Experimental Study of Spectral Properties of a Frenkel-Kontorova System

We report on microwave emission from linear parallel arrays of underdamped Josephson junctions, which are described by the Frenkel-Kontorova (FK) model. Electromagnetic radiation is detected from the arrays when biased on current singularities (steps) appearing at voltages Vn=Φ0(nc¯/L), where Φ0=2.07×10-15Wb is the magnetic flux quantum, and c¯, L, and n are, respectively, the speed of light in the transmission line embedding the array, L its physical length, and n an integer. The radiation, detected at fundamental frequency c¯/2L when biased on different singularities, indicates shuttling of bunched 2π kinks (magnetic flux quanta). Resonance of flux-quanta motion with the small-amplitude oscillations induced in the arrays gives rise to fine structures in the radiation spectrum, which are interpreted on the basis of the FK model describing the resonance. The impact of our results on design and performances of new digital circuit families is discussed

A quantitative study of the evolution of open source software communities

Typically, virtual communities exhibit the well-known phenomenon of participation inequality, which means that only a small percentage of users is responsible of the majority of contributions. However, the sustainability of the community requires that the group of active users must be continuously nurtured with new users that gain expertise through a participation process. This paper analyzes the time evolution of Open Source Software (OSS) communities, considering users that join/abandon the community over time and several topological properties of the network when modeled as a social network. More specifically, the paper analyzes the role of those users rejoining the community and their influence in the global characteristics of the network

Relative topological properties

"In this thesis we study the concepts of relative topological properties and give some basic facts and relations among them. Our main focus is on various versions of relative normality, relative regularity and relative compactness. We give examples which answer some open questions and contract some conjectures in the literature. The theory of relative topological properties was introduced by A. V. Arhangelskii and H. M. M Genedi in 1989. Our three main results are (1) an example which presents a way to modify any Dowker space and get a normal space X such that X x [0, 1] is not kappa-normal (Example 4.2.14). (2) A theorem which implies the existence of a non-Tychonoff space that is internally compact is a larger regular space (Theorem 5.2.6), and (3) a theorem that characterizes those subspaces of the Niemytzki plane that are normal subspaces. "--Abstract from author supplied metadata

Investigation of the Influence of Nanodispersed Compositions Obtained by Plasmochemical Synthesis on the Crystallization Processes of Structural Alloys

The state of the problem of stabilizing the structure, improving the quality and properties of structural alloys is studied. To solve the problem, it is proposed to modify melts of low–alloyed alloys with nanodispersed compositions obtained by plasma–chemical synthesis. Process technological parameters are developed. Nanopowders of carbide and carbonitride class SiC and Ti (C, N) with a size of 50 ... 100 nm are obtained. The crystallographic parameters of the nanocompositions and the specific surface are determined, and the dependency curves are plotted. The macro– and microstructure of structural steels and alloys was studied before and after the modification. A significant (in 2 ... 3.5 times) grain refinement and stabilization of the alloy structure as a result of nanopowder modification of titanium carbonitride have been achieved. Thermodynamic calculations of the dimensions of crystalline seeds during the crystallization of steels and alloys are carried out. A complex criterial estimation of the efficiency of nanodispersed compositions in a steel melt is proposed. The features of crystallization and structure formation of modified structural steels are studied. The obtained results are of theoretical and practical importance for production of critical parts from structural steels and high–quality alloys

Homeomorphic subspaces in the plane

The idea of topological equivalence, or homeomorphic, is one of the basic considerations in any study of topology. Mrs. Yandell [3], in her master's thesis, compared pairs of spaces in the plane to determine whether or not they were homeomorphic. Decisions as to whether or not a pair of spaces were homeomorphic were based on several topological properties, including compactness and connectedness. In this thesis three additional topological properties are defined and used for the purpose of increasing the number of decisions that could be made with only the topological properties discussed in [33- In Chapter I, locally compact is defined and general theorems are proved concerning this property. In addition localy compactness is shown to be a topological property. In Chapter II, locally connected is defined, general theorems are proved, and local connectedness is shown to be a topological property. In Chapter III, connected im kleinen is defined, related to local connectedness, and shown to be a topological property. In Chapter IV, examples are given to show that indeed the studies in [3] have been extended

The Entropy of Co-Compact Open Covers

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: 1) it does not require the space to be compact, and thus generalizes Adler, Konheim and McAndrew's topological entropy of continuous mappings on compact dynamical systems, and 2) it is an invariant of topological conjugation, compared to Bowen's entropy that is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system (R, f) defined by f(x) = 2x, the co-compact entropy is zero, while Bowen's entropy for this system is at least log 2. More general, it is found that co-compact entropy is a lower bound of Bowen's entropies, and the proof of this result generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces, too

Lightning network: a second path towards centralisation of the Bitcoin economy

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.Comment: 11 pages, 7 figure

Examples of integrable sub-Riemannian geodesic flows

Motivated by a paper of Bolsinov and Taimanov DG/9911193 we consider non-holonomic situation and exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy. Moreover the Riemannian examples are obtained as "holonomization" of sub-Riemannian ones. A feature of non-holonomic situation is non-compactness of the phase space. We also exhibit a Liouvulle-integrable Hamiltonian system with topological entropy of all integrals positive.Comment: 21 pages; Answer to the self-posed question is added: Is it possible to construct Liouville-integrable Hamiltonian system with positive topological entropies of all integrals? Yes and we present an exampl

Floquet Energies and Quantum Hall Effect in a Periodic Potential

The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the Schroedinger equation in the co-moving frame). By this relation one can analyze the dependence of the Hall conductivity from the electric field. Sub-bands can be introduced by the time average of the expectation value of the Hamiltonian on the Floquet states. Moreover we prove previous results in form of sum rules as, for instance: the topological character of the Hall conductivity (being an integer multiple of e^2/h), the Diofantine equation which constrains the Hall conductivity by the rational number which measures the flux of the magnetic field through the periodicity cell. The Schroedinger equation fixes in a natural way the phase of the wave function over the reduced Brillouin zone: thus the topological invariant providing the Hall conductivity can be evaluated numerically without ambiguity.Comment: LaTex (revtex), 18 pages, 10 figures in .eps using epsf.sty. Changes in eq. (3.2). References adde

Interfacial layering in a three-component polymer system

We study theoretically the temporal evolution and the spatial structure of the interface between two polymer melts involving three different species (A, A* and B). The first melt is composed of two different polymer species A and A* which are fairly indifferent to one another (Flory parameter chi_AA* ~ 0). The second melt is made of a pure polymer B which is strongly attracted to species A (chi_AB 0). We then show that, due to these contradictory tendencies, interesting properties arise during the evolution of the interface after the melts are put into contact: as diffusion proceeds, the interface structures into several adjacent "compartments", or layers, of differing chemical compositions, and in addition, the central mixing layer grows in a very asymmetric fashion. Such unusual behaviour might lead to interesting mechanical properties, and demonstrates on a specific case the potential richness of multi-component polymer interfaces (as compared to conventional two-component interfaces) for various applications.Comment: Revised version, to appear in Macromolecule