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PubMed1999

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures.

We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air-liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. [Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman (Materials Research Society, Boston, 1996), Vol. 464, p. 237; Phys. Fluids A 9, 3645 (1997); O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998]. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow [Phys. Fluids A 10, 1234 (1998); "Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances," submitted to Phys. Fluids]. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. (c) 1999 American Institute of Physics.

Journal Article↗
PubMed2000

Effect of interfacial tension on propagating polymerization fronts.

This paper is devoted to the investigation of polymerization fronts converting a liquid monomer into a liquid polymer. We assume that the monomer and the polymer are immiscible and study the influence of the interfacial tension on the front stability. The mathematical model consists of the reaction-diffusion equations coupled with the Navier-Stokes equations through the convection terms. The jump conditions at the interface take into account the interfacial tension. Simple physical arguments show that the same temperature distribution could not lead to Marangoni instability for a nonreacting system. We fulfill a linear stability analysis and show that interaction of the chemical reaction and of the interfacial tension can lead to an instability that has another mechanism: the heat produced by the reaction decreases the interfacial tension and initiates the liquid motion. It brings more monomer to the reaction zone and increases even more the heat production. This feedback mechanism can lead to the instability if the frontal Marangoni number exceeds a critical value. (c) 2000 American Institute of Physics.

Journal Article↗
PubMed2004

Viscous fingering as a paradigm of interfacial pattern formation: recent results and new challenges.

We review recent results on dynamical aspects of viscous fingering. The Saffman-Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman-Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering.

Models, Statistical↗
PubMed2004

Interfacial stability of electrodeposition of cuprous oxide films.

Experiments on deposition of Cu(2)O films from basic copper sulfate solution show that copper also deposits. At low, but basic values of pH only copper deposits and at high pH only cuprous oxide deposits. In the intermediate range where both compete the system shows oscillations at "constant current." Linear stability analysis has been conducted for such an electrochemical cell to show that oscillations can take place in the parameter space identified in the experiments. The results are keeping with most of the experimental observations, which are many, but not with all. The physical mechanisms behind the oscillations are explained in terms of competing reactions.

Journal Article↗
PubMed2004

Taxonomy of nucleation and growth processes in isotropic systems.

We construct a taxonomy of transient behavior for one component coupled nucleation and growth based on linear and nonlinear stability analysis of a two species model. The two species are the condensable species and the condensed droplets or particles, respectively. Our model reproduces previously reported asymptotically stable and oscillatory transient nucleation behavior. Additionally, we show previously unreported possibilities of multiple stationary states and combinations of stationary states with limit cycles. We predict that multiple stationary states may be observed under near critical conditions. Estimates of suitable conditions for experimental verification are given for several systems of interest.

Journal Article↗
PubMed2005

A mathematical model of crystallization in an emulsion.

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker-Doring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers "sucking" monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Journal Article↗
PubMed2005

Lag and anticipating synchronization without time-delay coupling.

We describe a new method for achieving approximate lag and anticipating synchronization in unidirectionally coupled chaotic oscillators. The method uses a specific parameter mismatch between the drive and response that is a first-order approximation to true time-delay coupling. As a result, an adjustable lag or anticipation effect can be achieved without the need for a variable delay line, making the method simpler and more economical to implement in many physical systems. We present a stability analysis, demonstrate the method numerically, and report experimental observation of the effect in radio-frequency electronic oscillators. In the circuit experiments, both lag and anticipation are controlled by tuning a single capacitor in the response oscillator.

Models, Statistical↗
PubMed2005

Steady dark solitary waves emerging from wave-generated meanflow: the role of modulation equations.

