Biomedical subjects

M N Popescu

Publications and source records attributed to M N Popescu.

8 recordsLinked to original sources

PubMed2004

Exactly solvable model of monomer-monomer reactions on a two-dimensional random catalytic substrate.

We study the equilibrium properties of a monomer-monomer A+B--> reaction on a two-dimensional substrate containing randomly placed catalytic bonds. Interacting A and B species undergo continuous exchanges with particle reservoirs and react as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For annealed disorder in the placement of catalytic bonds the model is mapped onto a general spin S=1 model and solved exactly for the pressure in a particular case. At equal activities of the two species a second order phase transition is revealed.

Carbon Monoxide↗

PubMed2004

Anisotropic diffusion-limited aggregation.

Using stochastic conformal mappings, we study the effects of anisotropic perturbations on diffusion-limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant measure on a unit circle. Here we map m preferred directions for growth to a distribution on the unit circle, which is a periodic function with m peaks in [-pi,pi) such that the angular width sigma of the peak defines the "strength" of anisotropy kappa= sigma(-1) along any of the m chosen directions. The two parameters (m,kappa) map out a parameter space of perturbations that allows a continuous transition from DLA (for small enough kappa ) to m needlelike fingers as kappa--> infinity. We show that at fixed m the effective fractal dimension of the clusters D(m,kappa) obtained from mass-radius scaling decreases with increasing kappa from D(DLA) approximately 1.71 to a value bounded from below by D(min) = 3 / 2. Scaling arguments suggest a specific form for the dependence of the fractal dimension D(m,kappa) on kappa for large kappa which compares favorably with numerical results.

Journal Article↗

PubMed2004

Model for spreading of liquid monolayers.

Manipulating fluids at the nanoscale within networks of channels or chemical lanes is a crucial challenge in developing small scale devices to be used in microreactors or chemical sensors. In this context, ultrathin (i.e., monolayer) films, experimentally observed in spreading of nanodroplets or upon extraction from reservoirs in capillary rise geometries, represent an extreme limit which is of physical and technological relevance since the dynamics is governed solely by capillary forces. In this work we use kinetic Monte Carlo (KMC) simulations to analyze in detail a simple, but realistic model proposed by Phys. Rev. Lett. 76, 86 (1996)]] for the two-dimensional spreading on homogeneous substrates of a fluid monolayer which is extracted from a reservoir. Our simulations confirm the previously predicted time dependence of the spreading, X ( t--> infinity ) =A square root of t, with X (t) as the average position of the advancing edge at time t, and they reveal a nontrivial dependence of the prefactor A on the strength U0 of interparticle attraction and on the fluid density C0 at the reservoir as well as an U0 -dependent spatial structure of the density profile of the monolayer. The asymptotic density profile at long time and large spatial scale is carefully analyzed within the continuum limit. We show that including the effect of correlations in an effective manner into the standard mean-field description leads to predictions both for the value of the threshold interaction above which phase segregation occurs and for the density profiles in excellent agreement with KMC simulation results.

Computer Simulation↗

PubMed2004

Diffusion-limited aggregation with power-law pinning.

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth R(-gamma)(N) (where R(N) is the radius of the N-particle cluster). For gamma>1 the growth pattern is in the same universality class as diffusion limited aggregation (DLA), while for gamma<1 the resulting patterns have a lower fractal dimension D(gamma) than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at gamma=1/2, significantly smaller than might be expected from the lower bound alpha(min) approximately 0.67 of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for D(gamma) both close to the breakdown of DLA universality class, i.e., gamma less, similar 1, and close to the pinning transition, i.e., gamma greater, similar 1/2.

Journal Article↗

PubMed2003

Equilibrium properties of a monomer-monomer catalytic reaction on a one-dimensional chain.

We study the equilibrium properties of a lattice-gas model of an A+B-->0 catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species A and B are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed A and B particles appear at neighboring lattice sites, they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as a function of the chemical potentials of the two species.

Journal Article↗

PubMed2002

Conformal map modeling of the pinning transition in Laplacian growth.

In Laplacian growth processes pinning may be expected due to a nonlinear response of a material during dielectric breakdown, or due to stick-slip boundary conditions in two-fluid flow in a porous medium, while thermal noise will lead to depinning. Using a method recently proposed by Hastings and Levitov, the size R(max) approximately E(-alpha)(c) of the pinned pattern is shown to scale with the critical field E(c) (electric field for dielectric breakdown, pressure gradient for fluid flow). These pinned patterns have a lower effective fractal dimension d(f) than diffusion-limited aggregation due to the enhancement of growth at the hot tips of the developing pattern. At finite temperature, thermal noise leads to depinning and growth of patterns with a shape and dimensionality dependent on both E(c) and the thermal noise. Using multifractal analysis, scaling expressions are established for this dependency.

Journal Article↗

PubMed2001

Rate-equation approach to island capture zones and size distributions in epitaxial growth.

Understanding and predicting the effects of correlations between island size and the rate of monomer capture has been shown to be the central problem in predicting the island-size distribution in submonolayer growth. Here we summarize a method which involves a self-consistent coupling of evolution equations for the capture-zone distributions with rate equations for the island-size distribution. The method has been successfully applied to irreversible submonolayer growth in both one and two dimensions to predict the size-dependent capture numbers and island-size distributions.

Journal Article↗

PubMed2000

Disorder induced diffusive transport in ratchets.

The effects of quenched disorder on the overdamped motion of a driven particle on a periodic, asymmetric potential are studied. While for the unperturbed potential the transport is due to a regular drift, the quenched disorder induces a significant additional chaotic "diffusive" motion. Possible applications to experiments in nanoscale surfaces and particle separation are discussed.

Diffusion↗