Publications

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    ABSTRACT: This letter addresses the performance study of an adaptive controller in the presence of gain and delay uncertainties. The nonlinearities in the controller presented here do not allow an analytical study of the effect of uncertainties on performance. A numerical study is done instead using the sampling, learning, prediction, and optimization capabilities of the software Global Optimization, Sensitivity and Uncertainty in Models (GoSUM).
    IEEE Transactions on Control Systems Technology 04/2013; 21(3):1039. · 2.52 Impact Factor
  • Sophie Loire, Igor Mezić
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    ABSTRACT: A backward-in-time probabilistic method with spatial filter averaging is presented to solve linear second-order partial differential equations of the parabolic type. An advantage of this methodology is that while forward methods are subject to region with loss of density of particles and hence loss of spatial resolution of the solution, the solution given by backward methods is given on any desired grid. However, traditional backward time probabilistic method using Monte Carlo averaging are computationally expensive. We prove a convergence result and present several examples. The method leads to important improvement in computational efficiency and is expected to perform well to solve high dimensional problems where a solution is needed on a large grid.
    Journal of Computational Physics 01/2013; 233:175–191. · 2.14 Impact Factor
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    ABSTRACT: The irruption of gas and oil into the Gulf of Mexico during the Deepwater Horizon event fed a deep sea bacterial bloom that consumed hydrocarbons in the affected waters, formed a regional oxygen anomaly, and altered the microbiology of the region. In this work, we develop a coupled physical-metabolic model to assess the impact of mixing processes on these deep ocean bacterial communities and their capacity for hydrocarbon and oxygen use. We find that observed biodegradation patterns are well-described by exponential growth of bacteria from seed populations present at low abundance and that current oscillation and mixing processes played a critical role in distributing hydrocarbons and associated bacterial blooms within the northeast Gulf of Mexico. Mixing processes also accelerated hydrocarbon degradation through an autoinoculation effect, where water masses, in which the hydrocarbon irruption had caused blooms, later returned to the spill site with hydrocarbon-degrading bacteria persisting at elevated abundance. Interestingly, although the initial irruption of hydrocarbons fed successive blooms of different bacterial types, subsequent irruptions promoted consistency in the structure of the bacterial community. These results highlight an impact of mixing and circulation processes on biodegradation activity of bacteria during the Deepwater Horizon event and suggest an important role for mixing processes in the microbial ecology of deep ocean environments.
    Proceedings of the National Academy of Sciences 01/2012; · 9.81 Impact Factor
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    ABSTRACT: Electrokinetic flows lead to promising utilization for mixing, concentration, pumping and have applications from basic studies of convective flows to fully integrated lab on chip developments. Despite these wide applications, electrothermal flow models have been scarcely studied. We find that the model widely used by the microfluidic community does not fit correctly the measured ac electrothermal fluid flows at higher voltages (10 Vpp and above). We thus analyse both theoretically and experimentally the importance of electrothermal coupling and the buoyancy effect. Numerical simulations are compared with micro-particle image velocimetry measurements of the vortices. Our enhanced model successfully matches our measurements over a wide range of conductivities and voltages.
    Journal of Physics D Applied Physics 01/2012; 45(18). · 2.53 Impact Factor
  • Paul Kauffmann, Sophie Loire, Igor Mezic
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    ABSTRACT: Diagnostic and pharmacology processes could be greatly accelerated by appropriate mixing. Here electrothermal flows are explored to provide mixing of conductive physiological solutions (=1.6 S/m) in a 96 well plate. Three interdigitated electrodes provide an electric field (< 15Vpp, 1MHz) beneath each well. Polarization and conduction phenomenon of the fluid in a well will be first modeled numerically and compared to an electrical circuit model. Due to high conductivity and permittivity of the fluid, the impedance of the array of filled wells collapse dramatically (96 wells: R = 1Ohm, C=250nF). The power supply challenges accordingly raised by arrays of electrothermal micromixers will be then analyzed. The efficiency of different methods of mixing in those wells will be also compared: the addition of low frequency signal leading to AC electro-osmotic perturbations, a blinking vortices method. The experimental results will be compared to simulations.
    11/2011;
  • Sophie Loire, Paul Kauffmann, Igor Mezic
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    ABSTRACT: We compare simulations from new theory to experimental measurements on AC eletrothermal flows (ACET) for micromixing application on 96 microwell (10 μL) plate for high conductivity physiological solutions. This application leads to certain design constraints (electrode sizes, voltage range, conductivity). Beneath each microwell filled with saline solution (σ=0.02 mS/cm, to 16 mS/cm.), a sinusoidal voltage (0 to 40Vpp, 1MHz) is applied between 3 interdigitated gold electrodes 35 μm thick, separated by a 150μm gap. Due to this design, the ACET flows, measured by μPIV, doesn't follow the present theory. Similarly to natural convection, a bifurcation like behaviour is observed : the flows appear only above a critical voltage. The velocities scale as V^p with p>=4 with p increasing with conductivities. We analyse the validity conditions of the weak temperature gradient approximations. Accordingly we propose a thermal-electrical strong coupling model, which is traditionally neglected. We also study the competition between ACET and natural convection appearing in this configuration.
    11/2011;
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    ABSTRACT: Chaotic advection has served as the paradigm for mixing in fluid flows with simple time dependence. Its skeletal structure is based on analysis of invariant attracting and repelling manifolds in fluid flows. Here we develop a finite-time theory for two-dimensional incompressible fluid flows with arbitrary time dependence and introduce a new mixing diagnostic based on it. Besides stretching events around attracting and repelling manifolds, this allows us to detect hyperbolic mixing zones. We used the new diagnostic to forecast the spatial location and timing of oil washing ashore in Plaquemines Parish and Grand Isle, Louisiana, and Pensacola, Florida, in May 2010 and the flow of oil toward Panama City Beach, Florida, in June 2010.
