arXiv subjects

David Salac

Publications and source records attributed to David Salac.

At least 19 recordsLinked to original sources

arXiv2026

Damage Prediction of Sintered {\alpha}-SiC Using Thermo-mechanical Coupled Fracture Model

A three-way coupled thermo-mechanical fracture model is presented to predict the damage of brittle ceramics, in particular {\alpha}-SiC, over a wide range of temperatures (20-1400 C). Predicting damage over such a range of temperatures is crucial for thermal protection systems for many systems such as spacecraft. The model, which has been implemented in MOOSE, is divided into three modules: elasticity, damage phase field, and heat conduction. Analytical approaches for determining crack length scales are presented for both simple tension and simple shear. Validation tests are conducted for both flexural strength and fracture toughness over the specified range of temperatures. Flexural strength simulation results fall within the uncertainty region of the experimental data, and mode I fracture toughness simulation results are also in agreement with the experimental data. Mode II and mixed mode fracture toughness simulations results are presented with the modified G-criterion. Finally, the parallel computing capabilities of the model is considered in various scalability tests.

cond-mat.mtrl-sci↗

arXiv2026

The effect of chemical vapor infiltration process parameters on flexural strength of porous {\alpha}-SiC: A numerical model

The flexural strength variability of {\alpha}-SiC based ceramics at elevated temperatures creates the need for an Integrated Computational Materials Engineering (ICME) framework that relates the strength of a specimen directly to its manufacturing process. To create this ICME framework a model must first be developed which establishes a relationship between the chemical vapor infiltration (CVI) process and parameters, the resulting mesoscale pores, and the overall macroscale flexural strength. Here a nonlinear single pore model of CVI is developed used in conjunction with a four-way coupled themo-mechanical damage model. The individual components of the model are tested and a sample system under a four-point bending test is explored. Results indicate that specimens with an initial porosity greater than 30% require temperatures below 1273 K to maintain structural integrity, while those with initial porosities less than 30% are temperature-independent, allowing for optimization of the CVI processing time without compromising strength.

cond-mat.mtrl-sci↗

arXiv2025

A Modified Hermite Radial Basis Function for Accurate Interpolation

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data. Hermite Radial Basis Function (HRBF) methods are an extension of the RBF and improve the overall accuracy by incorporating both function and derivative information. Infinitely smooth kernels, such as the Gaussian, use a shape-parameter to describe the width of support and are widely used due to their excellent approximation accuracy and ability to capture fine-scale details. Unfortunately, the use of infinitely smooth kernels suffers from ill-conditioning at low to moderate shape parameters, which affects the accuracy. This work proposes a Modified HRBF (MHRBF) method that introduces an additional polynomial term to balance kernel behavior, improving accuracy while maintaining or lowering computational cost. Using standard double-precision mathematics, the results indicate that compared to the HRBF method, the MHRBF method achieves lower error for all values of the shape parameter and domain size. The MHRBF is also able to achieve low errors at a lower computational cost as compared to the standard HRBF method.

math.NA↗

arXiv2025

Stochastic Deep Learning Surrogate Models for Uncertainty Propagation in Microstructure-Properties of Ceramic Aerogels

This study presents an integrated computational framework that, given synthesis parameters, predicts the resulting microstructural morphology and mechanical response of ceramic aerogel porous materials by combining physics-based simulations with deep learning surrogate models. Lattice Boltzmann simulations are employed to model microstructure formation during material synthesis process, while a finite element model is used to compute the corresponding mechanical properties. To overcome the prohibitive computational demands of repeated physics-based simulations required for characterizing the impact of microstructure randomness on mechanical properties, surrogate models are developed using Convolutional Neural Networks (CNNs) for both microstructure generation and microstructure-property mapping. CNN training is formulated as a Bayesian inference problem to enable uncertainty quantification and provide confidence estimates in surrogate model predictions, under limited training data furnished by physics-based simulations. Numerical results demonstrate that the microstructure surrogate model effectively generates microstructural images consistent with the morphology of training data across larger domains. The Bayesian CNN surrogate accurately predicts strain energy for in-distribution microstructures and its generalization capability to interpolated morphologies are further investigated. Finally, the surrogate models are employed for efficient uncertainty propagation, quantifying the influence of microstructural variability on macroscopic mechanical property.

