Publications

A minimal model for aquatic self propelled locomotion

J. Sanchez, C. Raufaste  and M. Argentina, "A Minimal model for aquatic self propelled locomotion",  JFS 97, 103071 (2020)

Fish locomotion is a complicated problem in the context of fluid-structure interaction and it is still not understood what is linked to biology and what is linked to mechanics. Measurements performed on natural fish and artificial systems reveal that swimming at high Reynolds number is found in a narrow range of Strouhal numbers - a dimensionless combination of the swimming velocity, tail beat amplitude and frequency. With a simplified model of aquatic locomotion, we show that this number is set by a simple thrust-drag balance.
 

Curvature based, time delayed feedback as means of self propelled swimming

D. Gross, Y. Roux and M. Argentina, "Curvature-based, time delayed feedback as a means for self-propelled swimming", JFS 86, 186 (2019)

The development of bio-inspired robotics has lead to an increasing need to un- derstand the strongly coupled fluid-structure and control problem presented by swimming. Gazzola et al. [1] showed the possibility that a curvature based feedback with a time delay may be sufficient to generate a self-propulsive swimmer without the need for a central pattern generator. This work seeks to show that such a feedback based self-propulsion has different character- istics than swimming developed from an imposed central pattern generator. The influence of both the feedback delay and structral damping is examined. The swimmer is modelled as a thin, Euler-Bernoulli beam using a finite element representation which is coupled to an unsteady boundary element method for the rsolution of the fluid problem. The model is first tested on a flexible, thin foil in forced leading edge heave. The behavior of the swimmer when given an imposed traveling bending moment wave is then presented. This is then compared to a swimmer with delayed curvature-based feedback. Finally, a simplified model is shown to qualititatively produce the behavior in the peaks observed in the feedback swimmer

Study of the thrust-drag balance with a swimming robotic fish

F. Gibouin, C. Raufaste, Y. Bouret, and M. Argentina, "Study of the thrust–drag balance with a swimming robotic fish", POF 30, 091901 (2018)

A robotic fish is used to test the validity of a simplification made in the context of fish locomotion.<br />With this artificial aquatic swimmer, we verify that the momentum equation results from a simple balance between a thrust and a drag that can be treated independently in the small amplitude regime. The thrust produced by the flexible robot is proportional to A^2 f^2, where A and f are the respective tail-beat amplitude and oscillation frequency, irrespective of whether or not $f$ coincides with the resonant frequency of the fish.<br />The drag is proportional to U_0^2, where U_0 is the swimming velocity.<br />These three variables set the value of the Strouhal number in this regime, while for larger amplitudes, the Strouhal number increases as a result of a correction factor on the effective drag.

Shape and coarsening dynamics of strained islands

G Schifani, T Frisch, M. Argentina "Equilibrium and dynamics of strained islands, PRE 97, 062805 2018

G Schifani, T Frisch, M. Argentina &  J.-N.   Aqua Shape and coarsening dynamics of strained islands", PRE 94, 042808, 2016

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elastocapillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two-dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height h0 and they sit on top of a flat wetting layer with a thickness hw . We then consider two islands, and we report that they undergo a noninterrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasistatic dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale tc that is a function of the distance d between the islands and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height h∗0, its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.

Solitary-like wave in a liquid foam microchannel

Y. Bouret, A Cohen, N. Fraysse, M. Argentina  & C. Raufaste "Solitary-like waves in a liquid foam microchannel", PRF 1, 043902, 2016.

Plateau borders (PBs) are liquid microchannels located at the contact between three bubbles in liquid foams. They are stable, deformable, and can be thought of as quasi- one-dimensional model systems to study surface waves in fluid dynamics. We show that the burst of a bubble trapped in a PB produces local constrictions which travel along the liquid channel at constant velocity, without significant change in shape. These patterns are reminiscent of the depression solitary waves encountered in nonlinear systems. By coupling flow inertia to capillary stresses, we derive a simple model that admits solitonic solutions, which we characterized numerically and analytically in the limit of small deformation. These solutions capture most of the features observed experimentally.

Bubble dynamics inside an outgassing hydrogel confined in a Hele-Shaw cell

F. Haudin, X. Noblin, Y. Bouret, M. Argentina & C. Raufaste "Bubble dynamics inside an outgassing hydrogel confined in a Hele-Shaw cell", PRE 94, 023109, 2016.