    Science 10/2010; 330(6003):486-9. · 31.20 Impact Factor
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    ABSTRACT: (CO)1−x(Ar)x mixtures physisorbed on graphite experimentally display a novel phenomenon of increasing phase-transition temperature (stabilizing the system) with increasing Ar impurity concentration or uncertainty [ H. Wiechert and K.-D. Kortmann Surf. Sci. 441 65 (1999)]. We develop a two-dimensional Ising-type model that accurately captures the phase transition and its temperature dependence. The anomaly in transition temperature is due to formation of pinwheel regions of CO around Ar atoms. The dilemma of whether the ground state is head-to-head or head-to-tail ordered is reconciled in favor of the latter. The phase-transition curve in the presence of uncertainty in Ar impurity is computed using Monte Carlo (MC) and probabilistic collocation method (PCM). PCM computes the first two moments ≈2000 times faster than MC.
    Physical Review B 05/2009; 80(11):115413. · 3.66 Impact Factor
  • Sophie Loire, Igor Mezic
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    ABSTRACT: Uncharged particles in electrolytic solutions can be manipulated using a nonuniform AC electric field which generates a dielectrophoretic (DEP) force, acting on those particles. Nonuniform AC electric fields generated by coplanar microelectrodes also produce steady fluid flow in electrolytic solutions also called AC electroosmosis, ACEO. This fluid flow is explained by the presence of an electrode shielding or double layer where ions from the bulk fluid are distributed above electrodes when an electric field is applied. If the electric field is constant, the distribution of ions can be described by Debye and Huckel. If the electric field is alternating, as is the case in dielectrophoretic, the behavior of the double layer becomes more complex. The presence of this double layer is significant for microfluidic applications and combined use of ACEO and DEP have been used to manipulate micro and nano-particles. DEP force fields have been studied ignoring the presence of the double layer. We study the influence of the electrode shielding on the dielectrophoresis forces. We adopt the simple mathematical model used in previous simulations of ACEO pumps. Neglecting Faradaic reactions, the double layer on each electrode acts like a capacitor with a constant capacitance in the linear regime of small voltages. According to this approach, the DEP force field has interesting properties which could now give an understanding of some previously unexplained experimental observations.
    11/2008;
  • Sophie Loire, Igor Mezic
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    ABSTRACT: Advection diffusion equations can be studied using a Lagrangian approach to analyze transport of densities. The motion of diffusive particles is given by the Langevin equation d X =V dt + &surd;2D dW. The Feynmann-Kac formula establishes a link between the random paths of this stochastic process and the advection-diffusion equation. The solution can be written as an expectation with respect to the probability measure of the Wiener process. We applied this idea to a backward monte carlo method and compare it to a new method using gaussian averaging in space 1pisigmaexp( |x-x0|^22ˆ ). In the cases where the solution is desired on a lower dimensional subset of the domain, a backward method using Feynamnn-Kac formula can be very efficient. But if the grid in this subset is very fine the Feynmann-Kac method is limited by the fact that a high number of Wiener processes need to be simulated at each grid point then the gaussian averaging method becomes more efficient. We apply these methods to the study of electrokinetic device.
    11/2007;
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    ABSTRACT: The manipulation of biological objects from micrometer to nanometer scale particles plays an important role in many biological and colloidal science applications. As nanoparticles are subject to Brownian motion, their trapping is challenging. However, dynamic trapping can be achieved by using the combined effect of diffusion, fluid flow and electrical forces. We present numerical simulations and experiments on nanoparticle dielectrophoretic (DEP) trapping in a linear electrode array microchannel. We derived a dynamical model using an advection-diffusion equation where the advective term consists of the sum of a conservative (related to the fluid flow) and a non-conservative term (related to the DEP force). The numerical solution of this PDE predicts the intensity of the focusing of particles as small as 10 nm in diameter which fits our experimental measurements. We observe that the existence and location of the trapping regions depend not only on the size of the particles but also on the physical and design parameters. We characterize those influences.
    11/2006;
  • Sophie Loire
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    ABSTRACT: We present numerical simulations on dielectrophoretic (DEP) separation and trapping performed in a titanium-based microchannel linear electrode array. The use of electric field and in particular dielectrophoresis (DEP) have a great potential to help miniaturize and increase the speed of biomedical analysis. Precise control and manipulation of micro/nano/bio particles inside those miniaturized devices depend greatly on our understanding of the phenomena induced by AC electric field inside microchannels and how we take advantage of them. The device is designed to generate inhomogeneities in electric- field magnitude. This allows positive and negative DEP (p-DEP and n-DEP). Moreover, it can also produce inhomogeneities in electric-field phase, hence authorizing traveling wave DEP (twDEP). We show that fluid flow effects are substantial and can affect the particle motion in a positive (enhanced trapping) and negative (trapping when separation is desired) way. An advection-diffusion equation is used to numerically simulate the system. The study of the combination of the three electrical effects with diffusion, predicts the location of the trapping regions. We finally investigate the limits of particle size that can be accurately controlled.
    11/2005;
  • Dong Eui Chang, Sophie Loire, Igor Mezić
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    ABSTRACT: We derive closed-form solutions of electric fields, dielectrophoretic (DEP) forces, and time-averaged DEP forces in a parallel electrode array for three cases: first, the case of a two-phase DEP electrode array with a first-order approximate boundary condition; second, the case of a two-phase DEP electrode array with the exact boundary condition; and last, the case of a four-phase travelling wave DEP electrode array with a first-order approximate boundary condition. We also compare these analytic solutions with numerical solutions.
    Journal of Physics D Applied Physics 11/2003; 36(23):3073. · 2.53 Impact Factor

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