New universality class for the fragmentation of plastic materials

We present an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene particles of spherical shape against a hard wall. Experiments reveal a power law mass distribution of fragments with an exponent close to 1.2, which is significantly different from the known exponents of three-dimensional bulk materials. A 3D discrete element model is introduced which reproduces both the large permanent deformation of the polymer during impact, and the novel value of the mass distribution exponent. We demonstrate that the dominance of shear in the crack formation and the plastic response of the material are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena.Comment: 4 pages, 4 figures, appearing in Phys. Rev. Let

Universality class of the fragmentation of plastic materials

We carry out an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene (PP) particles of spherical shape against a hard wall. Our experiments revealed that the mass distribution of fragments has a power law behavior with an exponent close to 1.2, which is significantly different from the known exponents of threedimensional bulk materials. To understand the fragmentation of plastic materials we developed a threedimensional discrete element model where the sample is represented as a random packing of spherical particles connected by elastic beams. The model reproduces both the large permanent deformation of the polymer during impact, and the novel value of the mass distribution exponent. Computer simulations revealed that the dominance of shear in the crack formation and the healing of compressed crack surfaces are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena

Universality class of the fragmentation of plastic materials

We carry out an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene (PP) particles of spherical shape against a hard wall. Our experiments revealed that the mass distribution of fragments has a power law behavior with an exponent close to 1.2, which is significantly different from the known exponents of threedimensional bulk materials. To understand the fragmentation of plastic materials we developed a threedimensional discrete element model where the sample is represented as a random packing of spherical particles connected by elastic beams. The model reproduces both the large permanent deformation of the polymer during impact, and the novel value of the mass distribution exponent. Computer simulations revealed that the dominance of shear in the crack formation and the healing of compressed crack surfaces are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena

Observation of two-dimensional lattice interface solitons

We report on the experimental observation of two-dimensional solitons at the interface between square and hexagonal waveguide arrays. In addition to the different symmetry of the lattices, the influence of a varying refractive index modulation depth is investigated. Such variation strongly affects the properties of surface solitons residing at different sides of the interface.Comment: 14 pages, 5 figures, to appear in Optics Letter

Nonlinearity-induced broadening of resonances in dynamically modulated couplers

We report the observation of nonlinearity-induced broadening of resonances in dynamically modulated directional couplers. When the refractive index of the guiding channels in the coupler is harmonically modulated along the propagation direction and out-of-phase in two channels, coupling can be completely inhibited at resonant modulation frequencies. We observe that nonlinearity broadens such resonances and that localization can be achieved even in detuned systems at power levels well below those required in unmodulated couplers.Comment: 14 pages, 4 figures, to appear in Optics Letter

Anonymity and Rewards in Peer Rating Systems

When peers rate each other, they may choose to rate inaccurately in order to boost their own reputation or unfairly lower another’s. This could be successfully mitigated by having a reputation server incentivise accurate ratings with a reward. However, assigning rewards becomes a challenge when ratings are anonymous, since the reputation server cannot tell which peers to reward for rating accurately. To address this, we propose an anonymous peer rating system in which users can be rewarded for accurate ratings, and we formally define its model and security requirements. In our system ratings are rewarded in batches, so that users claiming their rewards only reveal they authored one in this batch of ratings. To ensure the anonymity set of rewarded users is not reduced, we also split the reputation server into two entities, the Rewarder, who knows which ratings are rewarded, and the Reputation Holder, who knows which users were rewarded. We give a provably secure construction satisfying all the security properties required. For our construction we use a modification of a Direct Anonymous Attestation scheme to ensure that peers can prove their own reputation when rating others, and that multiple feedback on the same subject can be detected. We then use Linkable Ring Signatures to enable peers to be rewarded for their accurate ratings, while still ensuring that ratings are anonymous. Our work results in a system which allows for accurate ratings to be rewarded, whilst still providing anonymity of ratings with respect to the central entities managing the system

Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-

Surface solitons at interfaces of arrays with spatially-modulated nonlinearity

We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear refractive index attains its maxima, we found that nonlinear surface waves exist and can be made stable only within a limited band of input energy flows, and for lattice depths exceeding a lower threshold.Comment: 13 pages, 3 figures, to appear in Optics Letter