Synthesis and aggregation behavior of four-arm star amphiphilic block copolymers in water

We report the first synthesis of amphiphilic four-arm star diblock copolymers consisting of styrene (STY) and acrylic acid (AA) made using reversible addition-fragmentation chain transfer (RAFT; Z group approach with no star-star coupling). The polymerization proceeded in an ideal living manner. The size of the poly(AA(132)-STYm)(4) stars in DMF were small and close to 7 nm, suggesting no star aggregation. Slow addition of water (pH = 6.8) to this mixture resulted in aggregates of 15 stars per micelle with core-shell morphology. Calculations showed that the polyAA blocks were slightly extended with a shell thickness of 15 nm. Treatment of these micelles with piperidine to cleave the block arms from the core resulted in little or no change on micelle size or morphology, but the polyAA shell thickness was close to 29 nm (33 nm is the maximum at full extension) suggesting a release of entropy when the arms are detached from the core molecule. In this work we showed through the use of star amphiphilic polymers that the micelle size, aggregation number, and morphology could be controlled.

Assembly of Human Papillomavirus Type-16 Virus-Like Particles: Multifactorial Study of Assembly and Competing Aggregation

Pentameric capsomeres of human papillomavirus capsid protein L1 expressed in Escherichia coli self-assemble into virus-like particles (VLPs) in vitro. A multifactorial experimental design was used to explore a wide range of solution conditions to optimize the assembly process. The degree of assembly was measured using an enzyme-linked immunosorbent assay, and a high-throughput turbidity assay was developed to monitor competing aggregation. The presence of zinc ions in the assembly buffer greatly increased the incidence of aggregation and had to be excluded from the experiment for meaningful analysis. Assembly of VLPs was optimal at a pH of about 6.5, calcium and sodium ions had no measurable effect, and dithiothreitol and glutathione inhibited assembly. Tryptophan fluorescence spectroscopy demonstrated that an increase in urea concentration reduced the rate of VLP formation but had no effect on the final concentration of assembled VLPs. This study demonstrates the use of the hanging-drop vapor-diffusion crystallization method to screen for conditions that promote aggregation and the use of tryptophan fluorescence spectroscopy for real-time monitoring of the assembly process.

On aggregation issues in spatial data management

Large amounts of information can be overwhelming and costly to process, especially when transmitting data over a network. A typical modern Geographical Information System (GIS) brings all types of data together based on the geographic component of the data and provides simple point-and-click query capabilities as well as complex analysis tools. Querying a Geographical Information System, however, can be prohibitively expensive due to the large amounts of data which may need to be processed. Since the use of GIS technology has grown dramatically in the past few years, there is now a need more than ever, to provide users with the fastest and least expensive query capabilities, especially since an approximated 80 % of data stored in corporate databases has a geographical component. However, not every application requires the same, high quality data for its processing. In this paper we address the issues of reducing the cost and response time of GIS queries by preaggregating data by compromising the data accuracy and precision. We present computational issues in generation of multi-level resolutions of spatial data and show that the problem of finding the best approximation for the given region and a real value function on this region, under a predictable error, in general is "NP-complete.

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.