Various classes of steady and unsteady dark solitary waves (DSWs) are known to exist in modulation equations for water waves in finite depth. However, there is a class of steady DSWS of the full water-wave problem which are missed by the classical modulation equations such as the Hasimoto-Ono, Benney-Roskes, and Davey-Stewartson. These steady DSWs, recently discovered by Bridges and Donaldson, are pervasive in finite depth, arise through secondary criticality of Stokes gravity waves, and are synchronized with the Stokes wave. In this paper, the role of DSWs in modulation equations for water waves is reappraised. The intrinsic unsteady nature of existing modulation equations filters out some interesting solutions. On the other hand, the geometry of DSWs in modulation equations is very similar to the full water wave problem and these geometrical properties are developed. A model equation is proposed which illustrates the general nature of the emergence of steady DSWs due to wave-generated mean flow coupled to a periodic wave. Although the existing modulation equations are intrinsically unsteady, it is shown that there are also important shortcomings when one wants to use them for stability analysis of DSWs.

Algorithms↗
PubMed2006

A study of the asymmetric Malkus waterwheel: the biased Lorenz equations.

In this work, the asymmetric case of the Malkus waterwheel is studied, where the water inflow to the system is biasing the system toward stable motion in one direction, like a Pelton wheel. The governing equations of this system, when expressed in Fourier space and decoupled to form a closed set, can be mapped into a four-dimensional space where they form a quasi-Lorenz system. This set of equations is analyzed in light of analogues of the Rayleigh Bernard convection and conclusions are drawn. The properties and behavior of the equations are studied and correlated to the physical model. Phase space behavior and linear stability analysis are used for this. Spectral analysis is used as a qualitative measure of chaos. Chaotic behavior is quantified through the calculation of the Lyapunov exponents and these are further correlated to the bifurcation diagrams for a conclusive analysis of the dynamical behavior of the system.

Journal Article↗
PubMed2006

Pair formation and global ordering of strongly interacting ferrocolloid mixtures: an integral equation study.

Using the reference hypernetted chain (RHNC) integral equation theory and an accompanying stability analysis we investigate the structural and phase behaviors of model bidisperse ferrocolloids based on correlations of the homogeneous isotropic high-temperature phase. Our model consists of two species of dipolar hard spheres (DHSs) which dipole moments are proportional to the particle volume. At small packing fractions our results indicate the onset of chain formation, where the (more strongly coupled) A species behaves essentially as a one-component DHS fluid in a background of B particles. At high packing fractions, on the other hand, the RHNC theory indicates the appearance of isotropic-to-ferromagnetic transitions (volume ratios close to one) and demixing transitions (smaller volume ratios). However, contrary with the related case of monodisperse DHS mixtures previously studied by us [Phys. Rev. E 70, 031201 (2004)], none of the present bidisperse systems exhibit demixing within the isotropic phase, rather we observe coupled ferromagnetic/demixing phase transitions.

Journal Article↗
PubMed2006

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches.

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.

Journal Article↗
PubMed2006

Stability and phase separation in mixed self-assembled monolayers.

Recent single molecule experiments rely on the self-assembly of binary mixtures of molecules with very different properties in a stable monolayer, in order to probe the characteristics of the interspersed molecule of interest in a controlled environment. However, not all efforts at coassembly have been successful. To study systematically the behavior of such systems, we derive the free energy of multicomponent systems of rods with configurational degrees of freedom, localized on a surface, starting from a generalized van der Waals description. The molecular parameters are determined by geometrical factors of the molecules and by their pairwise van der Waals interactions computed using molecular mechanics. Applying the model to two experimental situations, we are able to use the stability analysis of the respective mixtures to explain why coassembly was successful in one set of experiments (carotene and alkanethiol) and not in another (benzenethiols and alkanethiol). We outline general guidelines for suitable choices of molecules to achieve coassembly.

Journal Article↗
PubMed2003

Buoyancy-driven flow in a peat moss layer as a mechanism for solute transport.

