Integrating fluctuations into distribution of resources in transportation networks

We propose a resource distribution strategy to reduce the average travel time in a transportation network under a given generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra resources. The strategy distributes the essential resources by the average loads on the vertices and integrates the fluctuations of the instantaneous loads into the distribution of the extra resources. The fluctuations are calculated with the assumption of unlimited resources, where the calculation is incorporated into the calculation of the average loads without adding to the time complexity. Simulation results show that in scale-free networks, the fluctuation-integrated strategy provides shorter average travel time than a previous distribution strategy while keeping similar robustness; the benefit of our strategy is especially noticeable when the extra resources are scarce.     

Tracer diffusion in lattice gases

It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.     

Tracer diffusion in glassforming liquids

In the last decades, a wide collection of experimental evidence has been found in the study of supercooled glassformers on the existence of a crossover between two dynamical regimes at a temperature T_c. We discuss the validity of the Vogel-Fulcher-Tammann in both regions. The breakdown of the Stokes-Einstein relation below T_c is presented, indicating that the diffusion coefficient of a tracer becomes decoupled from the viscosity through an exponent ξ, and the diffusion process is intensified. We verify that a temperature shift on the diffusion coefficient introduces the same effect as the Stokes-Einstein breakdown equation. We present the dependence of this exponent on the ratio between the radii of the tracer and the host liquid molecule.     

Tracer diffusion in the presence of segregating obstacles

Tracer diffusion in an alloy in which the trajectories of one of the species is biased is examined as a model of mass transport with attendant segregation to extended defects (e.g., dynamic strain ageing, grain-boundary segregation). More specifically, we employ Monte Carlo simulation to describe the nonequilibrium diffusive behavior of the components of a two-dimensional lattice gas comprising A and B atoms wherein one of the species (B) interacts with randomly distributed line defects to create equilibrium atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of B-atom mobility and defect interaction strength on the transport behavior of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion.     

A simple model for the pore size distribution in random fibre networks

A heuristic approach based upon excluded volume arguments is developed for modelling the distribution of pore sizes in isotropic networks of randomly distributed cylindrical fibres. Our formalism accounts for the finite hard core diameters of the fibres, and leads to compact, analytically tractable expressions that span the complete range of volume fractions. Results are presented for the mean and mean-squared pore radii as functions of the fibre volume fraction, and for the partition coefficient of a spherical tracer particle into such a network under conditions such that steric effects are dominant.     

Tracer diffusion in a dislocated lamellar system

Many lamellar systems exhibit strongly anisotropic diffusion. When the diffusion across the lamellae is slow, an alternative mechanism for transverse transport becomes important. A tracer particle can propagate across the lamellae by encircling a screw dislocation. We calculate the statistical properties of this mode of transverse transport. When either positive or negative dislocations are in excess, transport across the lamellae is ballistic. When the average dislocation charge is zero, the mean square of the normal displacement grows like TlogT for large times. To obtain this result, the trajectory of the tracer must be smoothed over distances of order of the dislocation core size.     

Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion

We present, to the best of our knowledge, the first experimental demonstration by direct detection of the Bose-Einstein photon-number distribution of highly spatially multi-mode but temporally single mode spontaneous parametric down-conversion.Received: 20 November 2003, Published online: 6 January 2004PACS: 42.50.-p Quantum optics - 42.50.Ar Photon statistics and coherence theory - 42.65.-k Nonlinear optics - 42.65.Lm Parametric down conversion and production of entangled photons     

A theoretical validation of the B-matrix spatial distribution approach to diffusion tensor imaging

The recently presented B-matrix Spatial Distribution (BSD) approach is a calibration technique which derives the actual distribution of the B-matrix in space. It is claimed that taking into account the spatial variability of the B-matrix improves the accuracy of diffusion tensor imaging (DTI). The purpose of this study is to verify this approach theoretically through computer simulations.Assuming three different spatial distributions of the B-matrix, diffusion weighted signals were calculated for the six orientations of a model anisotropic phantom. Subsequently two variants of the BSD calibration were performed for each of the three cases; one with the assumption of high uniformity of the model phantom (uBSD-DTI) and the other taking into account imperfections in phantom structure (BSD-DTI). Several cases of varying degrees of phantom uniformity were analyzed and the distributions of the B-matrix obtained were used for the calculation of the diffusion tensor of a model isotropic phantom. The results were compared with standard diffusion tensor calculation.The simulations confirmed the improvement of accuracy in the determination of the diffusion tensor after the calibration. BSD-DTI improves accuracy independent of both the degree of uniformity of the phantom and the inhomogeneity of the B-matrix. In cases of a relatively good uniformity of the phantom and minor distortions in the spatial distribution of the B-matrix, the uBSD-DTI approach is sufficient.     

