Mixing time of the fifteen puzzle

The mixing time of the fifteen puzzle

We show that there are universal positive constants c and C such the mixing time τmix for the fifteen puzzle in an n× n torus satisfies cn logn ≤ τmix ≤ Cn log n.

Introducing an Invention: Puzzle Shaped Cast for Upper Limb Fractures

Upper limb fractures are prevalent injuries. An essential element of fracture healing is to maintain the bones alignment. However there are lots of complications associated with traditional ways of treatment, such as compartment syndrome and stiffness due to immobility for long time. Also evaluation and observation of the limb under the casts for potential infections and skin issues are n...

درمان آلوپسی (ریزش مو) و اسکار (جای زخم) روی سر با چند بافت گستر و به روش زیگزاگ (پازل): یک روش جدید

Background and Objective: Repairing scalp scar and alopecia is a concern of surgeons. Treating it with tissue expander has indicated promising results in recent decades. This study provides a new method of using two tissue expanders simultaneously for tissue over expansion and repairing flaps’ edge with puzzle method. Materials and Methods: This study was conducted on fifteen 5 to 34- year- ol...

A “Fifteen Puzzle” in Fran

Fluid Dynamics in a Copper Converter: an Investigation on Mixing Phenomena in an Experimental Model

In this study, the mixing phenomena and fluid dynamics in a copper converter have been experimentally investigated using a physical model. The physical model is a 1:5 horizontal tank made of Plexiglas. The mixing phenomena have been characterized by experimentally measuring the mixing time using a tracer dispersion technique. Moreover, the effects of the air flow rate and lance submergence on t...