cs.CE↗

arXiv2022

Modeling Droplets with Slippery Interfaces

Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential velocity of the inner and outer fluid can differ, with the jump in velocity dependent not only the material properties of the interface but also the stresses applied by the surrounding fluid. In this work a numerical model is presented which is capable of investigating general multiphase fluid systems involving interfacial slip in both two- and three-dimensions. To make the system computationally feasible, a hybrid Navier-Stokes projection method is used, whereby the viscosity, density, and pressure are assumed to be continuous across the interface while the velocity field can experience a jump, which is handled via the Immersed Interface Method. The numerical model is compared to experimental results involving polymer-polymer mixtures and computational results for droplets in extensional flows, showing excellent agreement with both. It is then used to explore the influence of interfacial slip in a number of common multiphase fluid systems, including the shearing of a planar interface, droplet and filament relaxation, and droplets in shear flow, both unbounded and wall-bound.

physics.flu-dyn↗

arXiv2022

On the order of accuracy for finite difference approximations of partial differential equations using stencil composition

Stencil composition uses the idea of function composition, wherein two stencils with arbitrary orders of derivative are composed to obtain a stencil with a derivative order equal to sum of the orders of the composing stencils. In this paper, we show how stencil composition can be applied to form finite difference stencils in order to numerically solve partial differential equations (PDEs). We present various properties of stencil composition and investigate the relationship between the order of accuracy of the composed stencil and that of the composing stencils. We also present comparisons between the stability restrictions of composed higher-order PDEs to their compact versions and numerical experiments wherein we verify the order of accuracy by convergence tests. To demonstrate an application to PDEs, a boundary value problem involving the two-dimensional biharmonic equation is numerically solved using stencil composition and the order of accuracy is verified by performing a convergence test. The method is then applied to the Cahn-Hilliard phase-field model. In addition to sample results in 2D and 3D for this benchmark problem, the scalability, spectral properties, and sparsity is explored.

math.NA↗

arXiv2021

Swinging and tumbling of multicomponent vesicles in flow

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations we develop a reduced order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane in two dimensions with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid body tumbling behavior. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.

cond-mat.soft↗

arXiv2020

Non-equilibrium dynamics of initially spherical vesicles in general flow

Many vesicles have a spherical resting shape and exposure to fluid flows induces an exchange between sub-optical area and visible (systematic) deformation, while the total area is conserved. The dynamics which controls the exchange between sub-optical and visible area depends on membrane properties such as bending rigidity and initial tension. Conversely, observation of these dynamics can be used to determine the membrane properties. The goal of this work is to create a general numerical model which accounts for the exchange between sub-optical and visible area. Unlike prior modeling efforts, the model does not pre-assume a shape type, such as nearly-spherical, or applied flow field, allowing the model to capture a wider variety of flow conditions. Based on implicit interface tracking and using a volume-preserving multiphase Navier-Stokes solver, the model is compared to several experimental results, showing excellent agreement. It is used to explore regimes not possible with previously published models, such as the variable viscosity case, and how these system properties influence experimentally measurable parameters such as deformation parameter. By creating a more generalized framework for the modeling of vesicles with sub-optical area, it will now be possible to make predictions on vesicle material properties from a wider variety of experimental results.

cond-mat.soft↗

arXiv2018

Three-Dimensional Multicomponent Vesicles: Dynamics & Influence of Material Properties