We report an experimental study of bubble dynamics in a non-Newtonian fluid subjected to a pressure decrease. The fluid is a hydrogel, composed of water and a synthetic clay, prepared and sandwiched between two glass plates in a Hele-Shaw geometry.  As the imposed pressure decreases, the gas initially dissolved in the hydrogel triggers bubble formation. Different stages of the process are observed: bubble nucleation, growth, interaction, and creation of domains by bubble contact or coalescence. Initially bubble behave independently. They are trapped and advected by the mean deformation of the hydrogel, and the bubble growth is mainly driven by the diffusion of the dissolved gas through the hydrogel and its outgassing at the reactive-advected hydrogel-bubble interface. A  model is proposed and gives a simple scaling that relates the bubble growth rate and the imposed pressure.

Gait and speed selection in slender inertial swimmers

M. Gazzola, M. Argentina & L. Mahadevan,  "Gait and speed selection in slender inertial swimmers",    PNAS, doi:10.1073/pnas.1419335112, 2015.

Inertial swimmers use flexural movements to push water and generate thrust. We quantify this dynamical process for a slender body in a fluid by accounting for passive elasticity and hydrody- namics and active muscular force generation and proprioception. Our coupled elastohydrodynamic model takes the form of a non- linear eigenvalue problem for the swimming speed and locomo- tion gait. The solution of this problem shows that swimmers use quantized resonant interactions with the fluid environment to enhance speed and efficiency. Thus, a fish is like an optimized diode that converts a prescribed alternating transverse motion to forward motion. Our results also allow for a broad comparative view of swimming locomotion and provide a mechanistic basis for the empirical relation linking the swimmer’s speed U, length L, and tail beat frequency f, given by U=L ∼ f [Bainbridge R (1958) J Exp Biol 35:109–133]. Furthermore, we show that a simple form of proprioceptive sensory feedback, wherein local muscle activation is function of body curvature, suffices to drive elastic instabilities associated with thrust production and leads to a spontaneous swimming gait without the need for a central pattern generator. Taken together, our results provide a simple mechanistic view of swimming consistent with natural observations and suggest ways to engineer artificial swimmers for optimal performance.

One-dimensional capillary jumps

M.  Argentina, A. Cohen, Y. Bouret, N. Fraysse & C. Raufaste "One dimensional capillary jumps",  J.F.M., 765, 1-16, 2015

In flows where the ratio of inertia to gravity varies strongly, large variations in the fluid thickness appear and hydraulic jumps arise, as depicted by Rayleigh. We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. The Bond number – which measures the importance of gravitational body forces compared to surface tension – must be small in order to observe such objects using capillarity as a driving force. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses, which dominate inertia, and capillary jumps should not be described by the inertial shock wave theory that one would deduce from Bélanger or Rayleigh for hydraulic jumps. In order to get rid of viscous shears, we consider Plateau borders, which are the microchannels defined by the merging of three films inside liquid foams, and we show that capillary jumps propagate along these deformable conduits. We derive a simple model that predicts the velocity, geometry and shape of such fronts. A strong analogy with Rayleigh’s description is pointed out. In addition, we carried out experiments on a single Plateau border generated with soap films to observe and characterize these capillary jumps. Our theoretical predictions agree remarkably well with the experimental measurements.

Scaling macroscopic aquatic locomotion

M . Gazzola, M. Argentina  & L. Mahadevan, "Scaling macroscopic aquatic locomotion", Nature Physics, 10,  758,  2014

Inertial aquatic swimmers that use undulatory gaits range in length L from a few millimetres to 30metres, across a wide array of biological taxa. Using elementary hydrodynamic arguments, we uncover a unifying mechanistic principle characterizing their locomotion by deriving a scaling relation that links swimming speed U to body kinematics (tail beat amplitude A and frequency f) and fluid properties (kinematic viscosity nu). This principle can be simply couched as the power law Re⇠Sw^a, where Re = UL/v 1 and Sw = AwL/v, with a= 4/3 for laminar flows, and a = 1 for turbulent flows. Existing data from over 1,000 measurements on fish, amphibians, larvae, reptiles, mammals and birds, as well as direct numerical simulations are consistent with our scaling. We interpret our results as the consequence of the convergence of aquatic gaits to the performance limits imposed by hydrodynamics. 

