Dipole Oscillations of a Bose-Einstein Condensate in Presence of Defects and Disorder

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.Comment: 4 pages, 4 figure

Violation of the isotropic-ℓ\ell approximation in overdoped La_{2-x}Sr_xCuO_4

Magnetotransport measurements on the overdoped cuprate La_{1.7}Sr_{0.3}CuO_4 are fitted using the Ong construction and band parameters inferred from angle-resolved photoemission. Within a band picture, the low temperature Hall data can only be fitted satisfactorily by invoking strong basal-plane anisotropy in the mean-free-path $\ell$. This violation of the isotropic-$\ell$ approximation supports a picture of dominant small-angle elastic scattering in cuprates due to out-of-plane substitutional disorder. We show that both band anisotropy and anisotropy in the elastic scattering channel strongly renormalize the Hall coefficient in overdoped La_{2-x}Sr_xCuO_4 over a wide doping and temperature range.Comment: 4 pages, 4 figure

Growth rates for subclasses of Av(321)

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates

Giant strongly connected component of directed networks

We describe how to calculate the sizes of all giant connected components of a directed graph, including the {\em strongly} connected one. Just to the class of directed networks, in particular, belongs the World Wide Web. The results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in,out-degree distribution $P(k_i,k_o)$. We show that if $P(k_i,k_o)$ does not factorize, the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in- and out-components. The calculations of the relative sizes of all the giant components are demonstrated using the simplest examples. We explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one.Comment: 4 pages revtex, 4 figure

Bose-Einstein condensation in complex networks

The evolution of many complex systems, including the world wide web, business and citation networks is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and non-equilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these non-equilibrium systems within the framework of equilibrium quantum gases predicts that the 'first-mover-advantage', 'fit-get-rich' and 'winner-takes-all' phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks

Letter graphs and geometric grid classes of permutations: characterization and recognition

In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a non-constructive way, a polynomial-time recognition of geometric grid classes of permutations and $k$-letter graphs for a fixed $k$. However, constructive algorithms are available only for $k=2$. In this paper, we present the first constructive polynomial-time algorithm for the recognition of $3$-letter graphs. It is based on a structural characterization of graphs in this class.Comment: arXiv admin note: text overlap with arXiv:1108.6319 by other author

Competition and adaptation in an Internet evolution model

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and the total number of connections in the Internet, both empirically measurable quantities. This fact place our model apart from others in which this exponent depends on parameters that need to be adjusted in a model dependent way. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity and traffic of the network.Comment: Minor content changes and inset of fig.

Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

Topology of evolving networks: local events and universality

Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can emerge, the connectivity distribution following either a generalized power-law or an exponential. We propose a continuum theory that predicts these two regimes as well as the scaling function and the exponents, in good agreement with the numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors.Comment: 13 pages, 3 figure