Modeling cascading failures in congested complex networks

Cascading failures occur commonly in congested complex networks, where it may be expressed as the process of generation, diffusion and dissipation of congestion. Different from betweeness centrality, we introduce congestion effects to determine the load on the node. In terms of user equilibrium condition, congestion effects can be described by cost functions or link performance functions, which map link flows to travel times. By introducing conceptual “practical capacity” dynamics to cost functions, cascading failures are well discussed in terms of the degree of congestion in complex networks. Moreover, the efficiency dynamics of the network due to cascading failures is also investigated, and a transition phenomenon is uncovered independent of clustering effect.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

Transport of waves in disordered waveguides: A potential model

We study the statistical properties of wave transport in a disordered waveguide. We first derive the properties of a “building block” (BB) of length δL starting from a potential model consisting of thin potential slices. We then find a diffusion equation—in the space of transfer matrices that describe our system—which governs the evolution with the length L of the disordered waveguide of the transport properties of interest. The latter depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. We have developed a numerical simulation in which the universal statistical properties of the BB found analytically are first implemented numerically, and then the various BBs are combined to construct the full waveguide. The reported results thus obtained are in good agreement with microscopic calculations, for both bulk and surface disorder.     

Understanding the time dependence of atomic level populations in evolving plasmas

The time dependence of atomic level populations in evolving plasmas is studied using an eigenfunction expansion of the non-LTE rate equations. The work aims to develop understanding without the need for, and as an aid to, numerical solutions. The discussion is mostly limited to linear systems, especially those for optically thin plasmas, but the implicitly non-linear case of non-LTE radiative transfer is briefly discussed. Eigenvalue spectra for typical atomic systems are examined using results compiled by Hearon. Diagonal dominance and sign symmetry of rate matrices show that just one eigenvalue is zero (corresponding to the equilibrium state), that the remaining eigenvalues have negative real parts, and that oscillations, if any, are necessarily damped. Gershgorin's theorems are used to show that many eigenvalues are determined by the radiative lifetimes of certain levels, because of diagonal dominance. With other properties, this demonstrates the existence of both “slow” and “fast” time-scales, where the “slow” evolution is controlled by properties of meta-stable levels. It is shown that, when collisions are present, Rydberg states contribute only “fast” eigenvalues. This justifies use of the quasi-static approximation, in which atoms containing just meta-stable levels can suffice to determine the atomic evolution on time-scales long compared with typical radiative lifetimes. Analytic solutions for two- and three-level atoms are used to examine the basis of earlier intuitive ideas, such as the “ionizing plasma” approximation. The power and limitations of Gershgorin's theorems are examined through examples taken from the solar atmosphere. The methods should help in the planning and interpretation of both experimental and numerical experiments in which atomic evolution is important. While the examples are astrophysical, the methods and results are applicable to plasmas in general.     

Quantum fields in toroidal topology

The standard representation of c^∗-algebra is used to describe fields in compactified space–time dimensions characterized by topologies of the type . The modular operator is generalized to introduce representations of isometry groups. The Poincaré symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space–time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2×2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein–Gordon and Dirac fields, and then formulate non-abelian gauge theories in . Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification.     

Spin-charge gauge compositeness of electron in HTS: Hints from metal-insulator crossover and entropy behavior

We show that the coexistence of Fermi arcs and metal-insulator crossover of the in-plane resistivity can give a hint of a peculiar “gauge compositeness” of the electron in hole-doped high T_c cuprates and a similar hint also comes from the negative intercept at T=0 of the electronic entropy extrapolated from moderate temperatures in the “pseudogap phase”. An implementation of this “compositeness” within the spin-charge gauge approach is outlined and is employed to discuss the above phenomena.     

Site-specific ϕ- and ψ-torsion angle determination in a uniformly/extensively 13C- and 15N-labeled peptide