The fern cavitation catapult: mechanism and design principles

C. Llorens, M. Argentina, N. Rojas, J. Westbrook, J. Dumais, X. Noblin, "The fern cavitation catapult: mechanism and design principles", Interface 13, 114, 20150930, 2016.

Leptosporangiate ferns have evolved an ingenious cavitation catapult to disperse their spores. The mechanism relies almost entirely on the annulus, a row of 12-25 cells which successively: i) stores energy by evaporation of the cell content, ii) triggers the catapult by internal cavitation and, iii) controls the time scales of energy release to ensure efficient spore ejection. Here we study in detail the three phases of spore ejection in the sporangia of the fern Polypodium aureum. We show first that the geometry of the cells is particularly well suited to induce bending deformations of the annulus thus allowing the sporangium to work as a catapult. We then present experiments that allowed us to measure the key parameters for each phase of the ejection. These experiments point to a critical cavitation pressure of approximately.  We also quantified the parameters that set the short and long time scales of the closing phase.  

Inertial transport in foams

CA. Cohen, N. Fraysse, J. Rajchenbach, M. Argentina, Y. Bouret & C. Raufaste,  "Inertial Mass Transport and Capillary Hydraulic Jump in a Liquid Foam Microchannel", Phys. Rev. Lett.  112, 218303, 2014

We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. In flows where the ratio inertia to gravity vary, strong variations in the fluid thickness appear and hydraulic jumps arise. In order to observe such objects using capillary as a driving force, the Bond number which measures the importance of surface tension to gravitation body forces must be small. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses which dominate inertia and capillary jump shall not be described by the shock wave theory introduced by Rayleigh for hydraulic jumps. In this study, we describe the capillary jumps travelling in Plateau borders, which are channels defined by the merging of three films inside foam. We derive a simple model which predicts the velocity, the geometry and the shape of such fronts. In this approach, we point out a strong analogy with Rayleigh's description. We carried out experiments with soap films to observe and characterize these hydraulic jumps mediated by capillarity. Our theoretical predictions are in great agreement with the experiences.  

Capturing intracellular pH dynamics by coupling its molecular mechanisms

Y. Bouret, M.  Argentina, L. Counillon  Capturing Intracellular pH Dynamics by Coupling Its Molecular Mechanisms within a Fully Tractable Mathematical Model. PLoS ONE 9(1):e85449. 2014.

We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on the individual coupling of the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad-hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. 

Personalized forecast decreases the number of unnecessary ICD implantations threefold

Argentina M, Krinski V, Guberman S, Zabel M, Sacher F, Napolitano C, Priori S, Hasenfuß G, Haïssaguerre M, Luther S.

We  aim at developing new and efficient approaches to treat the two related problems: 90% of victims of sudden cardiac death (SCD)  were not protected by ICD. B. 90-95% patients (Pts) are implanted with ICD. They do NOT need at that time and 70% will not need it in the next 5 years. No satisfactory results are reported to  decrease the number of unnecessary ICD implantations and to use liberated ICDs to protect pts from SCD. We created a personalized forecast for every pt based on the standard measurements performed by a cardiologist before the ICD implantation. The personalized forecast  decreases 2-3 fold the number of unnecessary ICD implantations for consecutive infarct survivors. 

The fern sporangium: a unique catapult

X. Noblin, N. Rojas , J. Westbrook, C. llorens, M.Argentina & J. Dumais, "The fern sporangium: a unique catapult”, Science, 335, 1322, 2012

Various plants and fungi have evolved ingenious devices to disperse their spores. One such mechanism is the cavitation-triggered catapult of fern sporangia. The spherical sporangia enclosing the spores are equipped with a row of 12 to 13 specialized cells, the annulus. When dehydrating, these cells induce a dramatic change of curvature in the sporangium, which is released abruptly after the cavitation of the annulus cells. The entire ejection process is reminiscent of human-made catapults with one notable exception: The sporangia lack the crossbar that arrests the catapult arm in its returning motion. We show that much of the sophistication and efficiency of the ejection mechanism lies in the two very different time scales associated with the annulus closure. 

