There is growing interest in applying phase field methods as quantitative tools in materials discovery and development. However, large driving forces, common in many materials systems, lead to unstable phase field profiles, thus requiring fine spatial and temporal resolution. This demands more computational resources, limits the ability to simulate systems with a suitable size, and deteriorates the capability of quantitative prediction. Here, we develop a strategy to map the driving force to a constant perpendicular to the interface. Together with the third-order interpolation function, we find a stable phase field profile that is independent of the magnitude of the driving force. The power of this approach is illustrated using three models. We demonstrate that by using the driving force extension method, it is possible to employ a grid size orders of magnitude larger than traditional methods. This approach is general and should apply to many other phase field models.

Biofilms are complex communities of bacteria that exhibit a variety of collective behaviors. These behaviors improve their ability to survive in many different environments. One of these collective behaviors seen in Bacillus subtilis is the ability for starving cells to stop the growth of other cells using potassium signaling and voltage changes. This signaling produces an oscillatory growth pattern so that during periods of low growth the nutrients diffuse deeper into the biofilm and reach the nutrient-starved, interior regions of the biomass. In this paper, we develop a mathematical model to describe this oscillatory behavior, and we use this model to develop a two-dimensional simulation that reproduces many of the important features seen in the experimental data. This simulation allows us to examine the spatial patterning of the oscillatory behavior to better understand the relationships between the various regions of the biofilm. Studying the spatial components of the metabolic and voltage oscillations could allow for the development of new control techniques for biofilms with complex shapes.

In this paper we propose an improved fast iterative method to solve the Eikonal equation, which can be implemented in parallel. We improve the fast iterative method for Eikonal equation in two novel ways, in the value update and in the error correction. The new value update is very similar to the fast iterative method in that we selectively update the points, chosen by a convergence measure, in the active list. However, in order to reduce running time, the improved algorithm does not run a convergence check of the neighboring points of the narrow band as the fast iterative method usually does. The additional error correction step is to correct the errors that the previous value update step may cause. The error correction step consists of finding and recalculating the point values in a separate remedy list which is quite easy to implement on a GPU. In contrast to the fast marching method and the fast sweeping method for the Eikonal equation, our improved method does not need to compute the solution with any special ordering in neither the remedy list nor the active list. Therefore, our algorithm can be implemented in parallel. In our experiments, we implemente our new algorithm in parallel on a GPU and compare the elapsed time with other current algorithms. The improved fast iterative method runs faster than the other algorithms in most cases through our numercal studies.

Biofilms are colonies of bacteria attached to surfaces. They play a critical role in many engineering and medical applications. Scientists study biofilm growth in flow cells but often have limited direct knowledge of the environmental conditions in the apparatus. Using fully resolved, numerical simulations to estimate conditions within a flow cell is computationally expensive. In this paper, we use asymptotic analysis to create a simulation of a biofilm system that has one growth-limiting substrate, and we show that this method runs quickly while maintaining similar accuracy to prior models. These equations can provide a better understanding of the environmental conditions in experiments and can establish the boundary conditions for further smaller-scale numerical simulations.

Riverbed sediments host important biogeochemical processes that play a key role in nutrient dynamics. Sedimentary nutrient transformations are mediated by bacteria in the form of attached biofilms. The influence of microbial metabolic activity on the hydrochemical conditions within the hyporheic zone is poorly understood. We present a hydrobiogeochemical model to assess how the growth of heterotrophic and autotrophic biomass affects the transport and transformation of dissolved nitrogen compounds in bed form‐induced hyporheic zones. Coupling between hyporheic exchange, nitrogen metabolism, and biomass growth leads to an equilibrium between permeability reduction and microbial metabolism that yields shallow hyporheic flows in a region with low permeability and high rates of microbial metabolism near the stream‐sediment interface. The results show that the bioclogging caused by microbial growth can constrain rates and patterns of hyporheic fluxes and microbial transformation rate in many streams.

