Universality class of fiber bundles with strong heterogeneities

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<\alpha<1 of fibers is unbreakable, while the remaining 1-\alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components \alpha_c which separates two qualitatively different regimes of the system: below \alpha_c the burst size distribution is a power law with the usual exponent \tau=5/2, while above \alpha_c the exponent switches to a lower value \tau=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena

Plasmon geometric phase and plasmon Hall shift

The collective plasmonic modes of a metal comprise a pattern of charge density and tightly-bound electric fields that oscillate in lock-step to yield enhanced light-matter interaction. Here we show that metals with non-zero Hall conductivity host plasmons with a fine internal structure: they are characterized by a current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This non-trivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wavepackets to acquire geometric phases as they scatter. Strikingly, at boundaries these phases accumulate allowing plasmon waves that reflect off to experience a non-reciprocal parallel shift along the boundary displacing the incident and reflected plasmon trajectories. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displays the chirality of the plasmon's current distribution and can be probed by near-field photonics techniques. Anomalous plasmon dynamics provide a real-space window into the inner structure of plasmon bands, as well as new means for directing plasmonic beams

Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal $S$-matrix correlations on the cross section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy ion collisions, bimolecular chemical reactions and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed $\simeq (3:1)$ intermediate complex, Schr\"odinger cat states and quantum-classical transition are studied for $^{24}$Mg+$^{28}$Si heavy ion scattering.Comment: 10 pages including 2 color ps figures. To be published in Physics of Atomic Nuclei (Yadernaya fizika

Large optical conductivity of Dirac semimetal Fermi arc surfaces states

Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persists as a large Drude weight of Fermi arc carriers when the system is doped. As a result, large and anisotropic Fermi arc conductivity provides a novel means of optically interrogating the topological surfaces states of Dirac semimetals.Comment: 8 pages, 3 figure

Slip avalanches in a fiber bundle model

We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an entire slip avalanche. Slip avalanches are characterized by the number slipping fibers, by the slip length, and by the load increment, which triggers the avalanche. Our calculations revealed that all three quantities are characterized by power law distributions with universal exponents. We show by analytical calculations and computer simulations that varying the amount of disorder of slip thresholds and the number of allowed slips of fibers, the system exhibits a disorder induced phase transition from a phase where only small avalanches are formed to another one where a macroscopic slip appears.Comment: 6 pages, 6 figure

Disorder induced brittle to quasi-brittle transition in fiber bundles

We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual components. For continuously distributed Young modulus the tail of the distribution proved to play a decisive role since fibers break in the decreasing order of their stiffness. Using power law distributed stiffness values we demonstrate that the system exhibits a disorder induced brittle to quasi-brittle transition which occurs analogously to continuous phase transitions. Based on computer simulations we determine the critical exponents of the transition and construct the phase diagram of the system.Comment: 6 pages, 6 figure

Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space. However, since these manifolds belong to non-Euclidean topological spaces, exploiting their structures is computationally expensive, especially when one considers the clustering analysis of massive amounts of data. To this end, we propose an efficient framework to address the clustering problem on Riemannian manifolds. This framework implements random projections for manifold points via kernel space, which can preserve the geometric structure of the original space, but is computationally efficient. Here, we introduce three methods that follow our framework. We then validate our framework on several computer vision applications by comparing against popular clustering methods on Riemannian manifolds. Experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases