
Nonlinear Physics and Far from Equilibrium Systems






Papers Laureano
RamírezPiscina
1 L. RamirezPiscina and J.M. Sancho.
Higher order colored noise effects in multivariable systems.
Physical Review A 37, 44694473 (1988).
Abstract: We extend the partial resummation technique of FokkerPlanck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higherorder terms which are left out in that technique. On the contrary, the systematic τexpansion approach can explain the analog results.
2 F.J. de la Rubia, E. PeacockLopez, G.P. Tsironis, K. Lindenberg, L. RamirezPiscina and J.M. Sancho.
Escape over a potential barrier driven by colored noise: Large but finite correlation time
Physical Review A 38, R3827R3829 (1988).
Abstract: The recent theory of Tsironis and Grigolini for the mean firstpassage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times.
3 L. RamirezPiscina, J.M. Sancho, F.J. de la Rubia, K. Lindenberg and G.P. Tsironis.
FirstPassage time in a bistable potential with colored noise
Physical Review A 40, 21202127 (1989).
Abstract: A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean firstpassage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.
4 K. Lindenberg, L. RamirezPiscina, J.M. Sancho and F.J. de la Rubia
Insight toward the FirstPassage Time in a bistable potential with highly colored noise
Physical Review A 40, R4157R4160 (1989).
Abstract: The exponential coefficient in the firstpassagetime problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of τV0/D up to ∼20, where V0 is the barrier height, τ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all largeτ theories is achieved for even larger values of τV0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.
5 F. Sagues, L. RamirezPiscina and J.M. Sancho.
Stochastic dynamics of the chloriteiodide reaction
Journal of Chemical Physics 92, 47864792 (1990).
Abstract: A recently proposed theoretical framework appropriate to the study of the stochastic behavior of several chemical systems is used to analyze the irreproducibility of the observed reaction times in the chlorite–iodide clock reaction. Noise terms are incorporated through the kinetic constants and their intensity is further correlated with the inverse of the stirring rate. Analytical and simulation results are obtained for the first moments of the reaction time distribution. These results are compared with recent experimental data obtained by Nagypál and Epstein.
6 C.S. Yokoi, A. HernandezMachado and L. RamirezPiscina.
Some exact results for the lattice covering time problem
Physics Letters A 145, 8286 (1990).
Abstract: The lattice covering time of a random walk in finite lattices has recently been defined as the mean time taken by the lattice walker to visit all the sites of the lattice. We solve the lattice covering time problem exactly in one dimension both for reflecting and periodic boundary conditions.
7 L. RamirezPiscina, J.M. Sancho, K. Lindenberg and F.J. de la Rubia
Escape over a potential barrier driven by colored noise
in Noise in Physical Systems, pags 639643
Ed. A. Ambrozy. Akademiai Kiado, Budapest (1990).
8 F. Sagues, L. RamirezPiscina and J.M. Sancho.
Macroscopic stochasticity in the chloriteiodide reaction
Reaction Kinetics and Catalysis Letters 42, 427433 (1990).
9 L. RamirezPiscina and J.M. Sancho.
First Passage Times for a marginal state driven by colored noise
Physical Review A 43, 663668 (1991).
Abstract: The dynamical process through a marginal state (saddle point) driven by colored noise is studied. For small correlation time of the noise, the mean firstpassage time and its variance are calculated using standard methods. When the correlation time of the noise is finite or large, an alternative approach, based on simple physical arguments, is proposed. It will allow us to study also the passage times of an unstable state. The theoretical predictions are tested satisfactorily by the use of computer simulations.
10 J. GarciaOjalvo, J.M. Sancho and L. RamirezPiscina.
A nonequilibrium phase transition with colored noise
Physics Letters A 168, 3539 (1992).
Abstract: A Langevin equation for the Φ4 scalar continuum field model is studied. Fluctuations are modeled by a Gaussian additive noise, white in space and colored in time. A computer simulation evidences the presence of a nonequilibrium phase transition when the correlation time of the noise is used as control parameter.
11 J. GarciaOjalvo, J.M. Sancho and L. RamirezPiscina.
Generation of spatiotemporal colored noise
Physical Review A 46, 46704675 (1992).
Abstract: We develop an algorithm to simulate a Gaussian stochastic process that is nonδcorrelated in both space and time coordinates. The colored noise obeys a linear reactiondiffusion Langevin equation with Gaussian white noise. This equation is exactly simulated in a discrete Fourier space.
12 A. Careta, F. Sagues, L. RamirezPiscina and J.M. Sancho.
Effective diffusion in a stochastic velocity field
Journal of Statistical Physics 71, 235242 (1993).
Abstract: Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative spacetime correlated noise.
13 L. RamirezPiscina, A. HernandezMachado and J.M. Sancho.
Fluctuations in domain growth: GinzburgLandau equations with multiplicative noise
Physical Review B 48, 119124 (1993)
Abstract: GinzburgLandau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarsegrained methodology and expressions for the resulting concentrationdependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the CahnHilliard linearstability analysis. In particular, it introduces a delay in the domaingrowth dynamics.
14 L. RamirezPiscina, J.M. Sancho and A. HernandezMachado.
Numerical algorithm for GinzburgLandau equations with multiplicative noise: Application to domain growth
Physical Review B 48, 125131 (1993)
Abstract: We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.
15 J.M. Sancho, A. HernandezMachado, L. RamirezPiscina and A.M. Lacasta
Langevin equations with multiplicative noise: application to domain growth
Acta Physica Polonica B 24, 733750 (1993)
Abstract: Langevin Equations of GinzburgLandau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarsegrained methodology. The CahnHiliardCook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.
16 B. Caroli, C. Caroli and L. RamirezPiscina.
Initial front transients in directional solidification of thin samples of dilute alloys
Journal of Crystal Growth 132, 377388 (1993).
Abstract: We study the dynamics of recoil of a planar front in a directional solidification process, following a sudden jump from rest to a constant pulling velocity V. To this end, we solve numerically the full integral equation describing the front dynamics in the onesided model. We find, in particular, that the asymptotic (respectively initial) regimes, for which we derive analytical expressions for the front position, are restricted to such long (respectively short) times that they are in practice irrelevant for the analysis of experiments. We show that the results obtained from the heuristic approximation recently proposed by Warren and Langer are in remarkably good agreement with the exact ones in the regimes relevant to planar recoil experiments. Equally good agreement is found for the velocity threshold and the critical wavelength of the cellular instability after a large velocity jump, as calculated in the adiabatic approximation.
17 A. HernandezMachado, L. RamirezPiscina and J.M. Sancho.
Multiplicative noise in domain growth: stochastic GinzburgLandau equations
en Growth Patterns in Physical Sciences and Biology
Eds. E. Louis, L.M. Sander, P. Meakin and J.M. GarciaRuiz.
NATO ASI Series B 304, pp. 353361.
Plenum Press (1993).
18 J.L. Mozos, A.M. Lacasta, L.RamirezPiscina and A.HernandezMachado
Interfacial instability induced by external fluctuations
Phys Rev E 53, 14591464 (1996)
Abstract: The dynamics of an interface separating the two coexistent phases of a binary system in the presence of external fluctuations in temperature is studied. An interfacial instability is obtained for an interface that would be stable in the absence of fluctuations or in the presence of internal fluctuations. Analytical stability analysis and numerical simulations are in accordance with an explanation of these effects in terms of a quenchlike instability induced by fluctuations
19 J.Armero, A.Lacasta, L.RamirezPiscina, J.Casademunt, J.M. Sancho and F.Sagues
Pattern and velocity selection of fronts propagating in modulated media
Europhys Lett 33, 429434 (1996)
Abstract: We study the problem of pattern and velocity selection of morphologically stable twodimensional fronts propagating in a spatially modulated medium. The generic system is governed by a local equation and evolves towards a nontrivial steady state with a spatial structure which arises from nonlocal competition effects and does not necessarily mimic the local structure externally fixed by the modulation. The dynamical process leading to this steady state is studied both analytically and numerically.
20 J.Armero, J.M.Sancho, J.Casademunt, A.M.Lacasta, L.RamirezPiscina and F.Sagues
External fluctuations in front propagation
Phys Rev Lett 76, 30453048 (1996)
Abstract: We study the effects of external noise in a onedimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linearmarginalstability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.
21 T.T.Katona, T.Borzsonyi, Z.Varadi, J.Szabon, A. Buka, R.GonzalezCinca, L.RamirezPiscina, J.Casademunt, A.HernandezMachado
Pattern formation during mesophase growth in a homologous series
Phys Rev E 54, 15741583 (1996)
Abstract: Remarkable differences in the shape of the nematic–smecticB interface in a quasitwodimensional geometry have been experimentally observed in three liquid crystals of very similar molecular structure, i.e., neighboring members of a homologous series. In the thermal equilibrium of the two mesophases a faceted rectanglelike shape was observed with considerably different shape anisotropies for the three homologs. Various morphologies such as dendritic, dendriticlike, and faceted shapes of the rapidly growing smecticB germ were also observed for the three substances. Experimental results were compared with computer simulations based on the phase field model. The pattern forming behavior of a binary mixture of two homologs was also studied.
22 R.GonzalezCinca, L.RamirezPiscina, J.Casademunt, A.HernandezMachado, L.Kramer, T.T.Katona, T.Borzsonyi and A. Buka
PhaseField simulations and experiments of faceted growth in liquid crystals
Phys D 99, 359368 (1996)
Abstract: We present numerical simulations directed at the description of smecticB germs growing into the supercooled nematic phase for two different liquid crystalline substances. The simulations are done by means of a phasefield model appropriate to study strong anisotropy and also faceted interfaces. The most important ingredient is the angledependent surface energy, but kinetic effects are also relevant. The simulations reproduce qualitatively a rich variety of morphologies observed in the experiments for different value of undercooling, extending from the faceted equilibrium shape to fully developed dendrites.
23 J.Armero, A.Lacasta, L.RamirezPiscina, J.Casademunt, J.M. Sancho and F.Sagues
Front propagation in spatially modulated media
Phys Rev E 56, 54055412 (1997)
Abstract: A twodimensional reactiondiffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steadystate velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.
24 I.SendinaNadal, M.GomezGesteira, V.PerezMunuzuri, V.PerezVillar, J.Armero, L.RamirezPiscina, J.Casademunt, J.M. Sancho and F.Sagues
Wave competition in excitable modulated media
Phys Rev E 56, 62986301 (1997)
Abstract: The propagation of an initially planar front is studied within the framework of the photosensitive BelousovZhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steadystate velocity are experimentally validated.
25 A.M. Lacasta, L.RamirezPiscina, J.Casademunt, A.HernandezMachado, and M.A. Rodriguez
Growth of unstable interfaces in disordered media.
Phys Rev E 57, 57545760 (1998)
Abstract: The effects of a disordered medium in the growth of unstable interfaces are studied by means of two local models with multiplicative and additive quenched disorder, respectively. For short times and large pushing the multiplicative quAbstract: enched disorder is equivalent to a timedependent noise. In this regime, the linear dispersion relation contains a destabilizing contribution introduced by the noise. For long times, the interface always gets pinned. We model the systematics of the pinned shapes by means of an effective nonlinear model. These results show good agreement with numerical simulations. For the additive noise we find numerically that a depinning transition occurs.
26 D.Vives, J.Armero, A.Mati, L.RamirezPiscina, J.Casademunt, J.M. Sancho and F.Sagues
Propagating fronts in reactiondiffusion systems
J Math Chem 23, 239260 (1998)
Abstract: Propagating reaction–diffusion fronts constitute one of the paradigms in the realm of the
nonlinear chemical phenomena. In this paper different situations are considered. Firstly,
we discuss the problem of front propagation in a twovariable chemical system exhibiting
multiple stationary states. Emphasis is put on the question of velocity selection. In section 3
of our contribution, the question of front propagating in spatially modulated and noisy media
is addressed. Finally, we also brieﬂy comment on the problem of reaction–diffusion fronts
in nonquiescent media. In this particular scenario we simply aim at introducing the two
basic propagation modes, i.e., thin versus distributed reaction fronts, that are identiﬁed in
our numerical simulations.
27 I.SendinaNadal, A.P.PerezMunuzuri, D.Vives, V.PerezMunuzuri, J.Casademunt, L.RamirezPiscina, J.M. Sancho and F.Sagues
Wave propagation in a medium with disordered excitability.
Phys Rev Lett 80, 5437 (1998)
Abstract: The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the lightsensitive BelousovZhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (timeaveraged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a powerlaw dependence for the relative change of the propagation speed on the disorder amplitude.
28 I. SendinaNadal, D. Roncaglia, D. Vives, V.PerezMunuzuri, M. GomezGesteira, V. PerezVillar, J. Echave, J. Casademunt, L. RamirezPiscina and F. Sagues.
Percolation thresholds in chemical excitable media.
Phys Rev E 58, R1183R1186 (1998).
Abstract: The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the lightsensitive BelousovZhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the twostate medium considered.
29 R.GonzalezCinca, L.RamirezPiscina, J.Casademunt, A.HernandezMachado, T.T.Katona, T.Borzsonyi and A. Buka
Heat diffusion anisotropy in dendritic growth: Phasefield simulations and experiments in liquid crystals
Journal of Crystal Growth 193, 712719 (1998).
Abstract: An anisotropic heat diffusion coefficient is introduced in order to study some interfacial growth phenomena. This anisotropy has been incorporated in a phase field model which has been studied numerically to reproduce some fundamental solidification situations (needle crystal growth) as well as the dynamics of a nematic–smecticB interface. As a general result, we find that dendrites grow faster in the lower heat diffusion direction. Simulation results are compared with experiments with remarkable qualitative agreement.
30 J. Armero, J. Casademunt, L. RamirezPiscina and J.M. Sancho.
Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise
Phys Rev E 58, 54945500 (1998).
Abstract: We study the dynamics of reactiondiffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.
31 A. Penaranda, C.E. Auguet and L. RamirezPiscina
Transitions in disordered suspensions of superconducting granules under external magnetic field
Solid State Communications 109, 227 (1999).
Abstract: We perform simulations of transitions in threedimensional suspensions of superconducting granules, placed completely at random in a sample, when an external magnetic field is slowly increased. The results show that these transitions induce order in the system. This effect appears as advantageous in applications for Superheated Superconducting Granule detectors.
32 A. Penaranda, C.E. Auguet and L. RamirezPiscina
Surface field in an ensemble of superconducting spheres under external magnetic field
Nuclear Instruments and Methods in Physics Research A 424, 512522 (1999)
Abstract: We perform calculations of the magnetic field on the surface of an ensemble of superconducting spheres when placed into an external magnetic field, which is the configuration employed in superheated superconducting granule detectors. The Laplace equation is numerically solved with appropriate boundary conditions by means of an iterative procedure and a multipole expansion.
33 A.M. Lacasta, I.R. Cantalapiedra, C.E. Auguet, A. Penaranda and L. RamirezPiscina
Modelling of spatiotemporal patterns in bacterial colonies
Physical Review E 59, 7036 (1999)
Abstract: A diffusionreaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG01.
34 R. Folch, J. Casademunt, A. HernandezMachado and L. RamirezPiscina
Phasefield model for HeleShaw flows with arbitrary viscosity contrast I: theoretical approach
Physical Review E 60, 1724 (1999)
Abstract: We present a phasefield model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular HeleShaw cell. With asymptotic matching techniques we check the model to yield the right HeleShaw equations in the sharpinterface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phasefield model to the limiting HeleShaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.
35 R. Folch, J. Casademunt, A. HernandezMachado and L. RamirezPiscina
Phasefield model for HeleShaw flows with arbitrary viscosity contrast II: numerical study
Physical Review E 60, 1734 (1999)
Abstract: We implement a phasefield simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular HeleShaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary SaffmanTaylor fingers, and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.
36. I. SendinaNadal, V.PerezMunuzuri, M. GomezGesteira, A.P. PerezMunuzuri, V. PerezVillar, D. Vives, F. Sagues, J. Casademunt, J.M. Sancho and L. RamirezPiscina.
Effects of a quenched disorder on wave propagation in excitable media.
International Journal of Bifurcations and Chaos 9, 23532362 (1999).
Abstract: The behavior of autowaves under the effect of a quenched disorder is studied in the framework of the lightsensitive Belousov–Zhabotinsky reaction. This allows us to introduce spatial disorder on the excitability by projecting patterns of light transmittance. In particular, we have selected a dichotomic random distribution of levels of transmittance. If the two values of transmittance are equally probable and allows wave propagation without breaking the waves, we find an opposite effect on the wave front velocity and shape depending on the considered dimension. On the other hand, if one of the two values of the transmittance distribution is set on the nonexcitable region, percolation phenomena can arise by changing the number of excitable sites. The different addressed situations are analytically interpreted giving theoretical predictions for the experimental and numerical results.
37 I. SendinaNadal, S. Alonso, V.PerezMunuzuri, M. GomezGesteira, V. PerezVillar, L. RamirezPiscina, J. Casademunt, J.M. Sancho and F. Sagues.
Brownian motion of spiral waves driven by spatiotemporal structured noise.
Phys. Rev. Lett. 84, 2734 (2000).
Abstract: Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the lightsensitive BelousovZhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.
38 T.T.Katona, T.Borzsonyi, A. Buka, R.GonzalezCinca, L.RamirezPiscina, J.Casademunt, A.HernandezMachado and L. Kramer
Pattern forming Instabilities of the Nematic SmecticB interface
Physics Reports 337, 3765 (2000)
Abstract: Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasitwodimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced from the shape of the interface in thermal equilibrium. The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phasefield model. The simulations have reproduced qualitatively the rich variety of morphologies (extending from the faceted shape to fully developed dendrites) observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.
39 R. GonzalezCinca, L. RamirezPiscina, J. Casademunt, y A. HernandezMachado.
Sidebranching induced by external noise in solutal dendritic growth
Physical Review E 63, 051602 (2001)
Abstract: We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments. The effects of other possible sources of fluctuations (of an external origin) are examined by introducing nonconserved noise in a phasefield model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.
40 R. GonzalezCinca, L. RamirezPiscina, J. Casademunt, y A. HernandezMachado.
Sidebranching in solutal dendritic growth
in Branching in Nature, Dynamics and Morphogenesis of Branching Structures, from Cell to River Networks.
Les Houches School, Vol. 14, pp 403408
Eds. V. Fleury, J.F. Gouyet and M. Leonetti (SpringerVerlag and EDPSciences, Les Ulis, 2001).
41 I.R. Cantalapiedra, A.M. Lacasta, C.E. Auguet, A. Penaranda and L. RamirezPiscina.
Pattern Formation Modeling of Bacterial Colonies
in Branching in Nature, Dynamics and Morphogenesis of Branching Structures, from Cell to River Networks.
Les Houches School, Vol. 14, pp 359364
Eds. V. Fleury, J.F. Gouyet and M. Leonetti (SpringerVerlag and EDPSciences, Les Ulis, 2001).
42 A. HernandezMachado, J. Soriano, A. M. Lacasta, M.A. Rodriguez, L. RamirezPiscina and J. Ortin
Interface roughening in HeleShaw flows with quenched disorder: experimental and theoretical results
Europhysics Letters 55, 194200 (2001)
Abstract: We study the forced fluid invasion of an airfilled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the nonlocal character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent β1 = 5/6, a roughness exponent α1 = 5/2, and a dynamic exponent z1 = 3, and by β2 = 1/2, α2 = 1/2, and z2 = 1 at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times. The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions.
43 X. Ruiz, L. RamirezPiscina and J. Casademunt
Numerical studies of fluid flow in microgravity conditions for confined crystal growth
Astrophysics and Space Science 276, 135140 (2001)
Abstract: We study the convective ﬂow induced by residual accelerations in microgravity conditions
for different geometric arrangements which are relevant to crystal growth experiments. We consider
both constant and oscillating acceleration and focus mostly on the transient relaxation dynamics.
Results are relevant to estimate impact of more realistic residual accelerations in crystal growth
experiments.
44 A. Penaranda, C.E. Auguet and L. RamirezPiscina
Diamagnetic Interactions in Disordered Suspensions of Metastable Superconducting Granules
European Physical Journal B 25, 155165 (2002)
Abstract. The simulation of the transition sequence of superheated Type I superconducting granules (SSG) in disordered suspensions when an external magnetic ﬁeld is slowly increased from zero has been studied.
Simulation takes into account diamagnetic interactions and the presence of surface defects. Results have
been obtained for the transition sequence and surface ﬁelds distribution covering a wide range of densities.
These results are compared with previous analytical perturbative theory, which provides qualitative infor
mation on transitions and surface magnetic ﬁelds during transitions, but with a range of validity apparently
limited to extremely dilute samples. Simulations taking into account the complete diamagnetic interactions
between spheres appear to be a promising tool in interpreting SSG experiments, in applications such as
particle detectors, and in some fundamental calculations of Solid State Physics.
45 A. Rocco, L. RamirezPiscina and J. Casademunt
Kinematic reduction of reactiondiffusion fronts with multiplicative noise: Derivation of stochastic sharpinterface equations
Physical Review E 65, 056116 (2002)
Abstract: We study the dynamics of generic reactiondiffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reactiondiffusion Langevinlike field equations and the kinematic (eikonal) description in terms of a stochastic movingboundary or sharpinterface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a nonKardarParisiZhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noiseinduced pushedpulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reactiondiffusion field equations with multiplicative noise.
46 A. Penaranda, C.E. Auguet, L. RamirezPiscina and T.A. Girard
Diamagnetic interactions in superheadsuperconducting microgranules under an external magnetic field
Contributions to Science 2, 197207 (2002)
The study of the phase transitions produced in ensembles of metastable superconducting
granules by magnetic eld variations holds interest for fundamental physics and for applications in particle detectors. It is a problem whose theoretical study has been long hampered
by the di culty in treating diamagnetic interactions between granules. In this review we
describe the behaviour of such systems, develop the numerical procedures to deal with them,
and present some experimental and numerical results.
47 A. Penaranda and L. RamirezPiscina
Dynamical ordering induced by preferential transitions in Planar Arrays of Superheated Superconducting granules
Solid State Communications 127, 395400 (2003)
Abstract: We perform simulations of planar arrays of superheated superconducting granules (PASS) under an external magnetic field, analyzing transitions undergone by the system when the external field is slowly increased from zero. We observe, for high concentrations, the existence of an interval of external fields for which no transitions are induced. This effect is analogous to a ‘hot border zone’ identified in the response of superheated superconducting granule detectors. We explain such behaviour as produced by a geometrical ordering dynamically induced in the system by transitions in preferential sites due to diamagnetic interactions.
48 R. Benitez and L. RamirezPiscina
Initial Transients in the Symmetric Model for Directional Solidification
in 'Interface and Transport Dynamics, Computational Modelling',
Lecture Notes in Computational Science and Engineering, Vol. 32, p. 160165
Eds. Heike Emmerich, Britta Nestler and Michael Schreckenberg (SpringerVerlag, Berlin, 2003)
Abstract: We study the initial transient during the
directional solidification of a dilute mixture
in the symmetrical constantgap approximation.
We perform phasefield simulations of the transient recoil stages
and compare the results with predictions obtained
from the sharpinterface model.
In particular, we focus in the evolution of the front position and of the
transient dispersion relation,
obtaining quantitative agreement between theory and
simulations. Results are applied to the destabilization of the front by
fluctuations.
49 R. GonzalezCinca, R. Folch, R. Benitez, L. RamirezPiscina, J. Casademunt, A. HernandezMachado
Phasefield models in interfacial pattern formation out of equilibrium
in Advances in Condensed Matter and Statistical Mechanics, ed. by E. Korucheva and R. Cuerno, p. 203236, Nova Science Publishers (2004), arXiv:condmat/0305058
Review article on phasefield models, with application examples.
50 A. Penaranda, C.E. Auguet and L. RamirezPiscina
Simulations of Transitions in Superheated Superconducting Granules
Nuclear Instruments and Methods in Physics Research A 520, 201204 (2004)
Abstract: We perform simulations of both colloidal suspensions and planar arrays systems of superheated superconducting granules. Transitions induced by an increasing external field appear in both situations as an ordering mechanism. Concentrated planar arrays present an interval of external field for which no transitions are produced. These effects can be interesting in applications for superheated superconducting granule detectors.
51 E. Meca, I. Mercader, O. Batiste and L. RamirezPiscina
Blue sky catastrophe in doublediffusive convection
Physical Review Letters 92, 234501 (2004)
Abstract: A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddleloop bifurcation and becomes chaotic in a perioddoubling cascade just before its disappearance at the blue sky catastrophe.
52 R. Benitez and L. RamirezPiscina
Stochastic PhaseField Simulations of Symmetric Alloy Solidification
Fluctuation and Noise Letters 4, L505L510 (2004)
Abstract: We study initial transient stages in directional solidification by means of a nonvariational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke fluctuationdissipation theorem to account for the fluctuation statistics. We devote our attention to the transient regime during which concentration gradients are building up and fluctuations act to destabilize the interface. To this end, we calculate both the temporally dependent growth rate of each mode and the power spectrum of the interface evolving under the effect of fluctuations. Quantitative agreement is found when comparing the phasefield simulations with theoretical predictions.
53 E. Meca, I. Mercader, O. Batiste and L. RamirezPiscina
Complex dynamics in doublediffusive convection
Theoretical and Computational Fluid Dynamics 18, 231238 (2004)
Abstract: The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimensionthree degenerate Takens–Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=1.
54 R. GonzalezCinca and L. RamirezPiscina
Numerical study of the shape and integral parameters of a dendrite
Physical Review E 70, 051612 (2004)
Abstract: We present a numerical study of sidebranching of a solidifying dendrite by means of a phasefield model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have been distinguished outside the linear region: a first one in which sidebranching is in a competition process and a second one further down where branches behave as independent of each other. The shape of the dendrite and integral parameters characterizing the whole dendrite (contour length and area of the dendrite) have been computed and related to the characteristic tip radius for both surface tension and kinetic dominated dendrites. Conclusions about the different behaviors observed and comparison with available experiments and theoretical predictions are presented.
55 A. Penaranda and L. RamirezPiscina
Hotborder effects, ordering, and avalanches in planar arrays of superheated superconducting granules
Nuclear Instruments and Methods in Physics Research A 540, 188199 (2005)
Abstract: We present results of simulations of transitions in planar arrays of superheated superconducting granules (PASS) immersed in an external magnetic field parallel to the system. Analysis of the behaviour of the system when the external field is slowly increased from zero shows the existence of an interval of external fields for which no transitions are produced. This gap is found to be a consequence of ordering induced by transitions. However, this ordering is different for diluted and for concentrated systems. Avalanches of different sizes with distributions depending on concentration are observed.
56 R. Benitez and L. RamirezPiscina
SharpInterface Projection of a Fluctuating PhaseField Model
Physical Review E 71, 061603 (2005)
Abstract: We present a derivation of the sharpinterface limit of a generic fluctuating phasefield model for solidification. As a main result, we obtain a sharpinterface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuationdissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or nonvariational phasefield formulations. In particular, it can be used to introduce thermodynamical fluctuations in nonvariational formulations of the phasefield model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phasefield simulations in crystal growth while accounting for the proper fluctuations of the system.
57 I. Mercader, O. Batiste, L. RamirezPiscina, X. Ruiz, S. Rudiger and J. Casademunt
Bifurcations and chaos in singleroll natural convection with low Prandtl number
Physics of Fluids 17, 104108 (2005)
Abstract: Convective flows of a small Prandtl number fluid contained in a twodimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic singleroll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two NeimarkSacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex timedependent behavior does not break the basic, singleroll structure.
58 C. Corbella, B. Echebarria, L. RamirezPiscina, E. Pascual, J. L Andujar, and E. Bertran
Spontaneous formation of nanometric multilayers of metalcarbon films by uphill diffusion during growth
Applied Physics Letters 87, 213117 (2005)
Abstract: We report the spontaneous formation of multilayer structures with nanometric periodicity during Ti–C thinfilm growth by reactive magnetron sputtering. Their characterization was performed by transmission electron microscopy, xray photoelectron spectroscopy, xray diffraction, and secondary ion mass spectrometry. We discuss film structure and morphology as a function of metal content, and propose surfacedirected spinodal decomposition as the mechanism responsible for the segregation of species in separated layers by uphill diffusion.
59 J. Carrera, X. Ruiz, L. RamirezPiscina, J. Casademun and M. Dreyer
Generation of a Monodisperse Microbubble Jet in Microgravity
AIAA Journal 46, 20102019 (2008)
Abstract: A new method to create a jet of a virtually monodisperse microbubble suspension of prescribed bubble size into a
quiescent cavity is proposed. The method is insensitive to gravity and is based on the creation of a slug ﬂow at a T
junction in a capillary tube before injection. We develop a theoretical analysis that establishes the validity and
efﬁciency of the method, as controlled by the crossﬂow Weber number, and yields a simple explicit prediction for the
bubble size in terms of the injection parameters. The method operates efﬁciently for small Weber numbers, yet it
generates small bubbles of very uniform size. The reduced size dispersion is also explained within the theoretical
model. The method of bubble formation, injection, and spreading by the resulting turbulent jet is validated
experimentally in 4.7 s of free fall in the drop tower at the University of Bremen. Experiments demonstrate the
physical principle behind the method of bubble formation and allow us to explore the dynamics of the resulting
bubble jet after injection of the slug ﬂow into a quiescent cavity in microgravity conditions as an efﬁcient method of
bubble spreading and transport. Detailed measurements of average local velocities show that bubbles are essentially
passive with respect to the carrier mean ﬂow, and the inherent turbulence of the ﬂow is crucial for optimal spreading
of the bubble distribution and reduction of bubble coalescence. The shape of the bubble jet is studied as a function of
the Reynolds number. Finally, the degree of coalescence is also characterized and found to be remarkably small.
60 S. Arias, X. Ruiz, J. Casademunt, L. RamirezPiscina and R. GonzalezCinca
Experimental Study of a Microchannel Bubble Injector for Microgravity Applications
Microgravity  Science and Technology 21, 107111 (2009)
Abstract: We perform a quantitative characterization of a microbubble injector in conditions relevant to microgravity. The injector pregenerates a slug flow by using a capillary Tjunction, whose operation is robust to changes in gravity level. We address questions regarding the performance under different injection conditions. In particular we focus on the variation of both gas and liquid flow rates. The injection performance is characterized by measuring bubble injection frequency and bubble sizes. We obtain two distinct working regimes of the injector and identify the optimal performance as the crossover region between them.
61 C. Corbella, B. Echebarria, L. RamirezPiscina, E. Pascual, J.L. Andujar, E. Bertran
Growth kinetics of nanometric dendrites in metalcarbon thin films
Acta Materialia 57, 49484956 (2009)
Abstract: Tungstencarbon films deposited by pulsedDC reactive magnetron sputtering show the formation of a dendritic structure at the nanometric scale. The structure is formed by a combination of a polycrystalline β–W phase together with a nonstoichiometric WC1x phase. The nanodendrites coincide with Wrich zones, whereas Crich regions are located at the interstices. The characteristics of this nanostructure have been modulated by varying the metal concentration of the films. Composition, structure and morphology were characterized by XRay Photoelectron Spectroscopy, Electron Probe MicroAnalysis, Transmission Electron Microscopy, XRay Diffraction and Atomic Force Microscopy, whereas mechanical and tribological properties were evaluated by profilometry, nanoindentation and microscratch. The observed growth pattern is interpreted as the result of nucleation and growth of a W phase into a WC amorphous matrix, whose growth is controlled by diffusion of carbon. A simulation model based in phase field modelling presenting similar morphologies is formulated. This special structure combines properties of W and diamondlike carbon films, which enlarges the scope of applications towards selflubricant hard and lowfriction coatings with improved stability.
62 S. Arias, R. GonzalezCinca, X. Ruiz, L. RamirezPiscina and J. Casademunt
Characterization of the performance of a minibubble generator in conditions relevant to microgravity
Colloids and Surfaces A 365, 5255 (2010).
Abstract: We perform a characterization of a recently reported minibubbles (bubbles with a diameter of the order of 10^3 m) generator in microgravity related conditions. Generation of bubbles is based on the generation of a slug flow in a capillary Tjunction, whose operation is robust to changes in the gravity level. We address questions regarding the performance under different working regimes. In particular, we focus on the regimes found within a large range of gas and liquid injection flow rates. The injection performance is characterized by measuring bubble generation frequency. We propose curves obtained empirically for the behaviour of generation frequency and crossover between regimes.
63 E. Meca and L. RamirezPiscina
Transient convective instabilities in directional solidification
Physics of Fluids 22, 114110 (2010)
Abstract: We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic expansion for large Rayleigh number that permits a simpler analytical analysis and a better numerical behavior. We find a transient instability, i.e. a regime in which the system destabilizes during the transient whereas the final unperturbed steady state is stable. This could be relevant to growth mode predictions in solidification.
64 P. Bitlloch, X. Ruiz, L. RamirezPiscina and J. Casademunt
Spatial structure and velocity fluctuations in turbulent bubble jets in
microgravity
International Journal of Transport Phenomena 12, 189197 (2011)
We study the dynamics of turbulent jets of bubbles created by the injection of a slug flow into a quiescent cavity, both theoretically and experimentally using data from drop tower experiments. The generated bubble jets exhibit a remarkably low degree of coalescence leading to virtually monodisperse suspensions of spherical bubbles. The turbulence of the jet is responsible for the spatial dispersion of the bubble distribution in roughly conical jets. We propose a stochastic model for the dispersion of bubbles in the jet, in which the statistics of bubble concentration is computed within a kepsilon model of turbulence, coupled to a Langevin dynamics with an inhomogeneous diffusivity. Numerical integration is compared to experimental data, focussing on the spatial structure of the bubble jet. Results show that bubble interactions can be neglected as far as spatial dispersion is concerned, even though bubbles are not strictly passive tracers.
65 X. Ruiz, P. Bitlloch, L. RamirezPiscina, J. Casademunt
Impact of stochastic accelerations on dopant segregation in microgravity semiconductor crystal growth
Journal of Crystal Growth 355, 88100 (2012).
