Prospect for characterizing interacting soft colloidal structures using spin-echo small angle neutron scattering

Spin-echo small angle neutron scattering (SESANS) provides a new experimental tool for structural investigation. Due to the action of spin-echo encoding, SESANS measures a spatial correlation function in real space, as opposed to the structure factor S(Q), I(Q), in momentum (Q) space measured by conventional small angle neutron scattering. To establish the usefulness of SESANS in structural characterization, particularly for interacting colloidal suspensions, we have previously conducted a theoretical study of the SESANS correlation functions for model systems consisting of particles with uniform density profiles [X. Li, C.-Y. Shew, Y. Liu, R. Pynn, E. Liu, K. W. Herwig, G. S. Smith, J. L. Robertson, and W.-R. Chen J. Chem. Phys. 132, 174509 (2010)]. Within the same framework, we explore in the present paper the prospect of using SESANS to investigate the structural characteristics of colloidal systems consisting of particles with nonuniform intraparticle mass distribution. As an example, a Gaussian model of interacting soft colloids is used to investigate the manifestation of structural softness in a SESANS measurement. The exploration shows a characteristically different SESANS correlation function for interacting soft colloids, in comparison to that of a uniform hard sphere system. The difference arises from the Abel transform imbedded in the mathematical formalism bridging the SESANS spectra and the spatial autocorrelation function.     

Elastic interaction of interfacial spherical-cap cracks in hollow particle filled composites

This work analyzes the elastic interaction between two spherical-cap cracks present along the outer surface of a hollow particle embedded in a dissimilar medium under remote uniaxial tensile loading. A semi-analytical approach based on an enriched Galerkin method is adopted to determine stress and deformation fields as functions of particle wall thickness and cracks’ configuration. The present analysis is limited to multiple interfacial spherical-cap cracks; that is, crack propagation is restrained to the particle-matrix interface and possibility of crack kinking in the matrix is not considered. Interfacial crack growth characteristics, conditions for stable crack propagation, equal crack growth, and shielding are established through energy release rate analysis. The study is relevant to the analysis of tensile and flexural failure of syntactic foams used in marine and aerospace applications. Results specialized to glass-vinyl ester syntactic foams demonstrate that particle wall thickness can be used to control crack stability and growth characteristics as well as tailoring the magnitude of the shielding phenomenon. Predictions are compared to finite element findings for validation and to results for penny-shaped cracks to elucidate the role of crack curvature.     

Fisher information and matrix-valued valuations

All continuous and affinely contravariant matrix-valued valuations on the Sobolev space W1,2(Rn) are completely classified. It is shown that there is a unique such valuation. This valuation turns out to be the Fisher information matrix.     

Simulation of plastic deformation in glassy polymers: Atomistic and mesoscale approaches

The mechanism of deformation in glasses is very different from that of crystals, even though their general behavior is very similar. In this study, we investigated the deformation of polycarbonate on the atomistic scale with molecular dynamics and on the continuum scale with a new simulation approach. The results indicated that high atomic/segmental mobility and low local density enabled the formation (nucleation) of highly deformed regions that grew to form plastic defects called plastic shear transformations. A continuum-scale simulation was performed with the concept of plastic shear transformations as the basic region of deformation. The continuum simulations were able to predict the primary and secondary creep behavior. The slope of the secondary creep depended on the interactions between the plastic shear transformations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 994-1004, 2005     

Driven nonequilibrium lattice systems with shifted periodic boundary conditions

We present the first study of a driven nonequilibrium lattice system in the two-phase region, withshifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, we find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.     

Moduli Space of BPS Walls in Supersymmetric Gauge Theories

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N _F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N _C) gauge theory with N _F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N _C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.     

Branched Carbon Nanotube Junctions Predicted by Computational Nanotechnology and Fabricated through Nanowelding

Examples of progress in fabricating branched multi-terminal multi-wall and single-wall carbon nanotube junctions as predicted by nanotechnology simulations, using template growth and nanowelding techniques, respectively, have been briefly reviewed in this report. It is argued that similar general progress in computational nanotechnology-driven fabrication of applications in other nanomaterials such as nanotubes, fullerenes, nanowires, quantum dots, DNA molecules, and nanoparticle-based systems and devices are also feasible. This is because, at nanometer length scale, system sizes have shrunk sufficiently small such that it is feasible to simulate the structural, stability, and physical and chemical characteristics with very high accuracy predictive simulations.