arXiv subjects

Bryan Quaife

Publications and source records attributed to Bryan Quaife.

At least 19 recordsLinked to original sources

arXiv2026

Models of Wildland Fire and Ember Spread

In this Chapter we explore the nature and theory of ember transport using observations from controlled laboratory settings, prescribed fire, and wildland fire. Specific examples and statistics from fires are used to gain insight and motivate a hierarchy of modeling approaches from simple idealized models to full-physics atmospheric boundary layer models. The emphasis is on the fundamental processes involved in moving embers away from their sources in vegetation and structures on and near the ground or in the atmospheric boundary layer winds and turbulent flows. We describe the problem first in terms of basic theory about the rate of spread of wildland fire, examine the physical principles at work in ember transport for two principle modes of transport near the ground and in the atmosphere well above the surface, and connect these to statistical models for transport.

physics.ao-ph↗

arXiv2026

Statistical Models of Ember Wash and Their Impact on Wildfire Area Growth

Wildfire spread is strongly influenced by the transport and ignition of embers. While long-range spotting driven by plume lofting has received significant attention, embers transported near the surface by turbulent winds can also influence fire propagation. We develop a stochastic model for near-surface ember transport, referred to as ember wash. The model represents ember motion as a sequence of short displacements analogous to saltation-like transport and incorporates a probabilistic ignition process that depends on ember survival during transport. This formulation leads to an exponential distribution of ember flight times. The model is implemented within a simplified fire spread model to examine burn patterns and growth dynamics. Simulations demonstrate that ember wash produces spread behavior that differs fundamentally from classical plume-driven spotting. These results suggest that ember wash provides a plausible mechanism for wildfire spread regimes that differ from those predicted by geometric or plume-driven spread models.

physics.ao-ph↗

arXiv2025

Soft-Lubrication Drainage and Rupture in Particle-Driven Vesicles

The deformation and rupture of a lipid vesicle due to the forced normal approach of an inclusion are essential for optimizing the design of magnetic giant unilamellar vesicles [magGUVs, Malik et al., Nanoscale 17, 13720 (2025)], with implications for active colloid-membrane interactions and cellular-scale chemical delivery. Here, we investigate vesicles propelled by a force-driven rigid inclusion and reveal a robust elastohydrodynamic mechanism: the inclusion outpaces the vesicle, sustaining a thinning film that drains symmetrically and self-similarly, largely independent of initial shape. For soft membranes and small inclusions, coupling drives a monotonic tension increase that can exceed the lysis tension. Evaluating the maximal tension over a delivery distance, we map an operating window in vesicle reduced area and size relative to the inclusion.

cond-mat.soft↗

arXiv2025

N Bugs on a Circle

We describe and analyze a generalization of the classic ``Four Bugs on a Square'' cyclic pursuit problem. Instead of allowing the bugs to spiral towards one another, we constrain $N$ bugs to the perimeter of the unit circle. Depending on their configuration, each bug moves either clockwise or counterclockwise with a constant angular speed, or remains stationary. Unlike the original problem where bugs always coalesce, this generalization produces three possible steady states: all bugs coalescing to a single point, clusters of bugs located at two antipodal points, or bugs entering a stable infinite chase cycle where they never meet. We analyze the stability of these steady states and calculate the probability that randomly initialized bugs reach each state. For $N \leq 4$, we derive exact analytical expressions for these probabilities. For larger values, we employ Monte Carlo simulations to estimate the probability of coalescing, finding it approximately follows an inverse square root relationship with the number of bugs. This generalization reveals rich dynamical behaviors that are absent in the classic problem. Our analysis provides insight into how restricting the bugs to the circle's perimeter fundamentally alters the long-term behavior of pursuing agents compared to unrestricted pursuit problems.

math.DS↗

arXiv2025

The Ceiling Height of Wildland Fire Plumes in Sheared Boundary Layer Flow

Radar observations from a prescribed fire experiment reveal a large-scale, billow-like vorticity pair associated with the plume head at the onset of plume bending. The bending confines the ceiling height of the plume, delaying its smoke dispersion and increasing fire spotting risks. This study aims to investigate the onset of plume bending in a sheared crossflow and stratified atmospheric conditions, providing insights into smoke dispersion and fire behavior. Large Eddy Simulations (LES) using the Cloud Model 1 (CM1) are conducted to simulate the observed development of plume structure and its associated dynamical fields, with particular focus on the plume head and its evolution from initial plume development under different fire intensities and atmospheric boundary layer (ABL) conditions. A scaling analysis of plume ceiling height is proposed based on a modified Byram's convective number that accounts for sheared crossflow. The proposed scaling agrees well with the LES results, highlighting the critical roles of shear and stratification in controlling plume dynamics.

