Search results for "Radius"
showing 10 items of 708 documents
Determination of projection geometry from quantitative assessment of the distortion of spherical references in single-view projection radiography
2004
A method is introduced, inferring the three-dimensional (3-D) location from the 2-D radiographic shadow of an opaque spherical reference body of known radius by considering its elliptical distortion, the 2-D shadow location and a known source-to-receptor distance. Three noncollinear spheres fixed to a rigid object constitute all possible degrees of freedom, i.e., the entire 3-D imaging geometry. The method may be used (a) to determine the 3-D imaging geometry from a single 2-D view and (b) to correct for foreshortening of object distances coplanar with the plane defined by the sphere triplet. Apart from the mathematical background the article describes a small feasibility experiment, perfor…
Excess free energy of nanoparticles in a polymer brush
2008
Abstract We present an efficient method for direct determination of the excess free energy Δ F of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty Δ F ( R , D ) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds Δ F ∝ R 3 whereas for shallow nanoclusions Δ F ∝ R 2 , regardless of the particle interaction (…
Single-chain conformations in symmetric binary polymer blends: Quantitative comparison between self-consistent field calculations and Monte Carlo sim…
1998
Single-chain properties in a symmetric binary polymer blend are studied by self-consistent field calculations and Monte Carlo simulations. Within the self-consistent field scheme, the statistical mechanics of a cluster of neighboring polymers is solved. Interactions among the polymers of a cluster and composition fluctuations within a cluster are incorporated exactly, a mean field approximation is invoked for intercluster interactions and long-range fluctuations. The results are compared to large scale Monte Carlo simulations for a broad range of chain lengths. While we find nearly quantitative agreement for single chain propertiese.g., the reduction of the chain dimensions of the minority …
Relaxation of self-entangled many-arm star polymers
1989
We present a description of the relaxation of star polymers based on the conformational scaling properties predicted by Daoud and Cotton and confirmed in our recent simulations. We identify three typical relaxation mechanisms. The first describes elastic deformation of the overall shape. Its relaxation time is nearly independent off. A second type of relaxation occurs via rotational diffusion. We predict that the relaxation time should scale with Nwlfz-v where Y is the correlation length exponent. A third relaxation process is the disentanglement of two or more arms. Here the longest relaxation time should increase exponentially with f llz. We measure various relaxation processes by molecul…
Characterization of Polyorganosiloxane Nanoparticles in Aqueous Dispersion by Asymmetrical Flow Field-Flow Fractionation
2001
The advantages of asymmetrical flow field-flow fractionation (AF-FFF) for the characterization of aqueous dispersions of spherical polyorganosiloxane nanoparticles are discussed. With AF-FFF it was possible to obtain information about the synthesis, which is based on the hydrolysis and condensation of alkylalkoxysilanes in aqueous dispersion, and the average size of the spherical nanoparticles in the complex mixture in the presence of excess surfactant. The results are compared to measurements performed with dynamic light scattering (DLS). The size of the nanoparticles increases as a function of the amount of added monomer. Particles with radii between 2 and 50 nm are observed. If only the …
The Role of Internal Rotational Barriers in Polymer Melt Chain Dynamics
2002
We present molecular dynamics simulations on 1,4-polybutadiene comparing the dynamics of melt chains between chemically realistic models and a freely rotating chain version of one of the models. These models exhibit the same liquid structure, as measured by the structure factor, and meso- to large-scale chain structure, as measured by the Rouse-mode amplitudes. We show that in this case the Rouse-like chain dynamics as observable in the momentum transfer range of neutron spin-echo experiments is the same for the chains with and without torsion barriers. Our results bear on a recent comparative neutron spin-echo study of the chain dynamics of two polymers with similar chain structure which r…
The Magnus expansion and some of its applications
2008
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…
Small-angle X-ray scattering reveals differences between the quaternary structures of oxygenated and deoxygenated tarantula hemocyanin
1996
Small-angle X-ray scattering (SAXS) curves have been recorded for the oxygenated and deoxygenated states of the 4 x 6-meric hemocyanin from the tarantula Eurypelma californicum. A comparison of the curves shows that the quaternary structures of the two states are different by three criteria, which all indicate that the hemocyanin is less compact in the oxygenated compared to the deoxygenated form: (a) The radius of gyration is 8.65 +/- 0.05 nm for the deoxy- and 8.80 +/- 0.05 nm for the oxy-form. (b) The maximum particle dimension amounts to 25.0 +/- 0.5 nm for the deoxy- and to 27.0 +/- 0.5 nm for the oxy-form. (c) A dip in the intramolecular distance distribution function p(r) is more pro…
Reinterpretation of Classic Proton Charge Form Factor Measurements
2020
In 1963, a proton radius of $0.805(11)~\mathrm{fm}$ was extracted from electron scattering data and this classic value has been used in the standard dipole parameterization of the form factor. In trying to reproduce this classic result, we discovered that there was a sign error in the original analysis and that the authors should have found a value of $0.851(19)~\mathrm{fm}$. We additionally made use of modern computing power to find a robust function for extracting the radius using this 1963 data's spacing and uncertainty. This optimal function, the Pad\'{e} $(0,1)$ approximant, also gives a result which is consistent with the modern high precision proton radius extractions.
The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces
1997
AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.