Related papers: Transfer across Random versus Deterministic Fracta…
A grid comb model is a generalization of the well known comb model, and it consists of $N$ backbones. For $N=1$ the system reduces to the comb model where subdiffusion takes place with the transport exponent $1/2$. We present an exact…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
The analogy between frictional cracks, propagating along interfaces in frictional contact, and ordinary cracks in bulk materials is important in various fields. We consider a stress-controlled frictional crack propagating at a velocity…
To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
Enchanting ripple pattern exist on interface, and manifest them self in it's fluctuation profile as well. These ripples apparently flow as the interface struck with inhomogeneous externally driven field interface, moves fluctuating about it…
We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Based on a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects,…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
Analysis of experimental kinetic dependences and results of the computer modeling of pairwise interactions in the heterogeneous system have shown that a character of its fractal property variation in the evolution process would be different…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…