physics.flu-dyn↗

arXiv2024

Fire Dynamic Vision: Image Segmentation and Tracking for Multi-Scale Fire and Plume Behavior

The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal scales and image types, identifying physical phenomena in the system and providing insights useful for developing and validating models. Our method combines image segmentation and graph theory to delineate fire fronts and plume boundaries. We demonstrate that the method effectively distinguishes fires and plumes from visually similar objects. Results demonstrate the successful isolation and tracking of fire and plume dynamics across various image sources, ranging from synoptic-scale ($10^4$-$10^5$ m) satellite images to sub-microscale ($10^0$-$10^1$ m) images captured close to the fire environment. Furthermore, the methodology leverages image inpainting and spatio-temporal dataset generation for use in statistical and machine learning models.

cs.CV↗

arXiv2024

Data-Driven Fire Modeling: Learning First Arrival Times and Model Parameters with Neural Networks

Data-driven techniques are being increasingly applied to complement physics-based models in fire science. However, the lack of sufficiently large datasets continues to hinder the application of certain machine learning techniques. In this paper, we use simulated data to investigate the ability of neural networks to parameterize dynamics in fire science. In particular, we investigate neural networks that map five key parameters in fire spread to the first arrival time, and the corresponding inverse problem. By using simulated data, we are able to characterize the error, the required dataset size, and the convergence properties of these neural networks. For the inverse problem, we quantify the network's sensitivity in estimating each of the key parameters. The findings demonstrate the potential of machine learning in fire science, highlight the challenges associated with limited dataset sizes, and quantify the sensitivity of neural networks to estimate key parameters governing fire spread dynamics.

cs.LG↗

arXiv2023

Hydrodynamics of Multicomponent Vesicles Under Strong Confinement

We numerically investigate the hydrodynamics and membrane dynamics of multicomponent vesicles in two strongly confined geometries. This serves as a simplified model for red blood cells undergoing large deformations while traversing narrow constrictions. We propose a new parameterization for the bending modulus that remains positive for all lipid phase parameter values. For a multicomponent vesicle passing through a stenosis, we establish connections between various properties: lipid phase coarsening, size and flow profile of the lubrication layers, excess pressure, and the tank-treading velocity of the membrane. For a multicomponent vesicle passing through a contracting channel, we find that the lipid always phase separates so that the vesicle is stiffer in the front as it passes through the constriction. For both cases of confinement, we find that lipid coarsening is arrested under strong confinement and proceeds at a high rate upon relief from extreme confinement. The results may be useful for efficient sorting lipid domains using microfluidic flows by controlled release of vesicles passing through strong confinement

cond-mat.soft↗

arXiv2022

Effects of Tunable Hydrophobicity on the Collective Hydrodynamics of Janus Particles under Flows

Active colloidal systems with non-equilibrium self-organization is a long-standing, challenging area in biology. To understand how hydrodynamic flow may be used to actively control self-assembly of Janus particles (JPs), we use a model recently developed for the many-body hydrodynamics of amphiphilic JPs suspended in a viscous background flow (JFM, 941, 2022). We investigate how various morphologies arise from tuning the hydrophobic distribution of the JP-solvent interface. We find JPs assembled into uni-lamella, multi-lamella and striated structures. To introduce dynamics, we include a linear shear flow and a steady Taylor-Green mixing flow, and measure the collective dynamics of JP particles in terms of their (a) free energy from the hydrophobic interactions between the JPs, (b) order parameter for the ordering of JPs in terms of alignment of their directors, and (c) strain parameter that captures the deformation in the assembly. We characterize the effective material properties of the JP structures and find that the uni-lamellar structures increases orientation order under shear flow, the multilamellar structure behaves as a shear thinning fluid, and the striated structure possesses a yield stress. These numerical results provide insights into dynamic control of non-equilibrium active biological systems with similar self-organization.

