Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture...

The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such spaces provides a particular kind of spacetime-like structure that favors the aggregation of such deformations into fractal forms standing for massive objec...

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a po...

Phenol-formaldehyde/silica hybrid gel with hydrophobic character, high porosity, and thesmall pore size mean was prepared via sol-gel polymerization under solvent saturated vaporatmosphere and was dried by ambient drying method. The silica sols were prepared based onTetraethoxysilane (TEOS) and Methyltrimethoxysilane (MTES) as hydrophilic and hydrophobicprecursors, respectively. Phenol-formalde...

We investigate models of (1 + d)-D Lorentzian semi-random lattices with one random (space-like) direction and d regular (time-like) ones. We prove a general inversion formula expressing the partition function of these models as the inverse of that of hard objects in d dimensions. This allows for an exact solution of a variety of new models including critical and multicritical generalized (1 + 1...

The forecasting slope deformation potential is required to evaluate slope safety during open-pit mining, allowing us to formulate and promote effective emergency strategies in advance to prevent slope failure disasters. Although fractal models have been used to predict slope deformation, such limitations as low prediction accuracy, poor stability and the requirement for large amounts of data mu...