Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.     

Incorporation of Effects of Diffusion into Advection-Mediated Dispersion in Porous Media

The distribution of solute arrival times, W(t;x), at position x in disordered porous media does not generally follow Gaussian statistics. A previous publication determined W(t;x) in the absence of diffusion from a synthesis of critical path, percolation scaling, and cluster statistics of percolation. In that publication, W(t;x) as obtained from theory, was compared with simulations in the particular case of advective solute transport through a two-dimensional model porous medium at the percolation threshold for various lengths x. The simulations also did not include the effects of diffusion. Our prediction was apparently verified. In the current work we present numerical results related to moments of W(x;t), the spatial solute distribution at arbitrary time, and extend the theory to consider effects of molecular diffusion in an asymptotic sense for large Peclet numbers, P_e. However, results for the scaling of the dispersion coefficient in the range 1<P_e<100 agree with those of other authors, while results for the dispersivity as a function of spatial scale also appear to explain experiment.     

Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (t_e). t_e is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is d_f=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of t_e transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension d_f=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.     

Effects of the rate of evaporation and film thickness on nonuniform drying of film-forming concentrated colloidal suspensions

In this paper, we report on nonuniform distribution of film-forming waterborne colloidal suspensions above the critical concentration _c of the colloidal glass transition during drying. We found that colloidal suspension films dry nonuniformly when the initial rate of evaporation E and/or the initial thickness l₀ are high. We found that a Peclet number Pe, defined as Pe = El₀/D, where D is the diffusion coefficient of the colloids in the diluted suspensions, does not predict uniformity of drying of the concentrated suspensions, contrary to the reported work on drying of diluted suspensions. Since the colloidal particles are crowded and their diffusive motion is restricted in concentrated suspensions, we assumed that above _c water is transported to the drying surface by hydrodynamic flow along the osmotic pressure gradient. The permeability of water through channels between deforming particles is estimated by adapting the theory of foam drainage. We defined a new Peclet number Pe by substituting the transport coefficient of flow (defined as the permeability divided by the viscosity, multiplied by the osmotic pressure gradient) for the diffusion coefficient. This extended Peclet number predicted the nonuniform drying with a criterion of Pe > 1. These results indicate that the mechanism of water transport to the drying surface in concentrated suspensions is water permeation by osmotic pressure, which is faster than mutual diffusion between water and particles --that has been observed in diluted suspensions and discussed by Routh and Russel. The theory fits well the experimental drying curves for various thicknesses and rates of evaporation. The particle distribution in the drying films is also estimated and it is indicated that the latex distribution is nonuniform when Pe > 1.     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Statics and dynamics of adhesion between two soap bubbles

An original set-up is used to study the adhesive properties of two hemispherical soap bubbles put into contact. The contact angle at the line connecting the three films is extracted by image analysis of the bubbles profiles. After the initial contact, the angle rapidly reaches a static value slightly larger than the standard 120^° angle expected from Plateau rule. This deviation is consistent with previous experimental and theoretical studies: it can be quantitatively predicted by taking into account the finite size of the Plateau border (the liquid volume trapped at the vertex) in the free energy minimization. The visco-elastic adhesion properties of the bubbles are further explored by measuring the deviation Δθ_d(t) of the contact angle from the static value as the distance between the two bubbles supports is sinusoidally modulated. It is found to linearly increase with Δr _c/r _c , where r_c is the radius of the central film and Δr _c the amplitude of modulation of this length induced by the displacement of the supports. The in-phase and out-of-phase components of Δθ_d(t) with the imposed modulation frequency are systematically probed, which reveals a transition from a viscous to an elastic response of the system with a crossover pulsation of the order 1rad · s^-1. Independent interfacial rheological measurements, obtained from an oscillating bubble experiment, allow us to develop a model of dynamic adhesion which is confronted to our experimental results. The relevance of such adhesive dynamic properties to the rheology of foams is briefly discussed using a perturbative approach to the Princen 2D model of foams.     

