Martin Grant

• BSc (UPEI), MSc, PhD (Toronto)
• Professor at McGill University

In order to study the effect of cell elastic properties on the behavior of assemblies of motile cells, this paper describes an alternative to the cell phase field (CPF) we have previously proposed. The CPF is a multi-scale approach to simulating many cells which tracked individual cells and allowed for large deformations. Though results were largel...

We propose a multiscale model for monolayer of motile cells that comprise normal and cancer cells. In the model, the two types of cells have identical properties except for their elasticity; cancer cells are softer and normal cells are stiffer. The goal is to isolate the role of elasticity mismatch on the migration potential of cancer cells in the...

In this paper we present a model for an immune response to an invading pathogen. Particularly, we follow the motion of a neutrophil as it migrates to the site of infection guided by chemical cues, a mechanism termed chemotaxis, with the ability to reorient itself as the pathogen changes its position. In the process, the cell undergoes morphological...

We calculate the line tension between domains in phase separated, ternary membranes that comprise line active molecules (linactants) that tend to increase the compatibility of the two phase separating species. The predicted line tension, which depends explicitly on the linactant composition and temperature, is shown to decrease significantly as the...

Two essential elements required to generate a glass transition within phase-field-crystal (PFC) models are outlined based on observed freezing behaviors in various models of this class. The central dynamic features of glass formation in simple binary liquids are qualitatively reproduced across 12 orders of magnitude in time by applying a physically...

The interplay between liquid crystallinity and microphase separation in comblike liquid-crystalline diblock copolymers is examined via a Brazovskii-type phenomenological model using both analytical and numerical calculations. For symmetric diblock copolymers we determine a critical electric field that is required to tilt the orientation of the cons...

Crystalline solids undergo plastic deformation and subsequently flow when subjected to stresses beyond their elastic limit. In nature most crystalline solids exist in polycrystalline form. Simulating plastic flows in polycrystalline solids has wide ranging applications, from material processing to understanding intermittency of earthquake dynamics....

A new isotropic magneto-elastic phase field crystal (PFC) model to study the relation between morphological structure and magnetic properties of pure ferromagnetic solids is introduced. Analytic calculations were used to determine the phase diagram and obtain the relationship between elastic strains and magnetization. Time dependent numerical simul...

To simulate the motion of neutrophils and their morphodynamics in response to chemical cues, we construct a model based on the phase-field method utilizing a description with a free-energy functional and associated dynamics which captures the basic features of the phenomenon. We additionally incorporate spatial sensing by introducing an auxiliary f...

Chemotropism is the action of targeting a part of the cell by means of chemical mediators and cues, and subsequently delimiting the pathway that it should undertake. In a neural cell, this initiates axonal elongation. Herein we model this growth, where chemotropic forcing leads the axon, by a phase field method utilizing two dynamical fields assign...

We present a method for studying the influence of internal rotational degrees of freedom on the elastic properties of crystals composed of ellipsoidal particles. We derive the conditions under which a stretched-triangular lattice of ellipsoidal particles can exhibit a vanishing shear modulus. Analytical predictions are confirmed with numerical calc...

Plastic deformation in solids induced by external shear stress is of huge practical interest. Presence of local crystalline order in polycrystals, consisting of many grains, distinguishes its deformation pattern from that of amorphous materials. Despite strong anisotropy, induced by external stress, the plastic flow and the consequent deformation f...

We investigate the electrically induced lamellar contraction in microphase separated liquid-crystalline diblock copolymer using the phase field-crystal model. We demonstrate that collective rotations of the constituents liquid-crystal molecules relative to the layer normal can lead to unusually large changes of the lamellar spacing. We also demonst...

The role of space in determining species coexistence and community structure is well established. However, previous studies mainly focus on simple competition and predation systems, and the role of mutualistic interspecies interactions is not well understood. Here we use a spatially explicit metacommunity model, in which new species enter by a muta...

The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass for...

