arXiv subjects

Michael B. Partensky

Publications and source records attributed to Michael B. Partensky.

4 recordsLinked to original sources

arXiv2009

Spatial Localization Problem and the Circle of Apollonius

The Circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of mathematical physics, optics and electricity. Here we discuss its applications to the 'source localization' problems, e.g. pinpointing a radioactive source using the set of Geiger counters. The Circles of Apollonius help analyze these problems in transparent and intuitive manner. This discussion can be useful for High School Physics and Math curriculum.

physics.ed-ph↗

arXiv2005

Charges suspended by strings: a new twist to an old problem

A popular problem asks for the equilibrium separation between two identical (mutually repelling) charges suspended by strings fastened to a common point. We slightly modify this problem by considering two opposite (mutually attracting) charges and adding a finite separation between the suspension points. The discussion leading to the solution introduces important physical phenomena including "catastrophic" behavior and hysterisis.

physics.ed-ph↗

arXiv2003

Some peculiarities of equilibrium between springs and charges

A simple two charge system, one charge being suspended on a spring, exhibits complex behavior including bistability, hysteresis and catastrophic response to gradual variation of the external parameters. We discuss these complex features (that can be related, e.g., to membrane electroporation and voltage gating of ion channels) using only high school physics. Similar properties are displayed by a system comprised of magnets and springs. Using this analogy, a simple demonstration model was designed in collaboration with John Griffin, using components of the "Rogers Connections" magnetic construction toy.

physics.ed-ph↗

arXiv2002

The elastic capacitor and its unusual properties

The 'elastic capacitor' (EC) model was first introduced in studies of lipid bilayers (the major components of biological membranes). This electro-elastic model accounted for the compression of a membrane under applied voltage and allowed obtaining information about the membrane's elastic properties from the measurements of its capacitance. Later on, ECs were used to analyze the electrical breakdown of biological membranes. The EC model was also helpful in studies of electric double layers in various electrified interfaces (of which the electrode/ electrolyte interface is the most common example). This comparatively simple model, which analysis requires only high-school physics, has a close relationship to some real-life problems in physics, chemistry and biology. I hope that both teachers and students will find its discussion interesting, challenging and instructive.

physics.ed-ph↗