J-beveling of pipe ends with a hand-held tool

Adapted cutter, driven by a hand-held, variable-speed power drill, is used in the field to cut J-bevels on the ends of stainless-steel or aluminum pipe to be joined by precision welding. With this tool an acceptable bevel is cut within 3 percent of the time required for grinding and filing

Fractional Time Crystals

Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles force a system to evolve with a period which is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultra-cold atoms bouncing on an oscillating atom mirror and show that the system can spontaneously form a discrete time crystal where the ratio of a period of its motion and a driving period is a rational number. This kind of discrete time crystals requires higher order resonant driving which is analyzed here with the help of an original approach.Comment: version accepted for publication in Phys. Rev.

Market Model with Heterogeneous Buyers

In market modeling, one often treats buyers as a homogeneous group. In this paper we consider buyers with heterogeneous preferences and products available in many variants. Such a framework allows us to successfully model various market phenomena. In particular, we investigate how is the vendor's behavior influenced by the amount of available information and by the presence of correlations in the system.Comment: 26 pages, 15 figures, accepted to Physica