In this paper, we present a numerical method for solving reaction-diffusion equations on one dimensional branched structures. Through the use of a simple domain decomposition scheme, the many branches are decoupled so that the equations can be solved as a system of smaller problems that are tri-diagonal. This technique allows for locally adaptive time stepping, in which the time step used in each branch is determined by local activity. Though the method is presented in the specific context of electrical activity in neural systems, it is sufficiently general that it can be applied to other classes of reaction-diffusion problems and higher dimensions. Information in neurons, which can be effectively modeled as one-dimensional branched structures, is carried in the form of electrical impulses called action potentials. The model equations, based on the Hodgkin-Huxley cable equations, are a set of reaction equations coupled to a single diffusion process. Locally adaptive time stepping schemes are well suited to neural simulations due to the spatial localization of activity. The algorithm significantly reduces the computational cost compared to existing methods, especially for large scale simulations.

ABSTRACT Microbial biofilms and mineral precipitation commonly co-occur in engineered water systems, such as cooling towers and water purification systems, and both decrease process performance. Microbial biofilms are extremely challenging to control and eradicate. We previously showed that in situ biomineralization and the precipitation and deposition of abiotic particles occur simultaneously in biofilms under oversaturated conditions. Both processes could potentially alter the essential properties of biofilms, including susceptibility to biocides. However, the specific interactions between mineral formation and biofilm processes remain poorly understood. Here we show that the susceptibility of biofilms to chlorination depends specifically on internal transport processes mediated by biomineralization and the accumulation of abiotic mineral deposits. Using injections of the fluorescent tracer Cy5, we show that Pseudomonas aeruginosa biofilms are more permeable to solutes after in situ calcite biomineralization and are less permeable after the deposition of abiotically precipitated calcite particles. We further show that biofilms are more susceptible to chlorine killing after biomineralization and less susceptible after particle deposition. Based on these observations, we found a strong correlation between enhanced solute transport and chlorine killing in biofilms, indicating that biomineralization and particle deposition regulate biofilm susceptibility by altering biocide penetration into the biofilm. The distinct effects of in situ biomineralization and particle deposition on biocide killing highlight the importance of understanding the mechanisms and patterns of biomineralization and scale formation to achieve successful biofilm control.

In this paper, the limitations associated with implicit and explicit representations of cracks in the extended finite element method (XFEM) is recapitulated via numerical explorations followed by the development of a novel hybrid approach for the characterization of nonplanar 3D cracks along with its capability demonstration. In the XFEM, the crack geometry is independent of the structural mesh, and is often described implicitly by means of two level set functions. The implicit representation is very convenient for purposes of computing the crack front velocity and for handling situations where the crack front is concave and the velocity vectors may cross. The main difficulty of this implicit description is the formulation of an efficient and robust update scheme for the level set values after a propagation step. On the other hand, the crack geometry can be described by an explicit triangulated mesh which can be easily updated after a propagation step. The explicit representation has its own shortcomings, e.g., difficulties in handling crack overlaps and extraction of crack local coordinates. Given the difficulties associated with the use of either implicit or explicit method for the geometric description of complex crack geometry, a novel hybrid method is developed by a combination of an implicit level set representation of the crack and an explicit triangulated mesh representation. In the hybrid approach, the implicit representation is updated after each propagation step and disconnected crack surfaces are removed using a paint-fill algorithm based on the current explicit representation of the crack. Then, an updated explicit representation is constructed based on the updated implicit representation using the marching cubes algorithm. Finally, the implicit representation is rebuilt from the explicit representation. The use of the explicit representation ensures that the data in the level set representation is generated from a consistent crack description. The effectiveness of the developed hybrid approach is demonstrated by analyzing several 3D crack propagation problems including a quarter-circular crack in a complex helicopter component, a U-shaped crack and an inclined elliptical crack in cuboids, and an inclined edge crack in a three-point bending beam. (C) 2016 Elsevier Ltd. All rights reserved.

