Degree correlations in scale-free null models

We study the average nearest neighbor degree $a(k)$ of vertices with degree $k$. In many real-world networks with power-law degree distribution $a(k)$ falls off in $k$, a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that $a(k)$ indeed decays in $k$ in three simple random graph null models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph and the hyperbolic random graph. We consider the large-network limit when the number of nodes $n$ tends to infinity. We find for all three null models that $a(k)$ starts to decay beyond $n^{(\tau-2)/(\tau-1)}$ and then settles on a power law $a(k)\sim k^{\tau-3}$, with $\tau$ the degree exponent.Comment: 21 pages, 4 figure

Vacuum Rabi oscillation induced by virtual photons in the ultrastrong coupling regime

We present an interaction scheme that exhibits a dynamical consequence of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground state. Therefore the interaction scheme could serve as a probe of ground state structures in the ultrastrong coupling regime.Comment: 4 pages, 3 figure

Lean Limit Phenomena

The influence of stretch and preferential diffusion on premixed flame extinction and stability was investigated via two model flame configurations, namely the stagnation flame and the bunsen flame. Using a counterflow burner and a stagnation flow burner with a water-cooled wall, the effect of downstream heat loss on the extinction of a stretched premixed flame investigated for lean and rich propane/air and methane/air mixtures. It was demonstrated that extinction by stretch alone is possible only when the deficient reactant is the less mobile one. When it is the more mobile one, downstream heat loss or incomplete reaction is also needed to achieve extinction. The local extinction of bunsen flame tips and edges of hydrocarbon/air premixtures was investigated using a variety of burners. Results show that, while for both rich propane/air and butane/air mixtures tip opening occurs at a constant fuel equivalence ratio of 1.44 and is therefore independent of the intensity, uniformity, and configuration of the approach flow, for rich methane/air flames burning is intensified at the tip and therefore opening is not possible

Cubic order for spatial 't Hooft loop in hot QCD

Spatial 't Hooft loops of strength k measure the qualitative change in the behaviour of electric colour flux in confined and deconfined phase of SU(N) gauge theory. They show an area law in the deconfined phase, known analytically to two loop order with a ``k-scaling'' law k(N-k). In this paper we compute the O(g^3) correction to the tension. It is due to neutral gluon fields that get their mass through interaction with the wall. The simple k-scaling is lost in cubic order. The generic problem of non-convexity shows up in this order. The result for large N is explicitely given.Comment: 5 pages, appears in the proceedings of SEWM200

Power-law behavior and condensation phenomena in disordered urn models

We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point of the power-law behavior and randomness; it is clarified that quenched random parameters play an important role in generating power-law behavior. We evaluate the occupation probability $P(k)$ with which an urn has $k$ balls by using the concept of statistical physics of disordered systems. In the disordered urn model belonging to the Monkey class, we find that above critical density $\rho_\mathrm{c}$ for a given temperature, condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large $k$ regime. We also discuss an interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials.Comment: 16pages, 9figures, using iopart.cls, 2 new figures were adde