The role of space in determining species coexistence and community structure is well established. However, previous studies mainly focus on simple competition and predation systems, and the role of mutualistic interspecies interactions is not well understood. Here we use a spatially explicit metacommunity model, in which new species enter by a muta...

An approximate late time solution to the dynamics of phase separation for a nonconserved ordering order parameter (ø) coupled to a stable conserved field (c) is presented. In the Halperin Hohenberg(1) classification scheme this model is known as Model C with a symmetric coupling between nonconserved and conserved fields. The different time dependen...

The significant role of space in maintaining species coexistence and determining community structure and function is well established. However, community ecology studies have mainly focused on simple competition and predation systems, and the relative impact of positive interspecific interactions in shaping communities in a spatial context is not w...

Structural properties of flexible nematic diblock copolymers in the lamellar phase are investigated using a mean-field model. We address two complementary questions on the mechanics of the system: 1) How does the nematic order affect the elasticity of the one-dimensional solid? 2) What effect does the block copolymer microstructure has on the orien...

Positive interactions are widely recognized as playing a major role in the organization of community structure and diversity. As such, recent theoretical and empirical works have revealed the significant contribution of positive interactions in shaping species’ geographical distributions, particularly in harsh abiotic conditions. In this report, we...

Here we discuss experimental and theoretical evidences supporting an enhancement of water structure around non-polar solutes. This enhancement leads to the hydrophobic effect as described by the iceberg model. We emphasize that the iceberg model is useful and has accounted for insights into hydrophobicity but it should not be taken literally.

The significant role of space in maintaining species coexistence and determining community structure and function is well established. However, community ecology studies have mainly focused on simple competition and predation systems, and the relative impact of positive interspecific interactions in shaping communities in a spatial context is not w...

We use molecular dynamics to study the nucleation of cracks in a two-dimensional material without pre-existing cracks. We study models with zero and nonzero shear moduli. In both situations, the time required for crack formation obeys an Arrhenius law, from which the energy barrier and prefactor are extracted for different system sizes. For large s...

The dynamics of cellular organelles reveals important information about their functioning. The spatio-temporal movement patterns of vesicles in growing pollen tubes are controlled by the actin cytoskeleton. Vesicle flow is crucial for morphogenesis in these cells as it ensures targeted delivery of cell wall polysaccharides. Remarkably, the target r...

The time dependence of the Fourier transform phase of coherently scattered radiation from a system undergoing ordering is studied. Specifically, we derive a simple model that takes into account the known scaling laws for ordering dynamics to predict the statistical behavior of the Fourier transform phase. We consider a two-dimensional system of dom...

In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduc...

The hydrophobic effect is considered the main driving force for protein folding and plays an important role in the stability of those biomolecules. Cold denaturation, where the native state of the protein loses its stability upon cooling, is also attributed to this effect. It is therefore not surprising that a lot of effort has been spent in unders...

We use molecular dynamics to study the nucleation of cracks in a two dimensional material without pre-existing cracks. We study models with zero and non-zero shear modulus. In both situations the time required for crack formation obeys an Arrhenius law, from which the energy barrier and pre-factor are extracted for different system sizes. For large...

We find that curvature-driven growth of pores in electrically charged membranes correctly reproduces charge-pulse experiments. Our model, consisting of a Langevin equation for the time dependence of the pore radius coupled to an ordinary differential equation for the number of pores, captures the statistics of the pore population and its effect on...

We present an algorithm for phase retrieval based on improvements to the methods developed by Bates [see Optik 61, 247 (1982) ]. Specifically, we have developed a more precise way of calculating phase differences between adjacent actual sampling points. This leads to a reduction in the error buildup in a recursive phase propagation scheme. Our appr...

We present a spatial, individual-based predator–prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefine...

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pres...

Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal network is found to have soft shear deformations. T...

We examine a phase field crystal model for simple liquid-solid systems consisting of a free energy functional related to the Ramakrishnan-Yussouff free energy of classical density functional theory and an equation of motion capable of describing long-time-scale behavior in the deeply supercooled regime. The thermodynamics and dynamics of freezing a...