Numerical study of local and global persistence in directed percolation

The local persistence probability P _l (t) that a site never becomes active up to time t, and the global persistence probability P _g (t) that the deviation of the global density from its mean value does not change its sign up to time t are studied in a (1+1)-dimensional directed percolation process by Monte-Carlo simulations. At criticality, starting from random initial conditions, P _l (t) decays algebraically with the exponent . The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting is an universal exponent. The global persistence exponent is found to be equal or larger than . This contrasts with previously known cases where . It is shown that in the special case of directed-bond percolation, P _l (t) can be related to a certain return probability of a directed percolation process with an active source (wet wall). Received: 15 December 1997 / Revised: 6 April 1998 / Accepted: 29 May 1998     

Scalar Statistics along Inertial Particle Trajectory in Isotropic Turbulence

The statistics of a passive scalar along inertial particle trajectory in homogeneous isotropic turbulence with a mean scalar gradient is investigated by using direct numerical simulation. We are interested in the influence of particle inertia on such statistics, which is crucial for further understanding and development of models in non-isothermal gas-particle flows. The results show that the scalar variance along particle trajectory decreases with the increasing particle inertia firstly; when the particle＇s Stokes number St is less than 1.0, it reaches the minimal value when St is around 1.0, then it increases if St increases further. However, the scalar dissipation rate along the particle trajectory shows completely contrasting behavior in comparison with the scalar variance. The mechanical-to-thermal time scale ratios averaged along particle, （r）p, are approximately two times smaller than that computed in the Eulerian frame r, and stay at nearly 1.77 with a weak dependence on particle inertia. In addition, the correlations between scalar dissipation and flow structure characteristics along particle trajectories, such as strain and vorticity, are also computed, and they reach their maximum and minimum, 0.31 and 0.25, respectively, when St is around 1.0.     

Mean-Field Behavior for the Survival Probability and the Percolation Point-to-Surface Connectivity

We consider the critical survival probability (up to timet) for oriented percolation and the contact process, and the point-to-surface (of the ball of radiust) connectivity for critical percolation. Let θ_t denote both quantities. We prove in a unified fashion that, if θ_t exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then θ_t=t^-1 for the time-oriented models with d > 4 and θ_t=t^-2 for percolation with d > 7.     

Characterization of an ethylene free jet

The rotational population distribution in a free molecular jet of ethylene, C₂H₄, is found to be thermal over a range of distances below the nozzle (z/d=0.5–13.2, nozzle diameter d=0.50 mm). Results for on-axis rotational temperature, number density and flow velocity are presented. The average number of gas-kinetic collisions experienced by any molecule in travelling some distance along the jet axis is calculated.     

Study of random sequential adsorption by means of the gradient method

By using the gradient method (GM) we study random sequential adsorption (RSA) processes in two dimensions under a gradient constraint that is imposed on the adsorption probability along one axis of the sample. The GM has previously been applied successfully to absorbing phase transitions (both first and second order), and also to the percolation transition. Now, we show that by using the GM the two transitions involved in RSA processes, namely percolation and jamming, can be studied simultaneously by means of the same set of simulations and by using the same theoretical background. For this purpose we theoretically derive the relevant scaling relationships for the RSA of monomers and we tested our analytical results by means of numerical simulations performed upon RSA of both monomers and dimers. We also show that two differently defined interfaces, which run in the direction perpendicular to the axis where the adsorption probability gradient is applied and separate the high-density (large-adsorption probability) and the low-density (low-adsorption probability) regimes, capture the main features of the jamming and percolation transitions, respectively. According to the GM, the scaling behaviour of those interfaces is governed by the roughness exponent α = 1/(1 + ν), where ν is the suitable correlation length exponent. Besides, we present and discuss in a brief overview some achievements of the GM as applied to different physical situations, including a comparison of the critical exponents determined in the present paper with those already published in the literature.     