A solid-state rotational-echo double resonance (REDOR) NMR method was introduced to identify the ?- and ψ-torsion angle from a ¹H–¹⁵N or ¹H–¹³C′ spin system of alanine-like residues in a selectively, uniformly, or extensively ¹⁵N-/¹³C-labeled peptide. When a C_α(i) or a ¹⁵N peak is site-specifically obtainable in the NMR spectrum of a uniformly ¹⁵N/¹³C-labeled sample system, the ψ- or ?-torsion angle specified by the conformational structure of peptide geometry involving ¹⁵N(i)–¹H_αi–¹⁵N(i + 1) or ¹³C′(i − 1)–¹H^Ni–¹³C′(i) spin system can be identified based on ¹³C_α- or ¹⁵N-detected ¹H_α–¹⁵N or ¹H_N–¹³C REDOR experiment. This method will conveniently be utilized to identify major secondary motifs, such as α-helix, β-sheet, and β-turn, from a uniformly ¹⁵N-/¹³C-labled peptide sample system. When tested on a ¹³C-/¹⁵N-labeled model system of a three amino acid peptide Gly–[U–¹³C, ¹⁵N]Ala–[U–¹³C, ¹⁵N]Leu, the ψ-angle of alanine obtained experimentally, ψ = −40 ± 30°, agreed reasonably well with the X-ray determined angle, ψ = −39°.     

Origin of the defect states at ZnS/Si interfaces

Electrical characterisation of silicon surfaces contaminated by a zinc-sulphide overlayer has been carried out by forming Schottky diodes on the silicon after the ZnS has been etched off. The techniques include current-voltage, capacitance-voltage, and deep-level transieni spectroscopy. The Schottky diodes show clear memory of the presence of the ZnS overlayer and the electrical characteristics are far from ideal. Five deep levels in the sub-surface region of the silicon are detected, corresponding to the Zn⁺, Zn⁺⁺, S^–, S^–– states and probably to a Zn–B complex (p-type). Diffusion of the zinc and sulphur into the silicon is therefore confirmed and this diffusion is thought to create a compensated layer at the interface. These impurity states control the electrical characteristics of the surface in these diodes.     

Hadron interactions in lattice QCD

Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract NN potentials, hyperon potentials and the meson–baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.     

Effective action for strongly correlated electron systems

The su(2|1) coherent-state path-integral representation of the partition function of the t-J model of strongly correlated electrons is derived at finite doping. The emergent effective action is compared to the one proposed earlier on phenomenological grounds by Shankar to describe holes in an antiferromagnet [R. Shankar, Nucl. Phys. B 330 (1990) 433]. The t-J model effective action is found to have an important “extra” factor with no analogue in Shankar?s action. It represents the local constraint of no double electron occupancy and reflects the rearrangement of the underlying phase-space manifold due to the presence of strong electron correlation. This important ingredient is shown to be essential to describe the physics of strongly correlated electron systems.     

An extended clique degree distribution and its heterogeneity in cooperation-competition networks

After Xiao et al. [W.-K. Xiao, J. Ren, F. Qi, Z.W. Song, M.X. Zhu, H.F. Yang, H.Y. Jin, B.-H. Wang, Tao Zhou, Empirical study on clique-degree distribution of networks, Phys. Rev. E 76 (2007) 037102], in this article we present an investigation on so-called k-cliques, which are defined as complete subgraphs of k (k>1) nodes, in the cooperation-competition networks described by bipartite graphs. In the networks, the nodes named actors are taking part in events, organizations or activities, named acts. We mainly examine a property of a k-clique called “k-clique act degree”, q, defined as the number of acts, in which the k-clique takes part. Our analytic treatment on a cooperation-competition network evolution model demonstrates that the distribution of k-clique act degrees obeys Mandelbrot distribution, P(q)∝(q+α)^−γ. To validate the analytical model, we have further studied 13 different empirical cooperation-competition networks with the clique numbers k=2 and k=3. Empirical investigation results show an agreement with the analytic derivations. We propose a new “heterogeneity index”, H, to describe the heterogeneous degree distributions of k-clique and heuristically derive the correlation between H and α and γ. We argue that the cliques, which take part in the largest number of acts, are the most important subgraphs, which can provide a new criterion to distinguish important cliques in the real world networks.     

Variability of scaling parameters in non-conservative systems: Geophysical aspect

Newly obtained data on the critical dynamics of the drifting/fracturing sea ice in the Arctic Ocean were analyzed and compared with published data on the dynamic processes in the Earth’s crust. Substantial similarities were found in the scaling behavior of both geophysical systems; the most important of them is the b-value space/time variability including a pre-failure drop of this parameter. The b-value pattern of the ensemble of drifting ice floes is an analogue of the b-value distribution over areas and depths in tectonic structures. A common feature of the pre-failure state in the cryosphere and in the Earth’s crust is the increased degree of the energy conservation that manifests itself both in the sea ice consolidation prior to basin-wide ice pack fragmentations, and in involving harder geological formations in the fracture process before earthquakes, respectively. From the viewpoint of the conservative SOC concept, this relation between the system’s conservativity and the occurrence of large-scale fracture events means that the expected scale level of failure is determined by the system’s closeness to “true” SOC behavior.     

Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within “small size” phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to t≈10⁶) by a q-Gaussian (1<q<3) distribution and tend to a Gaussian (q=1) for longer times, as the orbits eventually enter into “large size” chaotic domains. However, in agreement with other studies, we find in certain cases that the q-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called “crossover” function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these q-Gaussian distributions to identify two energy regimes of “weak chaos”—one where the system melts and one where it transforms from liquid to a gas state-by observing where the q-index of the distribution increases significantly above the q=1 value of strong chaos.     

Atomic structure of CaF2/MnF2-Si(1 1 1) superlattices from X-ray diffraction

X-ray reflectivity and non-specular crystal truncation rod scans have been used to determine the three-dimensional atomic structure of the buried CaF₂-Si(1 1 1) interface and ultrathin films of MnF₂ and CaF₂ within a superlattice. We show that ultrathin films of MnF₂, below a critical thickness of approximately four monolayers, are crystalline, pseudomorphic, and adopt the fluorite structure of CaF₂. High temperature deposition of the CaF₂ buffer layer produces a fully reacted, CaF₂-Si(1 1 1) type-B interface. The mature, “long” interface is shown to consist of a partially occupied layer of CaF bonded to the Si substrate, followed by a distorted CaF layer. Our atomistic, semi-kinematical scattering method extends the slab reflectivity method by providing in-plane structural information.     

Solving the Gross-Neveu model with relativistic many-body methods

The Gross-Neveu model provides a unique opportunity to apply relativistic many-body techniques (Dirac-Hartree approximation, RPA) in a context where all calculations can be done analytically and — in the largeN limit — yield the exact results. The physical fermion as well as multifermion (baryon) and fermion-antifermion (meson) bound states are discussed in this spirit, with special emphasis on the role of the Dirac sea.Supported by the Bundesministerium für Forschung und Technologie     

Nonlinear Bogolyubov-Valatin transformations: Two modes

Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary transformations, is isomorphic to SO(6;R)/Z₂. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington’s E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin- and single-spin- systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin- and single-spin- Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of and SO(6;R) matrices (of respective sizes 4×4 and 6×6) and their mutual relation.     

Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors

Muon spin relaxation (μSR) studies of the “1111” and “122” FeAs systems have detected static magnetism with variably sized ordered moments in their parent compounds. The phase diagrams of FeAs, CuO, organic BEDT, A₃C₆₀ and heavy-fermion systems indicate competition between static magnetism and superconductivity, associated with first-order phase transitions at quantum phase boundaries. In both FeAs and CuO systems, the superfluid density n_s/m^* at T→0 exhibits a nearly linear scaling with T_c. Analogous to the roton-minimum energy scaling with the lambda transition temperature in superfluid ⁴He, clear scaling with T_c was also found for the energy of the magnetic resonance mode in cuprates, (Ba,K)Fe₂As₂, CeCoIn₅ and CeCu₂Si₂, as well as the energy of the superconducting coherence peak observed by angle resolved photo emission (ARPES) in the cuprates near (π,0). Both the superfluid density and the energy of these pair-non-breaking soft-mode excitations determine the superconducting T_c via phase fluctuations of condensed bosons. Combining these observations and common dispersion relations of spin and charge collective excitations in the cuprates, we propose a resonant spin-charge motion/coupling, “traffic-light resonance,” expected when the charge energy scale ε_F becomes comparable to the spin fluctuation energy scale ?ω_SF~J, as the process which leads to pair formation in these correlated electron superconductors.     

The dynamics of metric-affine gravity

Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy theories to study the properties of metric-affine gravity.     

Stabilization of the pentagonal surface of the icosahedral AlPdMn quasicrystal by controlled Si absorption

The Debye-temperature of the pentagonal surface of the icosahedral AlPdMn quasicrystal (QC) is measured by means of low-energy electron diffraction after the absorption of different amounts of Si. We observe an increase of the surface Debye-temperature from 300±7 K for the freshly prepared surface to 330±7 K after the absorption of 60-Å Si. Because the quasicrystalline order persists at the surface in spite of the diffusion of Si into the substrate, we suggest that the diffusion is dominated by a vacancy-mediated process.     

Is BTZ a separate superselection sector of CTMG?

We exhibit exact solutions of (positive) matter coupled to original “wrong G-sign” cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate “superselection” sector, one that unlike in GR, is not reachable by physical sources.