The residual accelerations that are typically present in microgravity environments (gjitters) contain a broad spectrum of frequencies and may be modeled as stochastic processes. Their effects on the quality of the semiconductor crystals are analyzed here quantitatively with direct numerical simulation. In particular we focus on the dopant segregation effects due to thermosolutal convection as a function of the parameters characterizing the statistics of the stochastic force. The numerical simulation is specified for material parameters of two doped semiconductors (Ge:Ga and GaAs:Se) in realistic conditions of actual microgravity environments. As a general result, we show that the segregation response is strongly dominated by the lowfrequency part of the gjitter spectrum. In addition, we develop a simplified model of the problem based on linear response theory that projects the dynamics into very few effective modes. The model captures remarkably well the segregation effects for an arbitrary timedependent acceleration of small amplitude, while it implies an enormous reduction of computer demands. This model could be helpful to analyze results from real accelerometric signals and also as a predictive tool for experimental design.
66 A.M. Lacasta, L. RamirezPiscina, J.M. Sancho, K. Lindenberg
Speeding chemical reactions by focusing
Journal of Chemical Physics 138, 144502 (2013)
We present numerical results for a chemical reaction of colloidal particles which are transported by a laminar fluid and are focused by periodic obstacles in such a way that the two components are well mixed and consequently the chemical reaction is speeded up. The roles of the various system parameters (diffusion coefficients, reaction rate, and obstacles sizes) are studied. We show that focusing speeds up the reaction from the diffusion limited rate ∼t−1/2 to very close to the perfect mixing rate, ∼t−1.
67 M.J. Skaug, A.M. Lacasta, L. RamirezPiscina, J.M. Sancho, K. Lindenberg and D.K. Schwartz
Singlemolecule di!usion in a periodic potential at
a solidliquid interface
Soft Matter 10, 753 (2014)
We used singlemolecule tracking experiments to observe the motion of small hydrophobic fluorescent molecules at the interface between water and a solid surface that exhibited periodic chemical patterns. The dynamics were characterized by nonergodic, continuous time random walk statistics. The stepsize distributions displayed enhanced probability of steps to periodic distances, consistent with theoretical predictions for diffusion in an atomic/molecular scale periodic potential. Surprisingly, this general behavior was observed here for surfaces exhibiting characteristic length scales three orders of magnitude larger than atomic/molecular dimensions, and may provide a new way to understand and control solid–liquid interfacial diffusion for molecular targeting applications.
68 L. RamirezPiscina and J.M. Sancho
Molecular Nachannel excitability from statistical physics
Europhysics Letters 108, 50008 (2014).
The excitable properties of the neural cell membrane is the driving mechanism of the neural pulses. Coordinated ionic fluxes across Na and K channels are the devices responsible of this function. Here we present a simple microscopic physical scenario which accounts for this phenomenology. The main elements are ions and channel doors that obey the standard formulation of statistical physics (overdamped Langevin equations) with appropriate nonlinear interacting potentials. From these equations we obtain the ionic flux and the dynamics of the membrane potential. We show that the excitable properties of the membrane are present in a single and simple Na channel. From this framework, additional microscopic information can be obtained, such as statistics of singlechannels dynamics or the energetics of action potential events.
69 E. Meca, I. Mercader and L. RamirezPiscina
Transitions between symmetric and nonsymmetric regimes in binarymixture convection
Physica D 303, 3949 (2015)
We present here a comprehensive picture of the different bifurcations found for small to moderate Rayleigh number in binarymixture convection with lateral heating and negative separation ratio (SS). The present work connects the symmetric regime found for pure fluid (S=0S=0) (Mercader et al., 2005) with the fundamentally nonsymmetric regime found for S=−1S=−1 (Meca et al., 2004) [2,3]. We give a global context as well as an interpretation for the different associations of bifurcations found, and in particular we interpret an association of codimensiontwo bifurcations in terms of a higher codimension bifurcation never found, to our knowledge, in the study of an extended system.
70 Pau Bitlloch, Xavier Ruiz, Laureano RamirezPiscina, Jaume Casademunt
Turbulent Bubble Jets in Microgravity. Spatial Dispersion and Velocity Fluctuations
Microgravity Science and Technology 27, 207220 (2015)
A detailed statistical analysis of bubble dispersion in turbulent jets based on data from drop tower experiments is presented here. A stochastic model is also introduced in order to capture these statistics to a large extent, treating bubbles as passive tracers with a local diffusivity given by a k ε description of the turbulence. Bubblebubble and bubbleflow interactions are neglected. Simple scaling analysis suggests that this approach is justified sufficiently far downstream. It is also found that, although interactions cannot be neglected very close to the inlet, the model predictions for the overall spatial distribution of the bubble ensemble are compatible with data within experimental uncertainty, and within the limited statistics of the experiments. In addition, the velocity fluctuations from the same experiments are analyzed, obtaining the local standard deviation of bubble velocities. We also find good agreement between experimental data and the effective model. Slight deviations between the model predictions and the experimental data are found at the jet margins, concerning the dependence on Reynolds number of jet angle and the relative velocity fluctuations. Consequently, significant bubbleflow interactions seem to be confined at the boundaries of the jets.







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