Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic...

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for highdimensional feature spaces which capture the slow dynamics of the underlying stoc...

We consider a six-dimensional braneworld model and we study the cosmological evolution of a (4+1) brane-universe. Introducing matter on the brane we show that the scale factor of the physical three-dimensional brane-universe is related to the scale factor of the fourth dimension on the brane, and the suppression of the extra dimension compared to the three dimensions requires the presence of da...

. In this paper the principle of fractal theory and fractal brownion motion(FBM) are analyzed in detail. And it also analyses the physical meaning of FBM’s two parameters H and σ . The improved Diamond-Square algorithm is discussed in light of fractal interpolation and use it to simulate cloud, two-dimension texture terrain surface and three-dimension terrain. There are many kinds of effect whe...

Embeddings are diffeomorphisms between some unseen physical attractor and a reconstructed image. Different embeddings may or may not be equivalent under isotopy. We regard embeddings as representations of the attractor, review the labels required to distinguish inequivalent representations for an important class of dynamical systems, and discuss the systematic ways inequivalent embeddings becom...

The optical bistability in a composite, composed of nonlinear metallic particles (spherical or cylindrical) with interfacial layers randomly embedded in a linear dielectric host, is investigated theoretically. It is shown that both interfacial property and the size of metallic particles can dramatically a!ect the optical bistable behavior, and the threshold value is more less in three dimension...

now days, citizens safety in urban spaces is one of the most important worries of urban managers. this may be reflected in different characters of urban spaces such as physical, social and economical and even political characters. with regard to increasing crimes and complexities of urban spaces, trying for achieve to sustainable, healthy and good cities mean in providing the safety environment...