In this work, the nonlinear dynamics of a fully three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase method, the dynamics are systematically studied as a function of the membrane bending rigidity difference between the components, the speed of diffusion compared to the underlying shear flow, and the strength of the phase domain energy compared to the bending energy. Using a pre-segregated vesicle, three dynamics are observed: stationary phase, phase-treading, and a new dynamic called vertical banding. These regimes are very sensitive to the strength of the domain line energy, as the vertical banding regime is not observed when line energy is larger than the bending energy. These findings demonstrate that a complete understanding of multicomponent vesicle dynamics require that the full three-dimensional system be modeled, and show the complexity obtained when considering heterogeneous material properties.

cond-mat.soft↗

arXiv2017

Modeling of Multicomponent Three-Dimensional Vesicles

In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled using a two-phase surface Cahn-Hilliard system, while the interface is captured using a level set jet scheme. The interface is coupled to the surrounding fluid via a variation of energy approach. Sample energies considered include the total bending, variable surface tension energy, and phase segregation energy. The fully coupled system for surface inhomogeneities, and thus varying interface material properties is presented, as are the associated numerical methods. Numerical convergence and sample results demonstrate the validity of the model.

cond-mat.soft↗

arXiv2017

Stochastic Phase Segregation on Surfaces

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modeled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analyzed on two sample surfaces: a unit sphere and a dumbbell using a variety and a statistical analysis of the growth rate is performed. The influence of noise level and mobility is also investigated. It is also shown that a log-normal distribution fits the results well.

cond-mat.soft↗

arXiv2016

Cahn-Hilliard on Surfaces: A Numerical Study

The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme is investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an incomplete Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.

math.NA↗

arXiv2016

Energy Variation of Soft Matter Interfaces

The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total curvature and an underlying surface concentration field, the energy due to an external field, and a phase segregation energy. When considering these energies the variation of material properties such a bending rigidity are taken into account, which results in more general variation expressions. These variations can be used to determine the equilibrium interface and concentration configuration or to determine the driving forces for non-equilibrium situations. While the focus of this work are energies associated with multicomponent vesicles, it can easily be extended to any soft matter interface.

cond-mat.soft↗

arXiv2016

A Stabilized Diffuse-Interface Electroporation Model with a Semi-Analytical Spectral Electrolyte Solver

We develop a diffuse-interface continuum model for membrane electroporation that couples a phase field for pore geometry to a quasi-static electrolyte potential and a spatially varying leaky-dielectric model for the transmembrane voltage. The main contribution is a stabilized time-integration strategy for transmembrane voltage $V_m$: the stiff leakage term is treated implicitly while the electrolyte-to-membrane ionic current is lagged, yielding a closed-form update that removes the restriction imposed by the fast dielectric relaxation time. The electrolyte potential is computed efficiently using a semi-analytical spectral Laplace solver: a 2D DCT in the membrane plane reduces the 3D problem to independent 1D ODEs in $z$, solved in closed form and reconstructed by an inverse transform. The coupled method is robust under grid refinement, reproduces the sharp-interface critical-radius bifurcation, and captures electric-field focusing through conductive pores. We also demonstrate stochastic pore nucleation by adding thermal noise to the phase-field dynamics, enabling fully emergent electroporation events without prescribing initial defects.

cond-mat.soft↗

arXiv2016

Vesicles in magnetic fields

Liposome vesicles tend to align with an applied magnetic field. This is due to the directional magnetic susceptibility difference of the lipids which form the membrane of these vesicles. In this work a model of liposome vesicles exposed to magnetic field is presented. Starting from the base energy of a lipid membrane in a magnetic field, the force applied to the surrounding fluids is derived. This force is then used to investigate the dynamics of vesicle in the presence of magnetic fields.

cond-mat.soft↗

arXiv2015

Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.

math.NA↗

arXiv2015

A General, Mass-Preserving Navier-Stokes Projection Method

The conservation of mass is common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. The fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.

physics.flu-dyn↗

arXiv2015

Dynamics of Three-Dimensional Vesicles in DC Electric fields

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of different fluid and membrane properties. The dynamics of vesicles in the presence of DC electric fields is considered, both in the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full Prolate-Oblate-Prolate transition.In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.

cond-mat.soft↗