A dynamical model of the Utricularia trap

C. llorens, M. Argentina, Y. Bourret, P. Marmottant & O. Vincent, "A dynamical model of the Utricularia trap”, Interface, 9, 3129-3139, 2012

We propose a model that captures the dynamics of a carnivorous plant,Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surround- ings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap.

Quasipatterns in parametrically forced thin films

M. Argentina & G. Iooss, "Quasipatterns in parametrically forced thin films”, Physica D, 241, issue 16, 1306-1321, 2012

We shake harmonically a thin horizontal viscous fluid layer (frequency forcing , only one harmonic), to reproduce the Faraday experiment and using our previously derived system invariant under horizontal rotations. When the physical parameters are suitably chosen, there is a critical value of the amplitude of the forcing such that instability occurs with at the same time the mode oscillating at half  the same frequency forcing. We give simple necessary conditions on coefficients, for obtaining the bifurcation of (formally) stable time-periodic quasipatterns.

An elasto hydrodynamical model of friction for the locomotion of Caenorhabditis elegans

P. Sauvage, M. Argentina, J. Drappier, T. Senden, J. Siméon and J.-M. di Meglio “An elasto hydrodynamical model of friction for the locomotion of Caenorhabditis elegans ”, Journal of Biomechanics 44, 6, 1117-1122, 2011.

Caenorhabditis elegans (C. elegans) is one of the most studied organisms by biologists. Composed of around one thousand cells, easy to culture and to modify genetically, it is a good model system to address fundamental physiological questions and in particular to investigate neuromuscular processes. Many C. elegans mutants can be distinguished by their locomotion phenotype and it then important to understand the biomechanics of their locomotion and in particular the mechanics of their undulating crawling motion on agar aqueous gels where they are commonly grown and observed. In this article, we present a mechanical model of the friction of the worms on their substrate where we have included capillarity (which pins the worm of the gel), the hydrodynamics of the lubrication film (between worm and gel) and the substrate/body elasticity. We determine the ratio of the transverse to longitudinal friction coefficients of the worm body on the culture gel as a function of a control parameter which describes the relative role of the deformation of the gel and the viscous dissipation in the lubrication film. Experimentally this ratio is – for soft gels – larger than the maximal value predicted by our model (this maximum is equal to 2, the value for an infinite cylinder in bulk liquid) and we propose to include the plasticity of the gel (i.e. the dissipation of the deformation of the gel) for a better description of the worm/gel interaction.

Faraday patterns in lubricated thin films

N. Rojas , M. Argentina , E. Cerda & E. Tirapegui, “Faraday patterns in lubricated thin films”, EJPD, 62, 1, 25-31, 2011.

We shake harmonically a thin horizontal viscous fluid layer (frequency forcing , only one harmonic), to reproduce the Faraday experiment and using our previously derived system invariant under horizontal rotations. When the physical parameters are suitably chosen, there is a critical value of the amplitude of the forcing such that instability occurs with at the same time the mode oscillating at half  the same frequency forcing. We give simple necessary conditions on coefficients, for obtaining the bifurcation of (formally) stable time-periodic quasipatterns. 

Dynamics of a bouncing ball on a vibrated elastic membrane

B. Eichwald, M. Argentina, X. Noblin, F. Celestini, “Dynamics of a bouncing ball on a vibrated elastic membrane”, Phys. Rev. E 82, 016203, 2010.

We investigate the dynamics of a ball bouncing on a vibrated elastic membrane. Beyond the classical solid-solid case, we study the effect of introducing new degrees of freedom by allowing substrate oscillations. The forcing frequency of the vibration strongly influences the different thresholds between the dynamical states. The simple model proposed gives good agreement between the experiments and the analytical expres- sion for the threshold at which the ball begins to bounce. Numerical simulations permit to qualitatively recover the experimental phase diagram. Finally, we discuss how this simple system can give new insights in the recent experimental studies on bouncing droplets. 

Inertial Lubrication theory

N. Rojas , M. Argentina , E. Cerda & E. Tirapegui, “Inertial Lubrication theory”, Phys. Rev. lett. 104, 18780, 2010.

Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime. 

Wave-train-induced termination of weakly anchored vortices in excitable media

Alain Pumir, Sitabhra Sinha, S. Sridhar, M. Argentina, Marcel Horning, Simonetta Filippi, Christian Cherubini, Stefan Luther, and Valentin Krinsky, ”Wave-train-induced termination of weakly anchored vortices in excitable media”, Phys. Rev. E 81, 010901, 2010.