cond-mat.soft↗

arXiv2021

Trapping of Planar Brownian Motion: Full First Passage Time Distributions by Kinetic Monte-Carlo, Asymptotic and Boundary Integral Methods

We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, simple moments of the distribution, such as the mean (MFPT) and variance, are not defined and it is necessary to obtain the full arrival statistics. We describe several methods to obtain these distributions and other associated quantities such as splitting probabilities. One approach combines a Laplace transform of the underlying parabolic equation with matched asymptotic analysis followed by numerical transform inversion. The second approach is similar, but uses a boundary integral equation method to solve for the Laplace transformed variable. To validate the results of this theory, and to obtain the arrival time statistics in very general configurations of absorbers, we introduce an efficient Kinetic Monte Carlo (KMC) method that describes trajectories as a combination of large but exactly solvable projection steps. The effectiveness of these methodologies is demonstrated on a variety of challenging examples highlighting the applicability of these methods to a variety of practical scenarios, such as source inference. A particularly useful finding arising from these results is that homogenization theories, in which complex configurations are replaced by equivalent simple ones, are remarkably effective at describing arrival time statistics.

math.NA↗

arXiv2021

Two-Dimensional Vesicle Hydrodynamics from Hydrophobic Attraction Potential

We develop a new model, to our knowledge, for the many-body hydrodynamics of amphiphilic Janus particles suspended in a viscous background flow. The Janus particles interact through a hydrophobic attraction potential that leads to self-assembly into bilayer structures. We adopt an efficient integral equation method for solving the screened Laplace equation for hydrophobic attraction and for solving the mobility problem for hydrodynamic interactions. The integral equation formulation accurately captures both interactions for near touched boundaries. Under a linear shear flow, we observe the tank-treading deformation in a two-dimensional vesicle made of Janus particles. The results yield measurements of inter-monolayer friction, membrane permeability, and at large shear rates, membrane rupture. The simulations studies include a vesicle in parabolic flow and vesicle-vesicle interactions in shear and extensional flows. The hydrodynamics of the Janus particles vesicle replicate the behaviour of an inextensible elastic vesicle membrane.

cond-mat.soft↗

arXiv2021

On the Spatial and Temporal Order of Convergence of Hyperbolic PDEs

In this work, we determine the full expression for the global truncation error of hyperbolic partial differential equations (PDEs). In particular, we use theoretical analysis and symbolic algebra to find exact expressions for the coefficients of the generic global truncation error. Our analysis is valid for any hyperbolic PDE, be it linear or non-linear, and employing finite difference, finite volume, or finite element discretization in space, and advanced in time with a predictor-corrector, multistep, or a deferred correction method, belonging to the Method of Lines. Furthermore, we discuss the practical implications of this analysis. If we employ a stable numerical scheme and the orders of accuracy of the global solution error and the global truncation error agree, we make the following asymptotic observations: (a) the order of convergence at constant ratio of $\Delta t$ to $\Delta x$ is governed by the minimum of the orders of the spatial and temporal discretizations, and (b) convergence cannot even be guaranteed under only spatial or temporal refinement. An implication of (a) is that it is impractical to invest in a time-stepping method of order higher than the spatial discretization. In addition to (b), we demonstrate that under certain circumstances, the error can even monotonically increase with refinement only in space or only in time, and explain why this phenomenon occurs. To verify our theoretical findings, we conduct convergence studies of linear and non-linear advection equations using finite difference and finite volume spatial discretizations, and predictor-corrector and multistep time-stepping methods. Finally, we study the effect of slope limiters and monotonicity-preserving strategies on the order of accuracy.

math.NA↗

arXiv2021

Hydrodynamics of a Semipermeable Vesicle Under Flow and Confinement

Lipid bilayer membranes have a native (albeit small) permeability for water molecules. Under an external load, provided that the bilayer structure stays intact and does not suffer from poration or rupture, a lipid membrane deforms and its water influx/efflux is often assumed negligible in the absence of osmolarity. In this work we use boundary integral simulations to investigate the effects of water permeability on the vesicle hydrodynamics due to a mechanical load, such as the viscous stress from an external flow deforming a vesicle membrane in free space or pushing it through a confinement. Incorporating the membrane permeability into the framework of Helfrich free energy for an inextensible, elastic membrane as a model for a semipermeable vesicle, we illustrate that, in the absence of an osmotic stress gradient, the semipermeable vesicle is affected by water influx/efflux over a sufficiently long time or under a strong confinement. Our simulations quantify the conditions for water permeation to be negligible in terms of the time scales, flow strength, and confinement. These results shed light on how microfluidic confinement can be utilized to estimate membrane permeability.

