The method of fundamental solutions for Signorini problems

We investigate the use of method of fundamental solutions (MFS)for the numerical solution of Signorini boundary value problems.The MFS is an ideal candidate for solving such problems becauseinequality conditions alternating at unknown points of the boundarycan be incorporated naturally into the least-squares minimizationscheme associated with the MFS. To demonstrate its efficiency,we apply the method to two Signorini problems. The first isa groundwater flow problem related to percolation in gentlysloping beaches, and the second is an electropainting application.For both problems, the results are in close agreement with previouslyreported numerical solutions.     

The compressible Newtonian extrudate swell problem

We solve the compressible Newtonian extrudate swell problem in order to investigate the effect of compressiblity on the shape of the extrudate. We employ a first-order equation of state relating the density to the pressure and use finite elements for the numerical solution of the problem. Our results show that the shape of the extrudate and the final extrudate swell ratio are not significanlty affected even at high compressibility values.     

Gravitational instabilities of isothermal spheres in the presence of a cosmological constant

Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in the microcanonical and the canonical ensembles, for which the corresponding instabilities are known as ‘gravothermal catastrophe’ and ‘isothermal collapse’, respectively. In the microcanonical ensemble, no equilibria can be found for radii larger than a critical value, which is increasing with increasing cosmological constant. In contrast, in the canonical ensemble, no equilibria can be found for radii smaller than a critical value, which is decreasing with increasing cosmological constant. For a positive cosmological constant, characteristic reentrant behavior is observed.     

Cooperative computing with fragmentable and mergeable groups

This work considers the problem of performing a set of N tasks on a set of P cooperating message-passing processors (PN). The processors use a group communication service (GCS) to coordinate their activity in the setting where dynamic changes in the underlying network topology cause the processor groups to change over time. GCSs have been recognized as effective building blocks for fault-tolerant applications in such settings. Our results explore the efficiency of fault-tolerant cooperative computation using GCSs. The original investigation of this area by (Dolev et al., Dynamic load balancing with group communication, in: Proc. of the 6th International Colloquium on Structural Information and Communication Complexity, 1999) focused on competitive lower bounds, non-redundant task allocation schemes and work-efficient algorithms in the presence of fragmentation regroupings. In this work we investigate work-efficient and message-efficient algorithms for fragmentation and merge regroupings. We present an algorithm that uses GCSs and implements a coordinator-based strategy. For the analysis of our algorithm we introduce the notion of view-graphs that represent the partially-ordered view evolution history witnessed by the processors. For fragmentations and merges, the work of the algorithm (defined as the worst case total number of task executions counting multiplicities) is not more than min{N·f+N,N·P}, and the message complexity is no worse than 4(N·f+N+P·m), where f and m denote the number of new groups created by fragmentations and merges, respectively. Note that the constants are very small and that, interestingly, while the work efficiency depends on the number of groups f created as the result of fragmentations, work does not depend on the number of groups m created as the result of merges.     

Cationic star polymer siRNA transfectants interconnected with a piperazine-based cationic cross-linker

Cationic star polymers of 2-(dimethylamino)ethyl methacrylate (DMAEMA) were prepared via the “arm-first” method under group transfer polymerization (GTP) conditions, and were interconnected using a novel, hydrophilic, positively ionizable dimethacrylate cross-linker which is essentially the cyclic dimer of DMAEMA, thus ensuring that the building units of the arms and the core of the star polymers were identical. After their physicochemical characterization, these star-like polyamines were evaluated for their ability to transfer small interfering RNA (siRNA) to murine myoblast cells. Suppression efficiency was found to increase with polymer loading and star branch size, attaining sufficiently high values, comparable to that observed with standard non-viral siRNA transfection systems, while cytotoxicity was kept reasonably low.     

How does the hydrophobic content of methacrylate ABA triblock copolymers affect polymersome formation?

Polymersomes are exciting self-assembled structures with great potential in pharmaceutical applications. A systematic investigation of a novel series of methacrylate-based polymersomes is reported in this study. Five well-defined ABA triblock copolymers with A being based on tri(ethylene glycol) methyl methacrylate and B being based on 2-(diethylamino)ethyl methacrylate (DMAEMA) were synthesized using a living polymerization method. The effect of the composition of the ABA triblock copolymers on the thickness of the hydrophobic membrane of the polymersomes and the release of a model drug is demonstrated.     

Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity

In this article, we analyze the singular function boundary integral method (SFBIM) for a two‐dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick‐slip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution, and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. By means of Green's theorem, the resulting discretized equations are posed and solved on the boundary of the domain, away from the point where the singularity arises. We analyze the convergence of the method and prove that the coefficients in the local asymptotic expansion, also referred to as stress intensity factors, are approximated at an exponential rate as the number of the employed expansion terms is increased. Our theoretical results are illustrated through a numerical experiment. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid

The isothermal, planar Poiseuille flow of a weakly compressible Oldroyd-B fluid is considered under the assumption that the density of the fluid obeys a linear equation of state. A perturbation analysis for all the primary flow variables is carried out with the isothermal compressibility serving as the perturbation parameter. The sequence of partial differential equations which results from the perturbation procedure is solved analytically up to second order. The effects of the compressibility parameter, the aspect ratio, and the Weissenberg number are discussed. In particular, it is demonstrated that compressibility has a significant effect on the transverse velocity and the first normal stress difference.     

Cessation of the lid-driven cavity flow of Newtonian and Bingham fluids

We provide benchmark results for a transient variant of the lid-driven cavity problem, where the lid motion is suddenly stopped and the flow is left to decay under the action of viscosity. Results include Newtonian as well as Bingham flows, the latter having finite cessation times, for Reynolds numbers Re ∈ [1, 1000] and Bingham numbers Bn ∈ [0, 10]. The finite-volume method and Papanastasiou regularisation were employed. A combination of Re and Bn, the effective Reynolds number, is shown to convey more information about the flow than either Re or Bn alone. A time scale which characterises the flow independently of the geometry and flow parameters is proposed.