Pseudomonas aeruginosa is a ubiquitous bacterium that survives in many environments, including as an acute and chronic pathogen in humans. Substantial evidence shows that P. aeruginosa behavior is affected by its motility, and appendages known as flagella and type IV pili (TFP) are known to confer such motility. The role these appendages play when not facilitating motility or attachment, however, is unclear. Here we discern a passive intercellular role of TFP during flagellar-mediated swarming of P. aeruginosa that does not require TFP extension or retraction. We studied swarming at the cellular level using a combination of laboratory experiments and computational simulations to explain the resultant patterns of cells imaged from in vitro swarms. Namely, we used a computational model to simulate swarming and to probe for individual cell behavior that cannot currently be otherwise measured. Our simulations showed that TFP of swarming P. aeruginosa should be distributed all over the cell and that TFP−TFP interactions between cells should be a dominant mechanism that promotes cell−cell interaction, limits lone cell movement, and slows swarm expansion. This predicted physical mechanism involving TFP was confirmed in vitro using pairwise mixtures of strains with and without TFP where cells without TFP separate from cells with TFP. While TFP slow swarm expansion, we show in vitro that TFP help alter collective motion to avoid toxic compounds such as the antibiotic carbenicillin. Thus, TFP physically affect P. aeruginosa swarming by actively promoting cell−cell association and directional collective motion within motile groups to aid their survival.he bacterium Pseudomonas aeruginosa is a ubiquitous organism that is a known opportunistic pathogen, causing both chronic and acute infections in susceptible populations, including individuals with cystic fibrosis or burn wounds, or Intensive Care Unit patients (1). Among questions that remain unanswered for nonobligate pathogens like P. aeruginosa is how these bacteria initiate infections after entering the host from the environment. Given that P. aeruginosa is among many bacteria that grow as a biofilm during infection, there is a need to understand how individual cells coordinate in space with each other to colonize new surfaces and subsequently transition to stationary biofilms.Many organisms coordinate their movement as a population, emerging as self-organized swarming groups. Even the untrained eye would note the coordinated swarming behavior of fish, birds, and insects. Many bacteria also exhibit collective motion by swarming over surfaces in a coordinated manner to move unimpeded at the same time (2-4). Our knowledge of the specific actions used by individual cells during collective motion is limited; the behavior of single cells within a dense population is difficult to discern experimentally. Previous attempts to study bacterial collective behavior have used computational models to test mechanisms hypothesized to influence collective motion, including directional r...
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to determine which one we should choose depending on which are the crucial aspects when we approximate the equations. Among the properties that we consider desirable to control are the time accuracy order, energy-stability, unique solvability and the linearity or nonlinearity of the resulting systems. In particular, we concern about the iterative methods used to approximate the nonlinear schemes and the constraints that may arise on the physical and computational parameters.Furthermore, we present the connections of the Cahn-Hilliard equation with other physically motivated systems (not only phase field models) and we state how the ideas of efficient numerical schemes in one topic could be extended to other frameworks in a natural way.
Abstract.A new mixed variational formulation for the Navier-Stokes equations with constant density and variable viscosity depending nonlinearly on the gradient of velocity, is proposed and analyzed here. Our approach employs a technique previously applied to the stationary Boussinesq problem and to the Navier-Stokes equations with constant viscosity, which consists firstly of the introduction of a modified pseudostress tensor involving the diffusive and convective terms, and the pressure. Next, by using an equivalent statement suggested by the incompressibility condition, the pressure is eliminated, and in order to handle the nonlinear viscosity, the gradient of velocity is incorporated as an auxiliary unknown. Furthermore, since the convective term forces the velocity to live in a smaller space than usual, we overcome this difficulty by augmenting the variational formulation with suitable Galerkin-type terms arising from the constitutive and equilibrium equations, the aforementioned relation defining the additional unknown, and the Dirichlet boundary condition. The resulting augmented scheme is then written equivalently as a fixed point equation, and hence the well-known Schauder and Banach theorems, combined with classical results on bijective monotone operators, are applied to prove the unique solvability of the continuous and discrete systems. No discrete inf-sup conditions are required for the well-posedness of the Galerkin scheme, and hence arbitrary finite element subspaces of the respective continuous spaces can be utilized. In particular, given an integer k ≥ 0, piecewise polynomials of degree ≤ k for the gradient of velocity, Raviart-Thomas spaces of order k for the pseudostress, and continuous piecewise polynomials of degree ≤ k + 1 for the velocity, constitute feasible choices. Finally, optimal a priori error estimates are derived, and several numerical results illustrating the good performance of the augmented mixed finite element method and confirming the theoretical rates of convergence are reported.
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