Related papers: Quasi-Sierpinski Structure for Uniform Load Distri…
In this work we propose a novel relationship between topology and damage propagation in Maxwell lattices that redefines fracture as a functional design feature rather than mere degradation. We demonstrate that topologically protected modes,…
In this work, we leverage the Hamiltonian kind structure for accurate uncertainty propagation through a nonlinear dynamical system. The developed approach utilizes the fact that the stationary probability density function is purely a…
This research is motivated by the study of the geometry of fractal sets and is focused on uniformization problems: transformation of sets to canonical sets, using maps that preserve the geometry in some sense. More specifically, the main…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of…
Single cluster covering approach provides a plausible mechanism for the formation and stability of octagonal and decagonal quasiperiodic structures. For dodecagonal quasiperiodic pattern such a single cluster covering scheme is still…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
We show that the two-dimensional structure of a rigidly rotating self-gravitating body is accessible with relatively good precision by assuming a purely spheroidal stratification. With this hypothesis, the two-dimensional problem becomes…
A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during…
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…
The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical…
We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and…
Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
We study a 2D quasi-static discrete {\it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces.…
In global seismology Earth's properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth's…
We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…
A spacelike surface in the Minkowski 3-space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface. These surfaces completely classified in [J. Math. Anal. Appl. 385…
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
We discuss various situations where the formation of rocky coast morphology can be attributed to the retro-action of the coast morphology itself on the erosive power of the sea. Destroying the weaker elements of the coast, erosion can…