Tracer diffusion of dimers on correlated heterogeneous surfaces

The diffusion of a single dimer adsorbed on highly correlated heterogeneous substrates is studied through Monte Carlo simulations. The topography has been characterized by patches of weak and strong adsorbing sites, arranged in a chessboard-like ordered structure. The time behavior of the mean-square displacement of the dimer is analyzed for different temperatures and patch size. Based on this analysis, a possible method for the characterization of the correlated heterogeneous topography from dimer diffusion measurements is discussed.     

The impact of connection density on scale-free distribution in random networks

Preferential attachment is considered as a fundamental mechanism that contributes to the scale-free characteristics of random networks, which include growth and non-growth networks. There exist some situations of non-growth random networks, particularly for very sparse or dense networks, where preferential attachments cannot consequentially result in true scale-free features, but only in scale-free-like appearances. This phenomenon implies that, a close relationship exists between the connection density p$p$ and the scaling. In this study, we propose a self-organized model with constant network size to study the phenomenon. We show analytically and numerically that there exists a certain critical point _pc$p_c$. Only when p=_pc$p=p_c$, the random network evolves into steady scale-free state. Otherwise, the network exhibits a steady scale-free-like state. The closer the p$p$ approximates _pc$p_c$, the closer the scale-free-like distribution approximates the true scale-free distribution. Our results show that, in random network lack of growth, a preferential scheme does not necessarily lead to a scale-free state, and a formation of scale-free is a consequence of two mechanisms: (i) a preferential scheme and (ii) appropriate connection density.     

Analysis of the impact degree distribution in metabolic networks using branching process approximation

Theoretical frameworks to estimate the tolerance of metabolic networks to various failures are important to evaluate the robustness of biological complex systems in systems biology. In this paper, we focus on a measure for robustness in metabolic networks, namely, the impact degree, and propose an approximation method to predict the probability distribution of impact degrees from metabolic network structures using the theory of branching process. We demonstrate the relevance of this method by testing it on real-world metabolic networks. Although the approximation method possesses a few limitations, it may be a powerful tool for evaluating metabolic robustness.     

Tracer diffusion in nanofluids measured by fluorescence correlation spectroscopy

Nanofluids exhibit some intriguing thermal properties, and have great potential to increase efficiency in various heat technological applications in micro- and nano-technology. Recent studies on mass transport in nanofluids yielded some interesting but controversial results. In this communication, we report the tracer diffusion of fluorescent dye in different nanofluids. Measurements were performed using fluorescence correlation spectroscopy (FCS). Nanoparticle concentration in the nanofluid varied up to 1.7 vol%, and the diffusion coefficient of fluorescent dye was measured. Our results showed no significant changes in diffusion of dyes in the concentration range used, and the results indicate that more research is needed to completely understand the diffusion in nanofluids. This communication brings upon the powerful FCS technique for the first time to study the dynamics of nanofluids.     

Tracer dispersion in a percolation network with spatial correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolationlike porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We find that the resulting statistical properties of the tracer show a transition from a subdiffusion regime at low Peclet number to an enhanced diffusion regime at high Peclet number.     

The spatial fluctuations of the magnetization in amorphous ferromagnets

The spatial variation of the magnetization of amorphous ferromagnets containing transition metal and metalloid atoms is shown to depend explicitly on that of the alloy concentration and of the nearest neighbour distance. This variation will thus be in general on an atomic scale for these materials.     

The future is noisy: the role of spatial fluctuations in genetic switching

A genetic switch may be realized by a certain operator sector on the DNA strand from which either genetic code, to the left or to the right of this operator sector, can be transcribed and the corresponding information processed. This switch is controlled by messenger molecules, i.e., they determine to which side the switch is flipped. Recently, it has been realized that noise plays an elementary role in genetic switching, and the effect of number fluctuations of the messenger molecules have been explored. Here we argue that the assumption of well stirredness taken in the previous models may not be sufficient to characterize the influence of noise: spatial fluctuations play a non-negligible part in cellular genetic switching processes.     

Measurement of polarization fluctuations in installed single-mode optical fibre cables

Measurements were made of the random polarization fluctuations of conventional single-mode fibres of five optical fibre cables installed in the city of Berlin (West). The measurements were performed with the aid of a semiconductor laser, the frequency (f) of which was 227.3 THz (wavelength 1320 nm). Such preliminary studies are very important for optically coherent transmission over cables not maintaining the polarizations. The signal intensity fluctuations as the fibre output can be represented both as a function of time and by the related spectral power density.     

Transitions in spatial networks

Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the Erdös–Rényi graph, and spatial networks display a large variety of behaviors. We will discuss here some (mostly recent) results about topological transitions, ‘localization’ transitions seen in the shortest paths pattern, and also about the effect of congestion and fluctuations on the structure of optimal networks. The importance of spatial networks in real-world applications makes these transitions very relevant, and this review is meant as a step towards a deeper understanding of the effect of space on network structures.