Application of dimensional analysis and group theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1966 - 16 Jan. 1967

Dimensional analysis and group theory methods of solving ordinary and partial differential equation

Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1967 - 16 Jan. 1968

Application of transformation groups to solution of partial differential equation

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report

Lie transformation group for solution of partial differential equation

Ion-channel-like behavior in lipid bilayer membranes at the melting transition

It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the $1/f^{\alpha}$ noise that is commonly observed in currents across biological and artificial membranes.Comment: 5 pages, 4 figure

Aerodynamic characteristics of GD B-15B booster during cruise and landing M equals 0.2

Aerodynamic characteristics of scale model of space shuttle booster at cruise and landing speed of Mach 0.

Space shuttle: Low speed cruise, takeoff and landing aerodynamic characteristics, including engine exhaust effects of the GD/C B-15B booster

Low speed wind tunnel tests of takeoff, landing, and cruise aerodynamic characteristics of space shuttle booster with exhaust effect simulatio

Developing guidelines for COVID-19 management: A moving target. An invited commentary on “Evidence based management guideline for the COVID-19 pandemic - Review article”

The COVID-19 pandemic is moving at a rapid rate, both in global transmission and in our knowledge about the disease. Health authorities across the world are scrambling to delineate best practices for everything from appropriate personal protective equipment, to antiviral therapy, and ARDS management strategies. It that context, Nicola et al. present an excellent consolidation of what we currently know about the disease and what evidence we have to support particular management approaches [1]. They offer an evidence-based summary of the known epidemiology of the disease and the preventative measures being used to slow transmission, including social distancing, school closures, and quarantining. They also review the current treatment recommendations for those with severe disease, including a brief discussion of experimental treatments