Abstract Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have achieved. Here, we study thermalization small that interact with large chaotic environments under the consideration Schrödinger evolution composite systems, from perspective zeroth law thermodynamics. Namely, consider a system is brought into contact environmental sys...

In milling, two different self-excited vibrations have been reported; regenerative and mode coupling chatter. The chatter mechanism has extensively studied validated with tests whereas was reported a long time ago for threading operations. presented models were based only on current of the system but not delayed vibrations. With increase in research carried out robotic milling operations, low f...

We prove that that the time averaged consistency error of the Nth approximate deconvolution LES model converges to zero uniformly in the kinematic viscosity and in the Reynolds number as the cube root of the averaging radius. We also give a higher order but non-uniform consistency error bound for the zeroth order model directly from the Navier-Stokes equations.

Let G(n; m) be a connected graph without loops and multiple edges which has n vertices and m edges. We ÿnd the graphs on which the zeroth-order connectivity index, equal to the sum of degrees of vertices of G(n; m) raised to the power − 1 2 , attains maximum.