We study the dependence of friction on surface roughness, sliding velocity, and temperature. Expanding on the classic treatment of Greenwood and Williamson, we show that the fractal nature of a surface has little influence on the real area of contact and the static friction coefficient. A simple scaling argument shows that the static friction exhib...

We elucidate the mechanism of cold denaturation through constant-pressure simulations for a model of hydrophobic molecules in an explicit solvent. We find that the temperature dependence of the hydrophobic effect induces, facilitates, and is the driving force for cold denaturation. The physical mechanism underlying this phenomenon is identified as...

Phase field crystals (PFC) are a tool for simulating materials at the atomic level. They combine the small length-scale resolution of molecular dynamics (MD) with the ability to simulate dynamics on mesoscopic time scales. We show how PFC can be interpreted as the result of applying coarse-graining in time to the microscopic density field of molecu...

The hydrodynamics of isothermal solids is studied via a nonlinear dynamic extension of classical density functional theory. Results are obtained for the diffusion coefficient, sound attenuation, sound speed, correlation functions, and other quantities. The domain of validity of phenomenological phase field models is examined and shown to be restric...

Dislocation and grain boundary melting are studied in three dimensions using the Phase Field Crystal method. Isolated dislocations are found to melt radially outward from their core, as the localized excess elastic energy drives a power law divergence in the melt radius. Dislocations within low-to-mid angle grain boundaries melt similarly until an...

We elucidate the mechanism of cold denaturation through constant-pressure simulations for a model of hydrophobic molecules in an explicit solvent. We find that the temperature dependence of the hydrophobic effect is the driving force/induces/facilitates cold denaturation. The physical mechanism underlying this phenomenon is identified as the destab...

We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefine...

In this paper the relationship between the classical density functional theory of freezing and phase-field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase-field crystal modeling and standard models of binary alloys (i.e....

Changes in the connections of neurons in the visual cortex occuring around the time of birth of a primate result in a pattern of occular dominance stripes on layer IV of the cortex itself in primates with normal visual experience. In the case of monocular deprivation during this period, the stripes are no longer regularily spaced and sometimes "cor...

We present a new deterministic algorithm for simulated annealing and demonstrate its applicability with several classical examples: the ground state energies of the 2d and 3d short range Ising spin glasses, the traveling salesman problem, and pattern recognition in computer vision. Our algorithm is based on a microcanonical Monte Carlo method and i...

The dynamics of the glass transition and structure of the disordered phase are studied using the Phase Field Crystal (PFC) model in two and three dimensions. It is shown that a kinetically driven glass transition is produced in 3D for sufficiently large cooling rates. Analysis of free energy barriers indicates that the glass phase is more accessibl...

We study the structural stability of models of proteins for which the selected folds are unusually stable to mutation, that is, designable. A two-dimensional hydrophobic-polar lattice model was used to determine designable folds and these folds were investigated through Langevin dynamics. We find that the phase diagram of these proteins depends on...

We show how an extended object's strain field is redistributed when the material ruptures under by thermal activation. Through analytical calculations and molecular dynamics simulations, we show that in a polymer chain the distribution is exponentially localized around the point of rupture. The length scale of localization is determined by the stra...

In this paper the relationship between the density functional theory of freezing and phase field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase field crystal modeling and standard models of binary alloys (i.e., regular...

We present a phase field model for the surface corrugation of elastically stressed films where the surface diffusion is a dominant mass-transport mechanism. The conserved order parameter is used to describe the state of system and the phase mobility is defined as a function of the order parameter in order to make the mass transport occur only in in...

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the phase field crystal model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two-dimensional hexagonal lattice. It is...

Among an infinite number of possible folds, nature has chosen only about 1000 distinct folds to form protein structures. Theoretical studies suggest that selected folds are intrinsically more designable than others; these selected folds are unusually stable, a property called the designability principle. In this paper we use the 2D hydrophobic-pola...

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the Phase Field Crystals (PFC) model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two dimensional hexagonal lattice...

