The general integral particle strength exchange (PSE) operators [J.D. Eldredge, A. Leonard, and T. Colonius, J. Comput. Phys. 180, 686-709 (2002)] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability. (2002)] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.

As a simple theoretical model of a cell adhering to a biological interface, we consider a rigid cylinder moving in a viscous shear flow near a wall. Adhesion forces arise through intermolecular bonds between receptors on the cell and their ligands on the wall, which form flexible tethers that can stretch and tilt as the base of the cell moves past the wall; binding kinetics is assumed to follow a standard model for slip bonds. By introducing a finite resistance to bond tilting, we use our model to explore the territory between previous theoretical models that allow for either zero or infinite resistance to bond rotation. A microscale calculation (for two parallel sliding plates) reveals a nonlinear force-speed relation arising from bond formation, tilting and breakage. Two distinct types of macroscale cell motion are then predicted: either bonds adhere strongly and the cell rolls (or tank treads) over the wall without slipping, or the cell moves near its freestream speed with bonds providing weak frictional resistance to sliding. The model predicts bistability between these two states, implying that at critical shear rates the system can switch abruptly between rolling and free sliding, and suggesting that sliding friction arising through bond tilting may play a significant dynamical role in some celladhesion applications.

We present a numerical study of the effect of DNA translocation on the ionic current through a nanopore. We use a coarse-grained model to solve the electrokinetic equations at the Poisson-Boltzmann level for the microions, coupled to a lattice-Boltzmann equation for the solvent hydrodynamics. In most cases, translocation leads to a reduction in the ionic current. However, at low salt concentrations (large screening lengths) we find ionic current enhancement due to translocation. In an unstructured pore, translocation of the helical charge distribution of the DNA has no effect on the ionic current. However, if a localized charge probe is placed on the wall of the nanopore, we observe ionic current modulations that, though weak, should be experimentally observable.

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We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two-and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement. AbstractWe present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two-and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

Large-eddy simulations (LES) of a turbulent interfacial gas-liquid flows are described in this paper. The variational multiscale approach (VMS) introduced by Hughes for single-phase flows is systematically assessed against direct numerical simulation (DNS) data obtained at a shear Reynolds number Re⋆=171, and compared to LES results obtained with the Smagorinsky model, modified by a near-interface turbulence decay treatment. The models are incorporated in the same pseudospectral DNS solver built within the boundary fitting method used by Fulgosi et al. for air-water flow. The LES are performed for physical conditions allowing low interface deformations that fall in the range of capillary waves of wave slope ak=0.01. The LES results show that both the modified Smagorinsky model and the VMS are capable to predict the boundary layer structure in the gas side, including the decay process, and to cope with the anisotropy of turbulence in the liquid blockage layer underneath the interface. Higher-order turbulence statistics, including the transfer of energy between the normal stresses is also well predicted by both approaches, but qualitatively the VMS results remain overall better than the modified Smagorinsky model. The study has demonstrated that the key to the prediction of the energy transfer mechanism is in the proper prediction of the fluctuating pressure field, which has been found out of reach of any of the LES methodologies. The superiority of the VMS is demonstrated through the analysis of the subgrid transport and exchange terms in the resolved kinetic energy, where it is indeed shown to be self-adaptive with regard to the eddy viscosity. Although VMS is shown to be sensitive to filter scale partition and model constant, the optimal setting can be easily translated in the interface tracking/finite-volume context, which makes it very useful for practical purposes. An important point is that the VMS approach yields very satisfactory results without the need for prescribing an ad-hoc damping function and the required distance to the interface.

In scientific simulations of partial differential equations one is often faced with the task of choosing a discretization scheme or tuning the parameters of a discretized differential operator to perform well on a given problem. While this is mostly done through benchmark simulations on test problems, a problem-independent performance model would be desirable. Based on results from numerical analysis, we present a set of problem-independent performance measures for diffusion operators in particle methods. These measures quantify an operator's accuracy, stability, and computational cost. They can be explicitly derived in closed form, hence enabling comparisons between different operators and operator parameter tuning without the need for running any benchmark simulations. If a small number of benchmarks is available, a regression over the quality measures can be calibrated to absolute CPU time, hence defining predictive performance models for the different operators. We demonstrate this on the example of PSE operators and show the computational savings that can be achieved by operator selection and tuning.

Numerous processes in live cells depend on active, motor-driven transport of cargo and organelles along the filaments of the cytoskeleton. Understanding the resulting dynamics and the underlying biophysical and biochemical processes critically depends on computational models of intra-cellular transport. A number of motorcargo models have hence been developed to reproduce experimentally observed transport dynamics on various levels of detail. Computer simulations of these models have so far exclusively relied on approximate time-discretization methods. Using a consensus motorcargo model that unites several existing models from the literature we demonstrate that this simulation approach is not correct. The numerical errors do not vanish even for arbitrarily small time steps, rendering the algorithm inconsistent. We propose a novel exact simulation algorithm for intra-cellular transport models that is also computationally more efficient than the approximate one. Furthermore, we introduce a robust way of analyzing the different time scales in the model dynamics using velocity autocorrelation functions. AbstractNumerous processes in live cells depend on active, motor-driven transport of cargo and organelles along the filaments of the cytoskeleton. Understanding the resulting dynamics and the underlying biophysical and biochemical processes critically depends on computational models of intra-cellular transport. A number of motor-cargo models have hence been developed to reproduce experimentally observed transport dynamics on various levels of detail. Computer simulations of these models have so far exclusively relied on approximate time-discretization methods. Using a consensus motor-cargo model that unites several existing models from the literature we demonstrate that this simulation approach is not correct. The numerical errors do not vanish even for arbitrarily small time steps, rendering the algorithm inconsistent. We propose a novel exact simulation algorithm for intra-cellular transport models that is also computationally more efficient than the approximate one. Furthermore, we introduce a robust way of analyzing the different time scales in the model dynamics using velocity autocorrelation functions.