Optimal paths in disordered complex networks

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2相似文献   

Dynamical robustness of Lévy search strategies

We study the role of dynamical constraints in the general problem of finding the best statistical strategy for random searching when the targets can be detected only in the limited vicinity of the searcher. We find that the optimal search strategy depends strongly on the delay time tau during which a previously visited site becomes unavailable. We also find that the optimal search strategy is always described for large step lengths l by a power-law distribution P(l) approximately l(-mu), with 1相似文献   

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamic and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the local minima energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.     

Crackling sound generation during the formation of liquid bridges: A lattice gas model

Due to abnormal mechanical instabilities, liquid bridges may form in the small airways blocking airflow. Liquid bridge ruptures during inhalation are the major cause of the crackling adventitious lung sound, which can be heard using a simple stethoscope. Recently, Vyshedskiy and colleagues (2009) [1] described and characterized a crackle sound originated during expiration. However, the mechanism and origin of the expiratory crackle are still controversial. Thus, in this paper, we propose a mechanism for expiratory crackles. We hypothesize that the expiratory crackle sound is a result of the energy released in the form of acoustic waves during the formation of the liquid bridge. The magnitude of the energy released is proportional to the difference in free energy prior and after the bridge formation. We use a lattice gas model to describe the liquid bridge formation between two parallel planes. Specifically, we determine the surface free energy and the conditions of the liquid bridge formation between two parallel planes separated by a distance 2h$2h$ by a liquid droplet of volume Ω$\Omega$ and contact angle Θ$\Theta$, using both Monte Carlo simulation of a lattice gas model and variational calculus based on minimization of the surface area with the volume and the contact angle constrained. We numerically and analytically determine the phase diagram of the system as a function of the dimensionless parameter hΩ^−1/3$h{\Omega }^{-1/3}$ and Θ$\Theta$. We can distinguish two different phases: one droplet and one liquid bridge. We observe a hysteresis curve for the energy changes between these two states, and a finite size effect in the bridge formation. We compute the release of free energy during the formation of the liquid bridge and discuss the results in terms of system size. We also calculate the force exerted from liquid bridge on the planes by studying the dependence of the free energy on the separation between the planes 2h$2h$. The simulation results are in agreement with the analytical solution.     

Communication activity in social networks: growth and correlations

We investigate the timing of messages sent in two online communities with respect to growth fluctuations and long-term correlations. We find that the timing of sending and receiving messages comprises pronounced long-term persistence. Considering the activity of the community members as growing entities, i.e. the cumulative number of messages sent (or received) by the individuals, we identify non-trivial scaling in the growth fluctuations which we relate to the long-term correlations. We find a connection between the scaling exponents of the growth and the long-term correlations which is supported by numerical simulations based on peaks over threshold. In addition, we find that the activity on directed links between pairs of members exhibits long-term correlations, indicating that communication activity with the most liked partners may be responsible for the long-term persistence in the timing of messages. Finally, we show that the number of messages, M, and the number of communication partners, K, of the individual members are correlated following a power-law, K ~ M ^λ , with exponent λ ≈ 3 / 4.     

Investigation of the high-frequency field of a plane electromagnetic wave inside a dielectric sphere

The field of a plane electromagnetic wave near a dielectric sphere is investigated. Contour integrals are separated out from the exact solution which at high frequencies represent waves multiply reflected from the inner surface of the sphere. The high-frequency asymptotic representation of the wave field in a neighborhood of the initial point of the caustic of the reflected and refracted rays is expressed in terms of standard special functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 59–77, 1974.     

Asymptotic methods in problems of the propagation of sound in oceanic waveguides and their numerical realization

The paper contains a survey of a number of results on the topic indicated in the title.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 39–77, 1981.     

Non-resonant microwave absorption studies of superconducting MgB2 and MgB2 + MgO

Non-resonant microwave absorption (NRMA) studies of superconducting MgB₂ and a sample containing ∼10% by weight of MgO in MgB₂ are reported. The NRMA results indicate near absence of intergranular weak links in the pure MgB₂ sample. A linear temperature dependence of the lower critical field H _c1 is observed indicating a non-s wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d wave symmetry is also not observed. In the MgB₂ + MgO sample, much larger low field dependent absorption is observed indicating the presence of intergranular weak links. The hysteretic behavior of NRMA is compared and contrasted in the two samples. In the pure MgB₂ sample, a large hysteresis is observed between the forward and the reverse scans of the magnetic field indicating strong pinning of flux lines. This hysteresis saturates a few degrees below T _c while in the MgB₂ + MgO sample, a much slower increase of hysteresis with decreasing temperature is observed, a signature of weaker pinning.     

Relating airway diameter distributions to regular branching asymmetry in the lung

We study the distribution Pi(n)(D) of airway diameters D as a function of generation N in asymmetric airway trees of mammalian lungs. We find that the airway bifurcations are self-similar in four species studied. Specifically, the ratios of diameters of the major and minor daughters to their parent are constants independent of N until a cutoff diameter is reached. We derive closed form expressions for Pi(N)(D) and examine the flow resistance of the tree based on an asymmetric flow division model. Our findings suggest that the observed diameter heterogeneity is consistent with an underlying regular branching asymmetry.