We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive ...

Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfaces can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via orthogonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex res...

W hat does it take to fracture a fluid? How hard and fast does the fluid need to be pulled in order to break? Ole Hassager, from the Technical University of Denmark, and colleagues [1] have tackled these challenging questions head-on by stretching fluids composed of polymer melts at sufficiently high strain rates to make the fluid break in the same way that a pane of glass would if pulled hard ...

In many practical applications, we encounter ellipsoid constraints, ellipsoid-shaped clusters, etc. A usual justification for this ellipsoid shape comes from the fact that many real-life quantities are normally distributed, and for a multi-variate normal distribution, a natural confidence set (containing the vast majority of the objects) is an ellipsoid. However, ellipsoids appear more frequent...

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. ...

Computational Fluid Dynamics (CFD) software was used to compare the performance of a handmade wind turbine blade with that of a conventional factory made model. The geometry was simplified to 2D aerofoils and the surrounding flow field was analysed at a Reynold’s number of 80,000. It was found that the lift/drag characteristics of the two aerofoils across a range of angles of attack were virtua...

The ellipsoid factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid that fits inside the structure and that contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prol...

We introduce a new iterative root-finding method for complex polynomials, dubbed Newton-Ellipsoid method. It is inspired by the Ellipsoid method, a classical method in optimization, and a property of Newton’s Method derived in [7], according to which at each complex number a half-space can be found containing a root. Newton-Ellipsoid method combines this property, bounds on zeros, together with...

The simplex algorithm was the first algorithm proposed for linear programming, and although the algorithm is quite fast in practice, no variant of it is known to be polynomial time. The Ellipsoid algorithm is the first polynomial-time algorithm discovered for linear programming. The Ellipsoid algorithm was proposed by the Russian mathematician Shor in 1977 for general convex optimization proble...