Transport of nutrients, CO2, methane, and oxygen plays an important ecological role at the surface of wetland ecosystems. A possibly important transport mechanism in a water-saturated peat moss layer (usually Sphagnum cuspidatum) is nocturnal buoyancy flow, the downward flow of relatively cold surface water, and the upward flow of warm water induced by nocturnal cooling. Mathematical stability analysis showed that buoyancy flow occurs in a cooling porous layer if the system's Rayleigh number (Ra) exceeds 25. For a temperature difference of 10 K between day and night, a typical Ra value for a peat moss layer is 80, which leads to quickly developing buoyancy cells. Numerical simulation demonstrated that fluid flow leads to a considerable mixing of water. Temperature measurements in a cylindrical peat sample of 50-cm height and 35-cm diameter were in agreement with the theoretical results. The nocturnal flow and the associated mixing of the water represent a mechanism for solute transport in water-saturated parts of peat land and in other types of terrestrializing vegetation. This mechanism may be particularly important in continental wetlands, where Ra values in summer are often much larger than the threshold for fluid flow.

Bryophyta↗
PubMed2022

Morphological instability and roughening of growing 3D bacterial colonies.

How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size-eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an "active fluid" whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies-as well as other forms of growing active matter, such as tumors and engineered living materials-in 3D environments.

Models, Biological↗
PubMed1998

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels.

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system's behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken's cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Animals↗
PubMed2000

Identification and initial characterization of four novel members of the interleukin-1 family.

Interleukin-1 (IL-1), fibroblast growth factors (FGFs), and their homologues are secreted factors that share a common beta-barrel structure and act on target cells by binding to cell surface receptors with immunoglobulin-like folds in their extracellular domain. While numerous members of the FGF family have been discovered, the IL-1 family has remained small and outnumbered by IL-1 receptor homologues. From expressed sequence tag data base searches, we have now identified four additional IL-1 homologues, IL-1H1, IL-1H2, IL-1H3, and IL-1H4. Like most other IL-1/FGFs, these proteins do not contain a hydrophobic leader sequence. IL-1H4 has a propeptide sequence, while IL-1H1, IL-1H2, and IL-1H3 encode only the mature protein. Circular dichroism spectra and thermal stability analysis suggest that IL-1H1 folds similarly to IL-1ra. The novel homologues are not widely expressed in mammals. IL-1H1 is constitutively expressed only in placenta and the squamous epithelium of the esophagus. However, IL-1H1 could be induced in vitro in keratinocytes by interferon-gamma and tumor necrosis factor-alpha and in vivo via a contact hypersensitivity reaction or herpes simplex virus infection. This suggests that IL-1H1 may be involved in pathogenesis of immune mediated disease processes. The addition of four novel IL-1 homologues suggests that the IL-1 family is significantly larger than previously thought.

Amino Acid Sequence↗
PubMed1996

One-Handed Juggling: A Dynamical Approach to a Rhythmic Movement Task.

The skill of rhythmically juggling a ball on a racket was investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system were analyzed by means of local and nonlocal stability analyses. These analyses showed that the task dynamics offer an economical juggling pattern that is stable even for open-loop actuator motion. For this pattern, two types of predictions were extracted: (a) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball, and (b) a nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment in which subjects (N = 6) performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The following predictions were confirmed: (a) For stable rhythmic performance, the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; and (b) for each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results permit one to conclude that humans reliably exploit the stable solutions inherent to the dynamics of the given task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle for generating different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.

Journal Article↗
PubMedDate not supplied

Stability of anthroposcopic and anthropometric estimates of physique in Belgian boys followed longitudinally from 13 to 18 years of age.

The stability of physique determined by the anthroposcopic 'Atlas' technique and the anthropometric Health-Carter method was examined in a sample of 210 healthy Belgian schoolboys studied longitudinally at yearly intervals from 13 to 18 years of age. The two rating systems were also compared. Results indicate that components of the same type in the two methods do not measure the same underlying factors, particularly for mesomorphy (anthroposcopic technique) and the second component (Health-Carter method). The methods cannot be considered as equivalent. The stability analysis reveals that the 'athletic' component tends to be less stable than the other two components, especially in the anthroposcopic Sheldon technique. In general, however, the constancy of the three somatotype components is fairly high during the growth period considered.

Adolescent↗