Equation of state of an ideal gas with nonergodic behavior in two connected vessels

Single-Crystal Lattice Filling in Connected Spaces inside 3D Networks

Connected vessel effects have been widely utilized from ancient times. It is quite interesting to know whether there are any special effects when single-crystal lattices fill the connected spaces inside 3D networks. In some single-crystal and 3D network pairs, there seems to exist a specific rule: when single-crystal lattices fill the connected spaces inside 3D networks, the front of the lattice in each channel is determined by the symmetrical center of the lattice structure. However, this needs to be validated by using various single-crystal lattice to fill the 3D networks with different compositions. Here we report a method to establish a gradient environment which can favor the formation of a micrometer-sized single crystal lattice across various 3D networks. The fronts of the filled lattices form the shapes which are the equilibrium shapes of the single crystals no matter what the single crystals or the 3D networks are, indicating the specific rule while the single-crystal lattices fill the 3D networks. The single crystals filled in the connected spaces inside 3D networks, which are functional materials, and had alternating properties, such as 4-fold higher electronic conductivity, which improve their performance in applications.

Billiard with a handle

We consider an open billiard with two holes, connected by a handle. The central billiard is chosen so that its closed form's islands of stability occupy a significant part of the phase space. Holes destroy these islands, which leads to almost all trajectories of the system being interleaved. We also study the unbalanced flow of billiard particles through the handle, which appears only after a small border site of nonspecular reflection is added to the system. With this site our system is rather a ratchet of a different type, since the site does not produce an explicitly acting force or violate the reversibility of trajectories.