ABSTRACT Microbially catalyzed precipitation of carbonate minerals is an important process in diverse biological, geological, and engineered systems. However, the processes that regulate carbonate biomineralization and their impacts on biofilms are largely unexplored, mainly because of the inability of current methods to directly observe biomineralization within biofilms. Here, we present a method for in situ , real-time imaging of biomineralization in biofilms and use it to show that Pseudomonas aeruginosa biofilms produce morphologically distinct carbonate deposits that substantially modify biofilm structures. The patterns of carbonate biomineralization produced in situ were substantially different from those caused by accumulation of particles produced by abiotic precipitation. Contrary to the common expectation that mineral precipitation should occur at the biofilm surface, we found that biomineralization started at the base of the biofilm. The carbonate deposits grew over time, detaching biofilm-resident cells and deforming the biofilm morphology. These findings indicate that biomineralization is a general regulator of biofilm architecture and properties.

Biofilms are surface-attached microbial communities that have complex structures and produce significant spatial heterogeneities. Biofilm development is strongly regulated by the surrounding flow and nutritional environment. Biofilm growth also increases the heterogeneity of the local microenvironment by generating complex flow fields and solute transport patterns. To investigate the development of heterogeneity in biofilms and interactions between biofilms and their local micro-habitat, we grew mono-species biofilms of Pseudomonas aeruginosa and dual-species biofilms of P. aeruginosa and Escherichia coli under nutritional gradients in a microfluidic flow cell. We provide detailed protocols for creating nutrient gradients within the flow cell and for growing and visualizing biofilm development under these conditions. We also present protocols for a series of optical methods to quantify spatial patterns in biofilm structure, flow distributions over biofilms, and mass transport around and within biofilm colonies. These methods support comprehensive investigations of the co-development of biofilm and habitat heterogeneity.

This paper presents an overview of our recent enhanced 3D extended finite element toolkit for Abaqus (XFA3D) for fatigue damage assessment of welded aluminum structures under block loading. To alleviate the computational burden associated with the insertion and propagation of arbitrary cracks in the presence of a welding induced residual stress field, a nodal enriched displacement field coupled with a level set description is integrated with a hybrid implicit and explicit crack representation approach. A simplified residual stress characterization is implemented without invoking two separate analyses during each step of the crack growth. A stress ratio dependent fatigue damage accumulation model is employed for the fatigue damage accumulation under an arbitrary multi-block loading spectrum. Capability demonstration is performed first for simulation of curvilinear fatigue crack growth prediction in a holed plate and a multi-hole beam followed by its application to three welded components with an initial flaw including a butt welded tensile specimen, a cruciform tensile specimen with a semi-elliptical surface flaw, and a welded T-joint with a through-the-thickness crack.

Previous models of biofilms growing in a microbial fuel cell (MFC) have primarily focused on modeling a single growth mechanism: growth via a conductive biofilm matrix, or growth utilizing diffusible electron shuttles or mediators. In this work, we implement both flavors of models in order to explore the competition for space and nutrients in a MFC biofilm populated by both species types. We find that the optimal growth conditions are for bacteria that utilize conductive EPS provided a minimal energy used to create the EPS matrix. Mediator-utilizing bacteria do have favorable niche regions, most notably close to the anode and where exposed to the bulk inflow, where oxidized mediator is readily available.

Biofilm cells are less susceptible to antimicrobials than their planktonic counterparts. While this phenomenon is multifactorial, the ability of the matrix to reduce antibiotic penetration into the biofilm is thought to be of limited importance studies suggest that antibiotics move fairly rapidly through biofilms. In this study, we monitored the transport of two clinically relevant antibiotics, tobramycin and ciprofloxacin, into non-mucoid Pseudomonas aeruginosa biofilms. To our surprise, we found that the positively charged antibiotic tobramycin is sequestered to the biofilm periphery, while the neutral antibiotic ciprofloxacin readily penetrated. We provide evidence that tobramycin in the biofilm periphery both stimulated a localized stress response and killed bacteria in these regions but not in the underlying biofilm. Although it is unclear which matrix component binds tobramycin, its penetration was increased by the addition of cations in a dose-dependent manner, which led to increased biofilm death. These data suggest that ionic interactions of tobramycin with the biofilm matrix limit its penetration. We propose that tobramycin sequestration at the biofilm periphery is an important mechanism in protecting metabolically active cells that lie just below the zone of sequestration.

