We “see” light only when some material detectors (dipoles) respond to the incident EM field. EM fields do not operate on each other to make themselves visible to us. Superposition of multiple fields becomes manifest only when the intrinsic properties of these dipoles allow them to respond to all the superposed fields simultaneously and thereby summing the effects of all the fields. Accordingly,...

A formula for the free energy of a stack of highly charged, semiflexible membranes, previously derived by Odijk (Odijk T. Langmuir, 1992), is shown _to be the first order term in a formal expansion of the free

The effectiveness of transmitting force by using undulation is well known, but it takes time for the whip to flex and then sequentially transmit force. An example of using undulation is a whip whose tip movement exceeds the speed of sound. The whip-like motion principle requires that the user firmly plant the feet on the ground – a position that may lead to physical damage. Experts note that th...

The radial viscosity of the mantle is generally thought to increase by ∼10–100 times from upper lower with a putative, abrupt at 660 km depth. Recently, low channel (LVC) between and 1,000 has been suggested. We conduct series time-dependent flow models either increasing or decreasing depth while tracking slab structure, state-of-stress, geoid. find that LVC will amplitude long wavelength (>5,0...

This book is a follow up to the volume Nematics and Cholesteric Liquid Crystals by the same authors in the Liquid Crystal Book Series edited by G.W. Gray, J.W. Goodby and A. Fukuda. Here, the authors, two well known experts from the Ecole Normale Supérieure, Lyon and the Université Paris-Sud, deal with liquid crystalline phases endowed with long range positional order in one or more dimensions,...