Finding Scientific Gems with Google

We apply the Google PageRank algorithm to assess the relative importance of all publications in the Physical Review family of journals from 1893--2003. While the Google number and the number of citations for each publication are positively correlated, outliers from this linear relation identify some exceptional papers or "gems" that are universally familiar to physicists.Comment: 6 pages, 4 figures, 2 tables, 2-column revtex4 forma

Boundary-induced nonequilibrium phase transition into an absorbing state

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.Comment: 4 pages, 4 figures; minor change

Dissolution in a field

We study the dissolution of a solid by continuous injection of reactive ``acid'' particles at a single point, with the reactive particles undergoing biased diffusion in the dissolved region. When acid encounters the substrate material, both an acid particle and a unit of the material disappear. We find that the lengths of the dissolved cavity parallel and perpendicular to the bias grow as t^{2/(d+1)} and t^{1/(d+1)}, respectively, in d-dimensions, while the number of reactive particles within the cavity grows as t^{2/(d+1)}. We also obtain the exact density profile of the reactive particles and the relation between this profile and the motion of the dissolution boundary. The extension to variable acid strength is also discussed.Comment: 6 pages, 6 figures, 2-column format, for submission to PR

Survival Probability in a Random Velocity Field

The time dependence of the survival probability, S(t), is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field, v_x(y). For a semi-infinite system with unbounded y and x>0, and with particle absorption at x=0, a qualitative argument is presented which indicates that S(t)~t^{-1/4}. This prediction is supported by numerical simulations. A heuristic argument is also given which suggests that the longitudinal probability distribution of the surviving particles has the scaling form P(x,t)~ t^{-1}u^{1/3}g(u). Here the scaling variable u is proportional to x/t^{3/4}, so that the overall time dependence of P(x,t) is proportional to t^{-5/4}, and the scaling function g(u) has the limiting dependences g(u) approaching a constant as u--->0 and g(u)~exp(-u^{4/3}) as u--->infinity. This argument also suggests an effective continuum equation of motion for the infinite system which reproduces the correct asymptotic longitudinal probability distribution.Comment: 6 pages, RevTeX, 5 figures includes, to be submitted to Phys. Rev.

Effective target arrangement in a deterministic scale-free graph

We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s), to 1, for a single peripheral target.Comment: 8 pages, 5 figure

Analysis of patterns formed by two-component diffusion limited aggregation

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.Comment: Accepted for publication in Physical Review

Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions

The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean field limit, the densities of different velocity species decay in time with different power law rates for many initial conditions. For a one-dimensional symmetric system containing particles with velocity 0 and $\pm 1$, there is a particular initial state for which the concentrations of all three species as decay as $t^{-2/3}$. For the case of a fast ``impurity'' in a symmetric background of $+$ and $-$ particles, the impurity survival probability decays as $\exp(-{\rm const.}\times \ln^2t)$. In a symmetric 4-velocity system in which there are particles with velocities $\pm v_1$ and $\pm v_2$, there again is a special initial condition where the two species decay at the same rate, t^{-\a}, with \a\cong 0.72. Efficient algorithms are introduced to perform the large-scale simulations necessary to observe these unusual phenomena clearly.Comment: 18 text pages, macro file included, hardcopy of 9 figures available by email request to S

Persistence of Randomly Coupled Fluctuating Interfaces

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2, however, is coupled to h_1 via a quenched random velocity field. In the limit d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t_0\to \infty, the stochastic process h_2, at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H_2=1-\beta_1/2, where \beta_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be \theta_s^2=1-H_2=\beta_1/2. These analytical results are verified by numerical simulations.Comment: 15 pages, 3 .eps figures include

Transport on Directed Percolation Clusters

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page

Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?

We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions that all start at the same position L to the right of the lamb and a haven at x=0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, S_N(x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine S_N(x,L) analytically for the special cases of N=1 and N--->oo. For large but finite N, we determine the unusual asymptotic form whose leading behavior is S_N(z)\simN^{-z^2}, with z=x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10^{500}.Comment: 13 pages, 6 figures, IOP format; v2: small changes in response to referee and editor comment