A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue. 

Robert Hooke’s Three- Body problem

M. Argentina, P. Coullet, J-M Gilli, M Monticelli & G Rousseaux ”Modern chaos in the ancient experiments of Robert Hooke on the inverted cone. ”, Proc. Roy. Soc. 453, 1259-1269, 2007.

During the winter 1679,  R. Hooke challenged I. Newton to predict the dynamics of an object submitted to a constant radial force. This correspondence influenced strongly I. Newton, that wrote four years later its "De Motu", real ancestor of "The Principia", published in 1687. R. Hooke's problem can be physically linked to the dynamics of a sphere sliding on an inverted cone due to gravitational effects.  If the symmetry axis of the cone is parallel to the gravitational field, the ball executes stable precessions. Breaking this symmetry induces the appearance of chaotic motions. After having derived the equations related to the position of the sphere, we analyze its dynamics, and we perform an approximated Floquet analysis that is compared to our numerical results. 

Taylor-like Vortices in Shear-Banding Flow of Giant Micelles

M. A. Fardin, B. Lasne, O. Cardoso, G. Grégoire, M. Argentina, J. P. Decruppe, and S. Lerouge “Taylor-like Vortices in Shear-Banding Flow of Giant Micelles”, Phys. Rev. Lett. 103, 028302, 2009.

Using flow visualizations in Couette geometry, we demonstrate the existence of Taylor-like vortices in the shear-banding flow of a giant micelles system. We show that vortices stacked along the vorticity direction develop concomitantly with interfacial undulations. These cellular structures are mainly localized in the induced band and their dynamics is fully correlated with that of the interface. As the control parameter increases, we observe a transition from a steady vortex flow to a state where pairs of vortices are continuously created and destroyed. Normal stress effects are discussed as potential mechanisms driving the three-dimensional flow. 

Nonlinear Faraday Waves at Low Reynolds Numbers

N. Rojas , M. Argentina , E. Cerda & E. Tirapegui, “Nonlinear Faraday Waves at Low Reynolds Numbers”, J. Mol. Liqu. 147, 166, 2009.

Faraday waves are nonlinear oscillations that appear on the surface of a fluid which is vertically and periodically accelerated. This phenomenon has been extensively studied in the last decades. Experiments show plenty of structures such as squares, rhomboids, hexagons, quasipatterns, solitary waves and transition to spatio-temporal chaos. Theoretical studies have been devoted to the linear analysis in viscous fluids, amplitude equations in the weakly nonlinear regime and phenomenological models.
A linearized model has been derived from the Navier– Stokes equations, but the nonlinear saturation is not addressed. In this work, we derive the nonlinear equations that govern the phenomena for thin films of viscous fluids at low Reynolds number. We show that the linear Mathieu equation is contained in our model and for highly viscous fluids, we get the Reynolds equation. 

Settling and swimming of flexible fluid-lubricated foils

M.Argentina, J.Skotheim & L.Mahadevan“Settling and swimming of flexible fluid-lubricated foils”, Phys. Rev. Lett. 99, 224503, 2007.

We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall. Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive settling and the active swimming of a foil. This also allows us to partly answer the long-standing question in cartoon physics—can carpets fly? Our analysis suggests a region in parameter space where one may realize this dream and move the virtual towards reality. 

Interface Instability in Shear-Banding Flows

S. Lerouge, M. Argentina, J. P. Decruppe. ”Interface Instability in Shear-Banding Flow”, Phys. Rev. Lett. 96, 088301, 2006.

We report on the spatiotemporal dynamics of the interface in shear-banding flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium nitrate in water) during a start-up experiment. Using the scattering properties of the induced structures, we demonstrate the existence of an instability of the interface between bands along the vorticity direction. Different regimes of spatiotemporal dynamics of the interface are identified along the stress plateau. We build a model based on the flow symmetry which qualitatively describes the observed patterns. 

Coarsening dynamics of the one-dimensional Cahn-Hilliard model

M.Argentina, M.Clerc, R.Rojas & E.Tirapegui.”Coarsening dynamics of the one-dimensional Cahn-Hilliard model”, PRE 71, 046210, 2005.