Detailed study of the effect of a short prepulse on soft X-ray spectra generated by a high-intensity KrF* laser pulse

The effect of a short prepulse (0.5 ps) on soft X-ray spectra from a plasma generated by a high intensity KrF* laser pulse (main pulse: 0.5 ps, intensity I _main=5.3×10¹⁵ W/cm²) on flat targets of Al and Cu has been studied in detail. The spectra have been measured as a function of the pulse separation t between the two pulses and the prepulse intensity I _pre. It was found that both the overall emission and the line emission increased with t (at constant I _pre) and with I _pre (at constant t). In particular, lines in the shorter wavelength region had higher intensity. The influence of the prepulse on the line emission of specific transitions in the Al spectra was investigated systematicly. An explanation for the observed effects is given.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

Longitudinal dispersion of solutes in porous media solely by advection

The purpose of this work is to predict the transport of non-sorbing solutes through water flow in the subsurface. We derive what we consider to be the first reliable calculations of the entire distribution of arrival times, W(t), for non-sorbing solutes in advective flow in strongly disordered porous media. Solutes treated can be contaminant plumes from any source or radioactive tracers, both experimentally and naturally generated. Our approach is microscopic and based on effects of disorder. It generates longitudinal dispersion (in the direction of flow) in the absence of diffusion. Effects on dispersion from a single capillary tube velocity distribution, known to produce long-tailed arrival time distributions, are also neglected. On the other hand, our calculations are based on effects generated from real porous media, such as wide pore-size distributions and complex connectivity. In particular, the calculation of the distribution of arrival times is based on a distribution of conserved fluxes and the known tortuosity of the associated geometrical paths. The results are found to be predictive when compared with simulations of two-dimensional flow on percolation structures, and appear to have relevance for experiments as well.     

Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media

A model based on invasion percolation was used to simulate the migration on a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form N_s(g)s^-2ƒ(s|g|^-z where z=1+(D−1)ν(ν+1). Here D is the fractal dimensionality of invasion percolation, with trapping, and ν is the ordinary percolation correlation length exponent.     

Anderson transition in 1D systems with spatial disorder

A simple Kronig-Penney model for 1D mesoscopic systems with δ peak potentials is used to study numerically the influence of spatial disorder on conductance fluctuations and distribution at different regimes. The Lévy laws are used to investigate the statistical properties of the eigenstates. It is found that an Anderson transition occurs even in 1D meaning that the disorder can also provide constructive quantum interferences. The critical disorder W_c for this transition is estimated. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results relative to conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models. At this transition, the conductance probability distribution has a system size independent shape with large fluctuations in good agreement with previous works.     

Die Übergangstemperatur verschiedener Supraleiter zweiter Art unter hydrostatischem Druck

An apparatus for production of hydrostatic pressure is described using a mixture of n-pentane and iso-pentane, which transmits pressure uniformly still at low temperatures. The superconductive transitions of the A 15(β- W type)-compounds Nb₃Sn, Nb₃Al, V₃Si and the B 1(NaCl type)-compound NbN have been measured under pressure up to 18 · 10³ kp/cm². The transition temperatures of the compounds V₃Si and NbN are increasing with pressure. Further measurements have been done on some selected ternary compounds, e.g. Nb₃(Al_1?x Ge _x ), to prove some predictions for the effect of pressure on superconductive transition.     

The strange man in random networks of automata

We have performed computer simulations of Kauffman’s automata on several graphs, such as the regular square lattice and invasion percolation clusters, in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent) and propagation speeds of the damage when one adds a damaging agent, nicknamed “strange man”. Despite the increase in the damaging efficiency, we have not observed any appreciable change of the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added, in comparison to when small initial damages are inserted in the system. Particularly, we have checked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution on the square lattice and to the degree of saturation on invasion percolation clusters.     

Pressure dependence study on the electron-phonon coupling of thulium hexachloroelpasolite

Raman spectra of Cs₂NaTmCl₆ have been recorded using a diamond anvil cell at ambient temperature. The vibrational energy of each of the Raman-active TmCl₆⁻³ moiety modes increases linearly with pressure. The integrated band areas of the ν₁(a_1g) and ν₂(e_g) modes are independent of applied pressure. However, the band area of the ν₅(t_2g) mode shows an anomalous behaviour, which has been qualitatively interpreted as due to electron-phonon coupling of the aΓ₅ electronic state with the Γ₁+ν₅(t_2g) vibronic state. This interaction between the coupled states is strongest between ca. 10 and 13 GPa at ambient temperature. The results serve to emphasize the specificity of the occurrence of strong electron-phonon coupling for particular transitions of a given rare earth ion.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in