Ricardo Cortez

Publications of Ricardo Cortez

• Boundary integral solutions of coupled Stokes and Darcy flows.

  Authors: Svetlana Tlupova, Ricardo Cortez

  J. Comput. Physics. 01/2009; 228:158-179.

• Interaction between arthropod filiform hairs in a fluid environment.

  Authors: Bree Cummins, Tomás Gedeon, Isaac Klapper, Ricardo Cortez

  Journal of theoretical biology. 08/2007; 247(2):266-80.

  Many arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of theMany arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of the abdomen. The biomechanical stimulus-response properties of individual filiform hairs have been investigated and modeled extensively in several earlier studies. However, only a few previous studies have considered viscosity-mediated coupling between pairs of hairs, and only in particular configurations. Here, we present a model capable of calculating hair-to-hair coupling in arbitrary configurations. We simulate the coupled motion of a small group of mechanosensory hairs on a cylindrical section of cercus. We have found that the coupling effects are non-negligible, and likely constrain the operational characteristics of the cercal sensory array.

• Modeling physiological resistance in bacterial biofilms.

  Authors: N G Cogan, Ricardo Cortez, Lisa Fauci

  Bulletin of mathematical biology. 08/2005; 67(4):831-53.

  A mathematical model of the action of antimicrobial agents on bacterial biofilms is presented. The model includes the fluid dynamics in and around the biofilm, advective and diffusive transport ofA mathematical model of the action of antimicrobial agents on bacterial biofilms is presented. The model includes the fluid dynamics in and around the biofilm, advective and diffusive transport of two chemical constituents and the mechanism of physiological resistance. Although the mathematical model applies in three dimensions, we present two-dimensional simulations for arbitrary biofilm domains and various dosing strategies. The model allows the prediction of the spatial evolution of bacterial population and chemical constituents as well as different dosing strategies based on the fluid motion. We find that the interaction between the nutrient and the antimicrobial agent can reproduce survival curves which are comparable to other model predictions as well as experimental results. The model predicts that exposing the biofilm to low concentration doses of antimicrobial agent for longer time is more effective than short time dosing with high antimicrobial agent concentration. The effects of flow reversal and the roughness of the fluid/biofilm are also investigated. We find that reversing the flow increases the effectiveness of dosing. In addition, we show that overall survival decreases with increasing surface roughness.

• A study of bacterial flagellar bundling.

  Authors: Heather Flores, Edgar Lobaton, Stefan Méndez-Diez, Svetlana Tlupova, Ricardo Cortez

  Bulletin of mathematical biology. 02/2005; 67(1):137-68.

  Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. EachCertain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion. We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of elastic springs while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When at least one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.

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• Interaction between arthropod filiform hairs in a fluid environment

  Authors: Bree Cummins, Tomáš Gedeon, Isaac Klapper, Ricardo Cortez

  Journal of Theoretical Biology.

  Many arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of theMany arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of the abdomen. The biomechanical stimulus–response properties of individual filiform hairs have been investigated and modeled extensively in several earlier studies. However, only a few previous studies have considered viscosity-mediated coupling between pairs of hairs, and only in particular configurations. Here, we present a model capable of calculating hair-to-hair coupling in arbitrary configurations. We simulate the coupled motion of a small group of mechanosensory hairs on a cylindrical section of cercus. We have found that the coupling effects are non-negligible, and likely constrain the operational characteristics of the cercal sensory array.

• Computation of three-dimensional Brinkman flows using regularized methods

  Authors: Ricardo Cortez, Bree Cummins, Karin Leiderman, Douglas Varela

  Journal of Computational Physics.

  The Brinkman equations of fluid motion are a model of flows in a porous medium. We develop the exact solution of the Brinkman equations for three-dimensional incompressible flow driven by regularizedThe Brinkman equations of fluid motion are a model of flows in a porous medium. We develop the exact solution of the Brinkman equations for three-dimensional incompressible flow driven by regularized forces. Two different approaches to the regularization are discussed and compared on test problems. The regularized Brinkman model is also applied to the unsteady Stokes equation for oscillatory flows since the latter leads to the Brinkman equations with complex permeability parameter. We provide validation studies of the method based on the flow and drag of a solid sphere translating in a Brinkman medium and the flow inside a cylindrical channel of circular cross-section. We present a numerical example of a swimming organism in a Brinkman flow which shows that the maximum swimming speed is obtained with a small but non-zero value of the porosity. We also demonstrate that unsteady Stokes flows with oscillatory forcing fall within the same framework and are computed with the same method by applying it to the motion of the oscillating feeding appendage of a copepod.