The phase separation kinetics of a binary fluid is studied analytically through an effective one-fluid model with a random force spectrum determined self-consistently: the rate of kinetic energy injection by the random force is consistent with the droplet coalescence rate. Our detailed results for the rates of energy dissipation and kinetic energy...

Atomic stick-slip processes have been studied in detail by means of friction force microscopy with high spatial and temporal resolution. The influence of the tip-sample contact on the thermal fluctuations of the force sensor and on the dynamics of the stick-slip process are characterized. Results are compared with simulations based on an extended T...

We use molecular dynamics to determine the force needed to rupture a chain molecule being stretched at constant loading rate and temperature. When all energy bonds of the molecule are identical, we find that the force F depends on the pulling rate r and temperature T according to F approximately const- T(1/3)|ln (r/T)|(1/3). When a single weak bond...

We introduce a phase field model which permits the study of the morphological evolution of second phase particles coherently precipitated from the mother phase in elastically stressed alloys. The model has three field variables: the concentration of solute atoms, the displacement field, and the phase field. These fields are coupled via interaction...

The phase field crystal (PFC) method of studying nonequilibrium phenomena involving elastic and plastic deformations was introduced. The method was applied to various phenomena including epitaxial growth, material hardness, grain growth, reconstructive phase transitions, crack propagation and spinodal decomposition. The phase diagram, linear elasti...

When coherent radiation is scattered from a phase-ordering material, a characteristic speckled pattern is formed. The speckled intensity is proportional to the square of the Fourier transform of the order parameter. However, the phase information is lost and the real-space image (inverse Fourier transform) cannot be reconstructed without it. We int...

We introduce a continuum model to describe the development of morphological instabilities and finger formation in strained polymer films. Such phenomena are commonly observed e.g. during the peeling of adhesives and craze growth in polymer glasses. We treat the polymer as a non-Newtonian viscous fluid and simulate the resulting free-boundary proble...

We introduce a continuum model of electrophotographic printing of paper and other disordered composite films. The model allows simulation of any dielectric distribution within a toner transfer gap. It is used to elucidate the role of mass density and paper thickness variations on toner transfer efficiency in Xerographic printing. Our simulations sh...

We simulate directional solidification using a phase-field model solved with adaptive mesh refinement. For small surface tension anisotropy directed at 45 degrees relative to the pulling direction we observe a crossover from a seaweed to a dendritic morphology as the thermal gradient is lowered, consistent with recent experimental findings. We show...

The non-equilibrium properties of a driven quasi-one dimensional superconducting ring subjected to a constant electromotive force ({\it emf}) is studied. The {\it emf} accelerates the superconducting electrons until the critical current is reached and a dissipative phase slip occurs that lowers the current. The phase slip phenomena is examined as a...

The nonequilibrium properties of a driven quasi-one-dimensional superconducting ring subjected to a constant electromotive force (emf) is studied. The emf accelerates the superconducting electrons until the critical current is reached and a dissipative phase slip occurs that lowers the current. The phase-slip phenomena is examined as a function of...

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read a...

A lattice Boltzmann model for viscoelastic flow simulation is proposed. Elastic effects are taken into account within the framework of a Maxwell model. To test the approach, we estimate the transverse velocity autocorrelation function for a freely evolving system, and find clear manifestations of shear at large frequencies. We then characterize bou...

We introduce a continuum model of elasticity in a nonequilibrium multiphase system—including smooth and singular strains, as well as their coupling to free surfaces—and apply it to the dynamics of misfitting heteroepitaxial films. Above a critical thickness, defects relieve strain, competing with an instability at the interface. Depending on their...

We introduce a continuum model of elasticity in a nonequilibrium multiphase system—including smooth and singular strains, as well as their coupling to free surfaces—and apply it to the dynamics of misfitting heteroepitaxial films. Above a critical thickness, defects relieve strain, competing with an instability at the interface. Depending on their...

