Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions

As a model of the second order elliptic equation with non-trivial boundary conditions, we consider the Laplace equation with mixed Dirichlet and Neumann boundary conditions on convex polygonal domains. Our goal is to establish that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon–Miranda) discrete maximum principle, and then prove the stability of the Ritz projection with mixed boundary conditions in \(L^\infty \) norm. Such results have a number of applications, but are not available in the literature. Our proof of the maximum-norm stability of the Ritz projection is based on converting the mixed boundary value problem to a pure Neumann problem, which is of independent interest.     

Flux-based level-set method for two-phase flows on unstructured grids

In this paper we deal with the application of the flux-based level set method to moving interface computations on unstructured grids. The focus lies on the overcoming of the known difficulties of level set methods, e.g. accurate computations of important geometric properties, reliable and precise reinitialization of the level set function and the adaption of standard discretization methods to the moving boundary case. The basic building block of our approach is the high-resolution flux-based level set method for general advection equation (Frolkovi? and Mikula in SIAM J Sci Comput 29(2):579–597, 2007, Frolkovi? and Wehner in Comput Vis Sci 12(6):626–650, 2009). We extend this method for the problem of reinitialization of the level set function on unstructured grids by using quadratic interpolation to compute distances for nodes close to the interface. To realize numerical simulation for some applications with moving boundaries, we adapt the approach of ghost fluid method (Gibou and Fedkiw in J Comput Phys 202:577–601, 2005) for unstructured grids. The idea is to describe the development of the moving boundary with a level set formulation while the computational grid remains fixed and the boundary conditions are enforced using some extrapolation. Our main motivation is the numerical solution of two-phase incompressible flow problems. Additionally to previously mentioned steps, we introduce further numerical schemes in the framework of finite volume discretization for the flow. Possible jumps of the pressure and the directional derivative of velocity at the interface are modeled directly within the method using the approach of extended approximation spaces. Besides that, an algorithm for the computations of curvature is considered that exhibits the second order accuracy for some examples. Numerical experiments are provided for the presented methods.     

Single pass text classification by direct feature weighting

The Feature Weighting Classifier (FWC) is an efficient multi-class classification algorithm for text data that uses Information Gain to directly estimate per-class feature weights in the classifier. This classifier requires only a single pass over the dataset to compute the feature frequencies per class, is easy to implement, and has memory usage that is linear in the number of features. Results of experiments performed on 128 binary and multi-class text and web datasets show that FWC??s performance is at least comparable to, and often better than that of Naive Bayes, TWCNB, Winnow, Balanced Winnow and linear SVM. On a large-scale web dataset with 12,294 classes and 135,973 training instances, FWC trained in 13?s and yielded comparable classification performance to a state of the art multi-class SVM implementation, which took over 15?min to train.     

Boundary properties of graphs for algorithmic graph problems

The notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature. In the present paper, we first survey recent results related to this notion and then apply it to two algorithmic graph problems: Hamiltonian cycle and vertexk-colorability. In particular, we discover the first two boundary classes for the Hamiltonian cycle problem and prove that for any k>3 there is a continuum of boundary classes for vertexk-colorability.     

Scrap tyre rubber depolymerization by nitrous oxide: products and mechanism of reaction

The development of effective methods for reclaiming scrap tyre rubbers attracts a great deal of attention. Earlier, we have proposed an alternative way for reclaiming waste rubber, which consists in its treatment with nitrous oxide (N₂O) at 180–230 °C and pressure of 2–5 MPa. In the present study, the reclaimed products obtained by this method from tyre crumb rubber were characterized for the first time by TGA, FTIR, NMR, and ultimate analysis techniques. The results showed that the sol fraction isolated from the reclaimed rubber consists mainly of diene oligomers with the carbonyl, predominantly ketone, groups. The remaining gel fraction includes some of the rubber polymer components and all the carbon black filler present in the initial vulcanizate. Based on the experimental results, a mechanism of vulcanized rubber interaction with nitrous oxide was suggested. The mechanism involves a selective 1,3-dipolar cycloaddition of N₂O molecules to C=C bonds of isoprene and butadiene units in vulcanized elastomers. The main reaction route proceeds without cleavage of initial C=C bonds leading to the formation of ketone groups randomly distributed along the polymer backbone. The cleavage of a certain amount of reacting C=C bonds leads to controllable scission of macromolecular chains and accordingly to depolymerization of the initial vulcanized rubber, thus yielding a plastic reclaim product. The sulfur cross-links do not appear to be broken in the course of waste rubber treatment.     

Self-assembly of charged microclusters of CdSe/ZnS core/shell nanodots and nanorods into hierarchically ordered colloidal arrays

A thermodynamically driven self-organization of microclusters of semiconductor nanocrystals with a narrow size distribution into periodic two-dimensional (2D) arrays is an attractive low-cost technique for the fabrication of 2D photonic crystals. We have found that CdSe/ZnS core/shell quantum dots or quantum rods, transferred in aqueous phase after capping with the bifunctional surface-active agent DL-cysteine, form on a poly-L-lysine coated surface homogeneously sized micro-particles, droplet-like spheroid clusters and hexagon-like colloidal crystals self-organized into millimetre-sized 2D?hexagonal assemblies. The presence of an organic molecular layer around the micro-particles prevents immediate contact between them, forming an interstitial space which may be varied in thickness by changing the origin of the molecular layer capping nanocrystals. Due to the high refractive index of CdSe and the low refractive index of the interstitial spaces, these structures are expected to have deep gaps in their photonic band, forming hierarchically ordered 2D arrays of potentially photonic materials.     

Stress‐Actuated Spiral Microelectrode for High‐Performance Lithium‐Ion Microbatteries

Miniaturization of batteries lags behind the success of modern electronic devices. Neither the device volume nor the energy density of microbatteries meets the requirement of microscale electronic devices. The main limitation for pushing the energy density of microbatteries arises from the low mass loading of active materials. However, merely pushing the mass loading through increased electrode thickness is accompanied by the long charge transfer pathway and inferior mechanical properties for long‐term operation. Here, a new spiral microelectrode upon stress‐actuation accomplishes high mass loading but short charge transfer pathways. At a small footprint area of around 1 mm², a 21‐fold increase of the mass loading is achieved while featuring fast charge transfer at the nanoscale. The spiral microelectrode delivers a maximum area capacity of 1053 µAh cm^?2 with a retention of 67% over 50 cycles. Moreover, the energy density of the cylinder microbattery using the spiral microelectrode as the anode reaches 12.6 mWh cm^?3 at an ultrasmall volume of 3 mm³. In terms of the device volume and energy density, the cylinder microbattery outperforms most of the current microbattery technologies, and hence provides a new strategy to develop high‐performance microbatteries that can be integrated with miniaturized electronic devices.     

Magnetic Suspension Array Technology: Controlled Synthesis and Screening in Microfluidic Networks

Information tagging and processing are vital in information‐intensive applications, e.g., telecommunication and high‐throughput drug screening. Magnetic suspension array technology may offer intrinsic advantages to screening applications by enabling high distinguishability, the ease of code generation, and the feasibility of fast code readout, though the practical applicability of magnetic suspension array technology remains hampered by the lack of quality administration of encoded microcarriers. Here, a logic‐controlled microfluidic system enabling controlled synthesis of magnetic suspension arrays in multiphase flow networks is realized. The smart and compact system offers a practical solution for the quality administration and screening of encoded magnetic microcarriers and addresses the universal need of process control for synthesis in microfluidic networks, i.e., on‐demand creation of droplet templates for high information capacity. The demonstration of magnetic suspension array technology enabled by magnetic in‐flow cytometry opens the avenue toward point‐of‐care multiplexed bead‐based assays, clinical diagnostics, and drug discovery.     

Blur identification by multilayer neural network based on multivalued neurons.

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time, this network has a number of specific different features. Its backpropagation learning algorithm is derivative-free. The functionality of MLMVN is superior to that of the traditional feedforward neural networks and of a variety kernel-based networks. Its higher flexibility and faster adaptation to the target mapping enables to model complex problems using simpler networks. In this paper, the MLMVN is used to identify both type and parameters of the point spread function, whose precise identification is of crucial importance for the image deblurring. The simulation results show the high efficiency of the proposed approach. It is confirmed that the MLMVN is a powerful tool for solving classification problems, especially multiclass ones.