Let gamma be a Jordan curve in S-2, considered as the ideal boundary of H-3. Under certain circumstances, it is known that for any c is an element of (-1, 1), there is a disc of constant mean curvature c embedded in H-3 with gamma as its ideal boundary. Using analysis and numerical experiments, we examine whether or not these surfaces in fact foliate H-3, and to what extent the known conditions on the curve can be relaxed.

Background: There are many products approved for aesthetic soft tissue augmentation. Despite this abundance, there is limited objective data regarding safety, longevity, and complication rates. Instead, most reports rely on subjective measures to report volume changes and outcomes, making product comparison difficult.Objectives: The authors developed and validated a mathematical model to prospectively calculate and analyze three-dimensional (3D) volumetric changes associated with nasolabial fold augmentation based on human acellular dermis.Methods: Seven consecutive patients were included in this prospective review. The patients underwent nasolabial fold treatment with BellaDerm (Musculoskeletal Transplant Foundation, Edison, NJ), administered by a single surgeon. 3D photographs were obtained and analyzed with a novel mathematical model to determine absolute volumetric changes and objective longevity.Results: Mean preoperative nasolabial fold volume was 0.17 mL. The mean one-, three-, and six-month postoperative fill volumes were 0.35, 0.19, and 0.07 mL, respectively. Fill volumes and contour changes returned to baseline by 24 weeks postoperatively in the majority of patients.Conclusions: The mathematical model utilized in this study provided prospective and objective data regarding longevity and volumetric changes associated with nasolabial fold augmentation. The analysis demonstrated minimal objective filler permanence beyond six months, with peak volume enhancement between one and three months. Adoption of objective 3D mathematical metrics into the assessment of soft tissue filler outcomes is critical to obtaining more accurate product-to-product comparisons.

In this paper, we investigate unsteady behavior of flexible vessels carrying a blood flow. Membrane model with constant tension for the vessel walls and incompressible newtonian fluid approximation for blood is adopted. Developed computational model is applied to simulate the coupled fluid-wall behavior in 2D collapsible channels and 3D collapsible tubes. INTRODUCTION Vessels carrying blood flow in a human body are known to be flexible tissues. Interaction of the internal blood flow with the vessel wall compliance, in addition to significant alteration of the fluid mechanical properties (such as shear and normal stresses) with respect to rigid wall cases, can also result in a variety of interesting mechanical phenomena, such as flow limitation, selfexciting oscillations (flutter), or tube collapse. These phenomena are especially pronounced at higher Reynolds number and thus are relevant to the medical condition of stenosis caused by atherosclerosis, which results in higher local flow rates and elevated risk of collapse manifestation. In the current paper, we investigate the flutter and collapse phenomena in application to 2D collapsible channels and 3D collapsible tubes. We model the elastic vessel wall as a biological membrane with the constant tension and no bending stiffness, supported by a common assumption of negligible bending stiffness in biological materials [1, 2]. We stress, however, that the tube law and the flow limitation regime depend strongly on the elasticity model. Thus, bending rigidity would act to reduce the wall collapse [3] and postpone the onset of divergence and flutter. ∗Address all correspondence to this author. E-mail:y-peet@northwestern.edu. NUMERICAL METHOD Numerical method consists of an Arbitrary LagrangianEulerian (ALE) formulation of incompressible Navier-Stokes equations coupled to a simple constant-tension geometrically nonlinear elastic wall model by the kinematic and traction boundary conditions:

In this paper, we investigate unsteady behavior of flexible vessels carrying a blood flow. Membrane model with constant tension for the vessel walls and incompressible newtonian fluid approximation for blood is adopted. Developed computational model is applied to simulate the coupled fluid-wall behavior in 2D collapsible channels and 3D collapsible tubes.