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We charac- terize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system. A set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations. We also compare these dynamics with the bubble dynam- ics deduced from the classical kink interaction computation where our model seems to be more appropriated. In the case of two bubbles, we deduce analytical expressions for the bubble’s position and the bubble’s width. Besides, a simple description of the ulterior dynamics is presented. 

Fluid-flow induced flutter of a flag

M. Argentina & L. Mahadevan, “Fluid-flow induced flutter of a flag”, PNAS 102, 6, 1829- 1834, 2005.

We give an explanation for the onset of fluid-flow-induced flutter in a flag. Our theory accounts for the various physical mechanisms at work: the finite length and the small but finite bending stiffness of the flag, the unsteadiness of the flow, the added mass effect, and vortex shedding from the trailing edge. Our analysis allows us to predict a critical speed for the onset of flapping as well as the frequency of flapping. We find that in a particular limit correspond- ing to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode. 

On the back fire instability

M. Argentina, O. Rudzick, & M. G. Velarde, “On the back fire instability”, Chaos 14, 777, 2004.

In spatially extended dynamical systems, the transition from complex behavior to ordered state may be under- stood in terms of synchronization. Here we focus atten- tion on the particular case of synchronization of oscilla- tions in a one-dimensional spatially extended system when an external resonant signal is injected. An example is an array of lasers submitted to an external electric field whose frequency is close to the self-oscillation of the units. Thus, we investigate the evolution of a nonlinear oscillatory medium submitted to a resonant signal. In the model equation describing the onset of the 1:1 paramet- ric resonance, the back-firing instability is observed. This instability appears when a localized propagating pulse becomes unstable and splits into two new counterpropa- gating solutions that upon an eventual collision disappear due to dissipation. 

Falkner-Skan approximation for gradually variable flows

M. Argentina & E. Cerda, “Falkner-Skan approximation for gradually variable flows” Non Linear Phenomena and Complex systems, 9, 87, 2004.

We discuss here a method for computation of gradually variable laminar flows for large Reynold number. The model consists in approximating locally the flow with self similar profiles. This approach permits a derivation of two coupled ordinary dif- ferential equations. One of them is the Falkner-Skan equation with specific bound- ary conditions that once solved permits to study variable flows in quite different problems or geometries. We apply the model to the problem of the Poiseuille flow, and compare it with the solution obtained by integrating directly the fluid motion equation. 

Saddle-node bifurcation : Appearance mechanism of pulses in the subcritical complex Ginzburg-Landau equation

O. Descalzi, M. Argentina, & E. Tirapegui. “Saddle-node bifurcation : Appearance mechanism of pulses in the subcritical complex Ginzburg-Landau equation”, Phys. Rev. E. 67. 015501(R), 2003.

We study stationary, localized solutions in the complex subcritical Ginzburg-Landau equation in the region where there exists coexistence of homogeneous attractors. Using a matching approach, we report on the fact that the appearance of pulses are related to a saddle-node bifurcation. Numerical simulations are in good agreement with our theoretical predictions. 

Van-der-Waals transition in fluidized granular media

M. Argentina, M. Clerc, & R. Soto, “Van-der-Waals transition in fluidized granular media” NonLinear Phenomena and Complex Systems, 9, 341, 2004.

A phase separation of fluidized granular matter is presented. Molecular dynamics simulations of a system of grains in two spatial dimensions, with a vibrating wall and without gravity, exhibit the ap- pearance, coalescence, and disappearance of bubbles. By identifying the mechanism responsible for the phase separation, we show that the phenomenon is analogous to the spinodal decomposition of the gas- liquid transition of the van der Waals model. We have deduced a macroscopic model for the onset of phase separation which agrees quite well with molecular dynamics simulations. 

Stationary localized solution in the subcrtitical complex GinzBurg-Landau equation

O. Descalzi, M. Argentina & E. Tirapegui. “Stationary localized solution in the subcrtitical complex GinzBurg-Landau equation”, Int. J. Bif. Chaos 12, 11, 2459-2465, 2002.

It is shown that pulses in the complete quintic one-dimensional Ginzburg–Landau equation with complex coefficients appear through a saddle-node bifurcation which is determined analytically through a suitable approximation of the explicit form of the pulses. The results are in excellent agreement with direct numerical simulations. 