cond-mat.soft↗

arXiv2019

Hydrodynamics and rheology of a vesicle doublet suspension

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.

physics.flu-dyn↗

arXiv2017

Pixel-Level Statistical Analyses of Prescribed Fire Spread

Wildland fire dynamics is a complex turbulent dimensional process. Cellular automata (CA) is an efficient tool to predict fire dynamics, but the main parameters of the method are challenging to estimate. To overcome this challenge, we compute statistical distributions of the key parameters of a CA model using infrared images from controlled burns. Moreover, we apply this analysis to different spatial scales and compare the experimental results to a simple statistical model. By performing this analysis and making this comparison, several capabilities and limitations of CA are revealed.

nlin.CG↗

arXiv2017

A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of these modes in the presence of multiple localized defects for a wide range of two-dimensional geometries. The defects result in eigenfunctions with a weak singularity that is resolved by decomposing the solution as a superposition of Green's functions plus a smooth regular part. This method is applied to a variety of regular and irregular domains and two key phenomena are observed. First, careful placement of clamping points can entirely eliminate particular eigenvalues and suggests a strategy for manipulating the vibrational characteristics of rigid bodies so that undesirable frequencies are removed. Second, clamping of the plate can result in partitioning of the domain so that vibrational modes are largely confined to certain spatial regions. This numerical method gives a precision tool for tuning the vibrational characteristics of thin elastic plates.

math.NA↗

arXiv2017

Low-resolution simulations of vesicle suspensions in 2D

Vesicle suspensions appear in many biological and industrial applications. These suspensions are characterized by rich and complex dynamics of vesicles due to their interaction with the bulk fluid, and their large deformations and nonlinear elastic properties. Many existing state-of-the-art numerical schemes can resolve such complex vesicle flows. However, even when using provably optimal algorithms, these simulations can be computationally expensive, especially for suspensions with a large number of vesicles. In this paper, we investigate the effect of a number of algorithmic empirical fixes in an attempt to make low-resolution simulations more stable and more predictive. Based on our empirical studies for a number of flow configurations, we propose a scheme that attempts to integrate these fixes in a systematic way. This low-resolution scheme is an extension of our previous work Quaife and Biros (2014) and Quaife and Biros (2016). Our low-resolution correction algorithms (LRCA) include anti-aliasing and membrane reparametrization for avoiding spurious oscillations in vesicles' membranes, adaptive time stepping and a repulsion force for handling vesicle collisions and, correction of vesicles' area and arc-length for maintaining physical vesicle shapes. We perform a systematic error analysis by comparing the low-resolution simulations of dilute and dense suspensions with their high-fidelity, fully resolved, counterparts. We observe that the LRCA enables both efficient and statistically accurate low-resolution simulations of vesicle suspensions, while it can be 10x to 100x faster.

physics.flu-dyn↗

arXiv2016

An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media

We consider an efficient preconditioner for boundary integral equation (BIE) formulations of the two-dimensional Stokes equations in porous media. While BIEs are well-suited for resolving the complex porous geometry, they lead to a dense linear system of equations that is computationally expensive to solve for large problems. This expense is further amplified when a significant number of iterations is required in an iterative Krylov solver such as GMRES. In this paper, we apply a fast inexact direct solver, the inverse fast multipole method (IFMM), as an efficient preconditioner for GMRES. This solver is based on the framework of $\mathcal{H}^{2}$-matrices and uses low-rank compressions to approximate certain matrix blocks. It has a tunable accuracy $\varepsilon$ and a computational cost that scales as $\mathcal{O} (N \log^2 1/\varepsilon)$. We discuss various numerical benchmarks that validate the accuracy and confirm the efficiency of the proposed method. We demonstrate with several types of boundary conditions that the preconditioner is capable of significantly accelerating the convergence of GMRES when compared to a simple block-diagonal preconditioner, especially for pipe flow problems involving many pores.

math.NA↗