Origin of the hub spectral dimension in scale-free networks

The return-to-origin probability and the first passage time distribution are essential quantities for understanding transport phenomena in diverse systems. The behaviors of these quantities typically depend on the spectral dimension $d_s$. However, it was recently revealed that in scale-free networks these quantities show a crossover between two power-law regimes characterized by $d_s$ and the so-called hub spectral dimension $d_s^{\textrm{(hub)}}$ due to the heterogeneity of connectivities of each node. To understand the origin of $d_s^{\textrm{(hub)}}$ from a theoretical perspective, we study a random walk problem on hierarchical scale-free networks by using the renormalization group (RG) approach. Under the RG transformation, not only the system size but also the degree of each node changes due to the scale-free nature of the degree distribution. We show that the anomalous behavior of random walks involving the hub spectral dimension $d_s^{\textrm{(hub)}}$ is induced by the conservation of the power-law degree distribution under the RG transformation.Comment: 10pages, 2figure

Synchronization transition of heterogeneously coupled oscillators on scale-free networks

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of \couplingcoeff k_i^{\eta-1}. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $\eta > \lambda-2$ ($\eta < \lambda-2$). We find eight different synchronization transition behaviors depending on the values of $\eta$ and $\lambda$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.Comment: 11 pages, 3 figures and two table

First passage time for random walks in heterogeneous networks

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.Comment: 5 pages, 3 figure

Study of component technologies for fuel cell on-site integrated energy system. Volume 2: Appendices

This data base catalogue was compiled in order to facilitate the analysis of various on site integrated energy system with fuel cell power plants. The catalogue is divided into two sections. The first characterizes individual components in terms of their performance profiles as a function of design parameters. The second characterizes total heating and cooling systems in terms of energy output as a function of input and control variables. The integrated fuel cell systems diagrams and the computer analysis of systems are included as well as the cash flows series for baseline systems

Study of component technologies for fuel cell on-site integrated energy systems

Heating, ventilation and air conditioning equipment are integrated with three types of fuel cells. System design and computer simulations are developed to utilize the thermal energy discharge of the fuel in the most cost effective manner. The fuel provides all of the electric needs and a loss of load probability analysis is used to ensure adequate power plant reliability. Equipment cost is estimated for each of the systems analyzed. A levelized annual cost reflecting owning and operating costs including the cost of money was used to select the most promising integrated system configurations. Cash flows are presented for the most promising 16 systems. Several systems for the 96 unit apartment complex (a retail store was also studied) were cost competitive with both gas and electric based conventional systems. Thermal storage is shown to be beneficial and the optimum absorption chiller sizing (waste heat recovery) in connection with electric chillers are developed. Battery storage was analyzed since the system is not electric grid connected. Advanced absorption chillers were analyzed as well. Recommendations covering financing, technical development, and policy issues are given to accelerate the commercialization of the fuel cell for on-site power generation in buildings