Periodic Nucleation solutions in the real Ginzburg- Landau equation in finite box

M.Argentina, O.Descalzi & E.Tirapegui. “Periodic Nucleation solutions in the real Ginzburg- Landau equation in finite box”, Int. J. Bif. Chaos 12, 10, 2219-2228, 2002.

We study the stationary solutions of the real Ginzburg–Landau equation with periodic boundary conditions in a finite box. We show explicitly how to construct nucleation solutions allowing transitions between stable plane waves.

Self parametric instability in extended systems

M. Argentina, P. Coullet & E. Risler, “Self parametric instability in extended systems”, Phys. Rev. Lett. 86, 807, 2001.

Bifurcations which occur in one parameter families of dynamical systems play an important role in the under- standing of universal physical phenomena [1]. In this Let- ter we report on the existence of a new type of instability which arises in spatially extended systems. We name it “self-parametric” instability since it is the consequence of anharmonicity of a spatially homogeneous limit cycle which acts as a parametric forcing on itself. More precisely we consider a partial differential equation which possesses a spatially independent time-periodic solution. This solu- tion is assumed to be stable with respect to homogeneous perturbations. We demonstrate that this solution is generi- cally unstable in respect to inhomogeneous perturbations, when it approaches an Andronov homoclinic bifurcation.

A simple generalized excitability model mimicking salient features of neurons dynamics

A. Giaquinta, M. Argentina & M. G. Velarde, “A simple generalized excitability model mi- micking salient features of neurons dynamics”, J. Stat. Phys. 101, (1/2), 665-678, 2000.

A generalization of the FitzHugh-Nagumo model for excitability is provided to account for salient features of Inferior Olive neurons. The base state is a limit cycle and excitability appears as spiking over peaks of the oscillations. The response of the model to various types of external stimulus is also presented. In particular, we show the relevance of an appropriate balance between amplitude and duration of the stimulus.

Head-on collisions of waves in an excitable FitzHugh-Nagumo system: a transition from wave annihilation to classical wave behavior

M. Argentina, P. Coullet & V. Krinsky,  “Head-on collisions of waves in an excitable FitzHugh- Nagumo system: a transition from wave annihilation to classical wave behavior”, J. Theor. Biol. 205, 47-52, 2000.

For the particular case of an excitable FitzHugh-Nagumo system with diffusion, we investigate the transition from annihilation to crossing of the waves in the head-on collision. The analysis exploits the similarity between the local and the global phase portraits of the system. We find that the transition has features typical of the nucleation theory of first-order phase transitions, and may be understood through purely geometrical arguments. In the case of periodic boundary conditions, the transition is an infinite-dimensional analog of the creation and the vanishing of limit cycles via a homoclinic Andronov bifurcation. Both before and after the transition, the behavior of a single cell continues to be typical for excitable systems: a stable equilibrium state, and a threshold above which an excitation pulse can be induced. The generality and qualitative character of our argument shows that the phenomenon described can be observed in excitable systems well beyond the particular case presented here.

Andronov Bifurcation and sea-shell patterns

M. Argentina & P. Coullet, “Andronov Bifurcation and sea-shell patterns”, Pattern Formation in Biology, Vision and Dynamics, Eds. A. Carbone, M. Gromov and Prusinkiewicz, World Scientific, 2000.

Tropical molluscs exhibit very complex pigmentation on their shells. In this paper, we intend to show that some of those patterns can be understood as the instability of limit cycles in spatially extended dynamical systems.

Chaotic nucleation of metastable domains

M. Argentina & P. Coullet, “Chaotic nucleation of metastable domains”, Phys. Rev. E 56, 3, R2359-R2362, 1997.

We describe a cavitation process that consists of chaotic nucleation of metastable domains. It can be generically observed in spatially extended nonequilibrium systems, whenever they exhibit bistability between a stationary and an oscillatory state, close to the Andronov homoclinic bifurcation, which leads to the disap- pearance of the former. In the bistable regime, the modulational instability of the homogenenous oscillations leads to inhomogenous nucleation of the stationary phase.

Colliding waves in a model excitable medium: preservation, annihilation and bifurcation

M. Argentina, P. Coullet & L. Mahadevan, Colliding waves in a model excitable medium: preservation, annihilation and bifurcation, Phys. Rev. Lett. 79, 2803-2807,1997.

We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homo- clinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions.