Flows on Graphs with Random Capacities

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.Comment: 8 pages, 6 figure

Magnetoresistance behavior of a ferromagnetic shape memory alloy: Ni_1.75Mn_1.25Ga

A negative-positive-negative switching behavior of magnetoresistance (MR) with temperature is observed in a ferromagnetic shape memory alloy Ni_1.75Mn_1.25Ga. In the austenitic phase between 300 and 120 K, MR is negative due to s-d scattering. Curiously, below 120K MR is positive, while at still lower temperatures in the martensitic phase, MR is negative again. The positive MR cannot be explained by Lorentz contribution and is related to a magnetic transition. Evidence for this is obtained from ab initio density functional theory, a decrease in magnetization and resistivity upturn at 120 K. Theory shows that a ferrimagnetic state with anti-ferromagnetic alignment between the local magnetic moments of the Mn atoms is the energetically favoured ground state. In the martensitic phase, there are two competing factors that govern the MR behavior: a dominant negative trend up to the saturation field due to the decrease of electron scattering at twin and domain boundaries; and a weaker positive trend due to the ferrimagnetic nature of the magnetic state. MR exhibits a hysteresis between heating and cooling that is related to the first order nature of the martensitic phase transition.Comment: 17 pages, 5 figures. Accepted in Phys. Rev.

Developing natural resource models using the object modeling system: feasibility and challenges

International audienceCurrent challenges in natural resource management have created demand for integrated, flexible, and easily parameterized hydrologic models. Most of these monolithic models are not modular, thus modifications (e.g., changes in process representation) require considerable time, effort, and expense. In this paper, the feasibility and challenges of using the Object Modeling System (OMS) for natural resource model development will be explored. The OMS is a Java-based modeling framework that facilitates simulation model development, evaluation, and deployment. In general, the OMS consists of a library of science, control, and database modules and a means to assemble the selected modules into an application-specific modeling package. The framework is supported by data dictionary, data retrieval, GIS, graphical visualization, and statistical analysis utility modules. Specific features of the OMS that will be discussed include: 1) how to reduce duplication of effort in natural resource modeling; 2) how to make natural resource models easier to build, apply, and evaluate; 3) how to facilitate long-term maintainability of existing and new natural resource models; and 4) how to improve the quality of natural resource model code and ensure credibility of model implementations. Examples of integrating a simple water balance model and a large monolithic model into the OMS will be presented

Review of two-dimensional materials for photocatalytic water splitting from a theoretical perspective

Two-dimensional (2D) materials have shown extraordinary performances as photocatalysts compared to their bulk counterparts. Simulations have made a great contribution to the deep understanding and design of novel 2D photocatalysts. Ab initio simulations based on density functional theory (DFT) not only show efficiency and reliability in new structure searching, but also can provide a reliable, efficient, and economic way for screening the photocatalytic property space. In this review, we summarize the recent developments in the field of water splitting using 2D materials from a theoretical perspective. We address that DFT-based simulations can fast screen the potential spaces of photocatalytic properties with the accuracy comparable to experiments, by investigating the effects of various physical/chemical perturbations. This, at last, will lead to the enhanced photocatalytic activities of 2D materials, and promote the development of photocatalysis

Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network

We study complex networks with weights, $w_{ij}$, associated with each link connecting node $i$ and $j$. The weights are chosen to be correlated with the network topology in the form found in two real world examples, (a) the world-wide airport network, and (b) the {\it E. Coli} metabolic network. Here $w_{ij} \sim x_{ij} (k_i k_j)^\alpha$, where $k_i$ and $k_j$ are the degrees of nodes $i$ and $j$, $x_{ij}$ is a random number and $\alpha$ represents the strength of the correlations. The case $\alpha > 0$ represents correlation between weights and degree, while $\alpha < 0$ represents anti-correlation and the case $\alpha = 0$ reduces to the case of no correlations. We study the scaling of the lengths of the optimal paths, $\ell_{\rm opt}$, with the system size $N$ in strong disorder for scale-free networks for different $\alpha$. We calculate the robustness of correlated scale-free networks with different $\alpha$, and find the networks with $\alpha < 0$ to be the most robust networks when compared to the other values of $\alpha$. We propose an analytical method to study percolation phenomena on networks with this kind of correlation. We compare our simulation results with the real world-wide airport network, and we find good agreement

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control

Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria which are often socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members. Here we assess this price of anarchy by analyzing the travel times in road networks of several major cities. Our simulation shows that uncoordinated drivers possibly waste a considerable amount of their travel time. Counterintuitively,simply blocking certain streets can partially improve the traffic conditions. We analyze various complex networks and discuss the possibility of similar paradoxes in physics.Comment: major revisions with multicommodity; Phys. Rev. Lett., accepte

Maximum flow and topological structure of complex networks

The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$ and $t$. The average of $q$ over all node pairs with smaller degree $k_{\rm min}$ is $_{k_{\rm min}} \simeq c k_{\rm min}$ for large $k_{\rm min}$ with $c$ a constant implying that the statistics of $q$ is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and $q$ can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient $c$. The applicability of our results to real world networks is tested for the Internet at the autonomous system level.Comment: 7 pages, 4 figure