Understanding the limiting distributions of translates of measures on submanifolds of homogeneous spaces of Lie groups lead to very interesting number theoretic and geometric applications. We explore this theme in various generalities, and in specific cases. Our main tools are Ratner’s theorems on unipotent flows, nondivergence theorems of Dani and Margulis, and dynamics of linear actions of se...

We consider nonresonant and weakly resonant Hopf bifurcation from periodic solutions and relative periodic solutions in dynamical systems with symmetry. In particular, we analyse phase-locking and irrational torus flows on the bifurcating relative tori. Results are obtained for systems with compact and noncompact symmetry group. In the noncompact case, we distinguish between bounded and unbound...

iranian islamic gardens like almost every cultures, represent beauty and happiness and improve the public perception. it has also special geometry with philosophical concept related to islam’s doctrine that is the focus of this research. following quran’s contents, paradise is a beautiful sophisticated garden that something flows under its trees. so the comparison between the somatic geometry o...

A technique was developed for measuring the deposition of aerosols from 0.01 to 1pm diameter in a turbulent, planar channel flow. The ultimate goal of this project was to investigate ultrafine aerosol deposition in lung passageways. A procedure was developed to measure ultrafine aerosol deposition in a turbulent planar channel. Titanium tetrachloride, TiCl4, reacting with atmospheric water vapo...

Large dams have been constructed on rivers to meet human demands for water, electricity, navigation, and recreation. As a consequence, flow and temperature regimes have been altered, strongly affecting river food webs and ecosystem processes. Experimental high-flow dam releases, i.e., controlled floods, have been implemented on the Colorado River, U.S.A., in an effort to reestablish pulsed floo...

Microscopic active droplets are able to swim autonomously in viscous flows. This puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilization and interfacial flows resulting these solutes’ gradients. Contrary asymmetric colloids, isotropic spontaneously by exploiting nonlinear coupling of transport self-generated Marangoni flo...

In the theory of traffic flows the main characteristics are: intensity, speed, and density.  They make it possible to use hydrodynamic models. In connection with the development of modern highways and road networks, traffic flows behavior is becoming more and more complex and diverse. In particular, the B.Kerner studies have shown that the laminar solution of hydrodynamic models is poorly corre...

We give a symbolic construction of Shunji Ito’s “transversal flow for a subshift of finite type” [I], along the lines of Vershik’s construction of an adic transformation. We then show how these flows arise naturally in the symbolic coding of horocycle flows on non-compact hyperbolic surfaces with finite area.