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at non-zero temperatures. We find that stick-slip motion occurs and that the average frictional force follows $|\ln v|^{2/3}$, where $v$ is the tip velocity. This compares well to recent experimental work (Gnecco et al, PRL 84, 1172), permitting the...

The curved actin "comet-tail" of the bacterium Listeria monocytogenes is a visually striking signature of actin polymerization-based motility. Similar actin tails are associated with Shigella flexneri, spotted-fever Rickettsiae, the Vaccinia virus, and vesicles and microspheres in related in vitro systems. We show that the torque required to produc...

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena that includes order-disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the "sharp-interface lim...

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read...

We simulate solidification in a narrow channel through the use of a phase-field model with an adaptive grid. In different regimes, we find that the solid can grow in fingerlike steady-state shapes, or become unstable, exhibiting unsteady growth. At low melt undercoolings, we find good agreement between our results, theoretical predictions, and expe...

The cytoplasm of living cells provides a complex fluid environment in which intracellular bacteria live and move. By analyzing the easily visible curved actin ``comet-tail'' of polymerization-based-motility bacteria such as Listeria monocytogenes, we can learn about sub-micron structure and dynamics of the tail and of the bacterial surface enzyme t...

We study the growth dynamics of strained heteroepitaxial films in two dimensions. We use a continuum model that, for the first time, incorporates elastic relaxation, dislocation nucleation, and dislocation dynamics. Our model recovers the Matthews-Blakeslee condition for the critical thickness. We find that the film morphology of supercritical film...

A new model is developed for crystal growth that directly incorporates the symmetries of a crystal phase into a continuum field. The model includes plastic and elastic deformations in a natural manner and is used to study crystal and epitaxial growth.

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface l...

A phase-field model of eutectic growth is proposed in terms of a free energy F, which is a functional of a liquid-solid order parameter psi, and a conserved concentration field c. The model is shown to recover the important features of a eutectic phase diagram and to reduce to the standard sharp-interface formulation of nonequilibrium growth. It is...

Numerical and analytical results( G. Brown, et al., Phys. Rev. E 56), 6601 (1997); 60, 5151 (1999). applicable to the time-dependent intensity covariance of the speckle intensity at wave vector k ne 0 are presented. That the covariance can be used to experimentally measure the two-time structure factor of phase-segregating materials is established...

Using Brownian dynamics, we simulate the fracture of polymer interfaces reinforced by diblock connector chains. We consider the mushroom regime, where connector chains are grafted with low surface density, for the case of large pulling velocities. We find that for short chains the interface fracture toughness depends linearly on the degree of polym...

We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, we find that the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of...

We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of channels of...

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as...

Using Brownian dynamics, we simulate the fracture of polymer interfaces reinforced by diblock connector chains. We find that for short chains the interface fracture toughness depends linearly on the degree of polymerization $N$ of the connector chains, while for longer chains the dependence becomes $N^{3/2}$. Based on the geometry of initial chain...

We present a new model for the entire process of phase-separation that combines steady-state homogeneous nucleation theory with the classical Lifshitz-Slyozov mechanism of ripening, modified to account for the substantial correlations among the droplets. A set of self-consistent interface equations describes the decay of metastable states, incorpor...

If there exists an asymptotic scaling regime for spinodal decomposition in phase-separating fluids where domain sizes follow L_tn, then, it is argued, the growth exponent n is no larger than 1/2.

The authors use Monte Carlo methods to investigate a purely dynamical model for structural glasses. They observe stretched exponential decays of the equilibrium autocorrelation function and measure the late-time relaxation times tau . These diverge with temperature following a Vogel-Fulcher law. They also study systems which are quenched deeply and...

A class of phase-front dynamics equations is investigated through a particular singular perturbative expansion in a late-time, restricted-wavelength limit. The approximate solution provides a detailed description of the dynamics of pattern formation in all dimensions and reproduces some aspects of marginal stability theory in one dimension. A unive...

65C05 Monte Carlo methods 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs 82C80 Numerical methods (Monte Carlo, series resummation, etc.) 82D25 Crystals (For crystallographic group theory, see 20H15)