables, Laplace transform method and Sturm–Liouville problem are used to solve the equation analytically. The asymptotic behaviors of the solution of a special case fractional differential equation are obtained directly from the analytical solution of the equation and by using the Tauberian theorems. The proposed model may be used for describing processes where the memory effects of complex media could not be neglected
- …