Alexander Panchenko

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving–Kirkwood–Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

Rise of atmospheric CO₂ is one of the main causes of global warming. Catastrophic climate change can be avoided by reducing emissions and increasing sequestration of CO₂. Trees are known to sequester CO₂ during photosynthesis, and then store it as wood biomass. Thus, breeding of trees with higher wood yield would mitigate global warming as well as augment production of renewable construction materials, energy, and industrial feedstock. Wood is made of cellulose-rich xylem cells produced through proliferation of a specialized stem cell niche called cambium. Importance of cambium in xylem cells production makes it an ideal target for the tree breeding programs; however our knowledge about control of cambium proliferation remains limited. The morphology and regulation of cambium are different from those of stem cell niches that control axial growth. For this reason, translating the knowledge about axial growth to radial growth has limited use. Furthermore, genetic approaches cannot be easily applied because overlaying tissues conceal cambium from direct observation and complicate identification of mutants. To overcome the paucity of experimental tools in cambium biology, we constructed a Boolean network CARENET (CAmbium REgulation gene NETwork) for modelling cambium activity, which includes the key transcription factors WOX4 and HD-ZIP III as well as their potential regulators. Our simulations predict that: (1) auxin, cytokinin, gibberellin, and brassinosteroids act cooperatively in promoting transcription of WOX4 and HD-ZIP III; (2) auxin and cytokinin pathways negatively regulate each other; (3) hormonal pathways act redundantly in sustaining cambium activity; (4) individual cambium cells can have diverse molecular identities. CARENET can be extended to include components of other signalling pathways and be integrated with models of xylem and phloem differentiation. Such extended models would facilitate breeding trees with higher wood yield.

Rise of atmospheric CO ₂ is one of the main causes of global warming. Catastrophic climate change can be avoided by reducing emissions and increasing sequestration of CO ₂ . Trees are known to sequester CO ₂ during photosynthesis, and then store it as wood biomass. Thus, breeding of trees with higher wood yield would mitigate global warming as well as augment production of renewable construction materials, energy, and industrial feedstock. Wood is made of cellulose-rich xylem cells produced through proliferation of a specialized stem cell niche called cambium. Importance of cambium in xylem cells production makes it an ideal target for the tree breeding programs; however our knowledge about control of cambium proliferation remains limited. The morphology and regulation of cambium differs from stem cell niches that control axial growth. For this reason, translating the knowledge about axial growth to radial growth has limited use. Furthermore, genetic approaches cannot be easily applied because overlaying tissues conceal cambium from direct observation and complicate identification of mutants. To overcome the paucity of experimental tools in cambium biology, we constructed a Boolean network CARENET (CAmbium Regulation gene NETwork) for modelling cambium activity, which includes the key transcription factors WOX4 and HD-ZIP III as well as their potential regulators. Our simulations revealed that: (1) auxin, cytokinin, gibberellin, and brassinosteroids act cooperatively in promoting transcription of WOX4 and HD-ZIP III ; (2) auxin and cytokinin pathways negatively regulate each other; (3) hormonal pathways act redundantly in sustaining cambium activity; (4) individual cells in the stem cell niches can have diverse molecular identities. CARENET can be extended to include components of other signalling pathways and be integrated with models of xylem and phloem differentiation. Such extended models would facilitate breeding trees with higher wood yield.

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields a stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

A simple model for simulating flows of active suspensions is investigated. The approach is based on dissipative particle dynamics. While the model is potentially applicable to a wide range of self-propelled particle systems, the specific class of self-motile bacterial suspensions is considered as a modeling scenario. To mimic the rod-like geometry of a bacterium, two dissipative particle dynamics particles are connected by a stiff harmonic spring to form an aggregate dissipative particle dynamics molecule. Bacterial motility is modeled through a constant self-propulsion force applied along the axis of each such aggregate molecule. The model accounts for hydrodynamic interactions between self-propelled agents through the pairwise dissipative interactions conventional to dissipative particle dynamics. Numerical simulations are performed using a customized version of the open-source LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) software package. Detailed studies of the influence of agent concentration, pairwise dissipative interactions, and Stokes friction on the statistics of the system are provided. The simulations are used to explore the influence of hydrodynamic interactions in active suspensions. For high agent concentrations in combination with dominating pairwise dissipative forces, strongly correlated motion patterns and a fluid-like spectral distributions of kinetic energy are found. In contrast, systems dominated by Stokes friction exhibit weaker spatial correlations of the velocity field. These results indicate that hydrodynamic interactions may play an important role in the formation of spatially extended structures in active suspensions.

We study the problem of derivation of an effective model of acoustic wave propagation in a two-phase, non-periodic medium modeling a fine mixture of linear elastic solid and a viscous Newtonian fluid. Bone tissue is an important example of a composite material that can be modeled in this fashion. We extend known homogenization results for periodic geometries to the case of a stationary random, scale-separated microstructure. The ratio ε between a typical size of microstructural inhomogeneity and the macroscopic length scale is a small parameter of the problem. We employ stochastic two-scale convergence in the mean to pass to the limit ε → 0 in the governing equations. The effective model describes a biphasic, viscoelastic material with long-time history dependence. Homogenized system describes macroscopically anisotropic media and is more general than the Biot system.

We outline the mathematical model of the time-harmonic ultrasonic response of wet cortical bone. Using two-scale asymptotics, we derive an effective model of acoustic wave propagation in a two-phase medium modeling a fine mixture of linear piezo-elastic solid and a viscous, Newtonian, ionic bearing fluid. Following the works of Moyne and Murad, and Lemaire et. al. for the quasi-static case, we develop a two-scale homogenization method for the dynamical system, albeit the time harmonic case. The idea is to connect the bulk pressure to the small displacement by an assumption used in acoustics, i.e. the pressure p ≈ - ρ_fa²_f divu; where ρ_f is the fluid density, a_f the speed of sound in the fluid, and u is the displacement. We investigate several time scales; one is associated with high frequency domination which leads to different hierarchies. The ratio ε of a typical size of the microstructural inhomogeneity and the macroscopic length scale is a small parameter of the problem. Another possibly small parameter is the Peclet number which influences the type of effective equations which are obtained. A brief asymptotic analysis is presented.

Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix---ferronematics--- as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and, simultaneously, cause reorientation of the nematic molecules, greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in a physical literature.

The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously derived by a number of authors. These equations are not in closed form because the stress and the heat flux cannot be evaluated without the knowledge of particle positions and velocities. We propose a closure method for approximating fluxes in terms of other meso-scale averages. The main idea is to rewrite the non-linear averages as linear convolutions that relate micro- and meso-scale dynamical functions. The convolutions can be approximately inverted using regularization methods developed for solving ill-posed problems. This yields closed form constitutive equations that can be evaluated without solving the underlying ODEs. We test the method numerically on Fermi-Pasta-Ulam chains with two different potentials: the classical Lennard-Jones, and the purely repulsive potential used in granular materials modeling. The initial conditions incorporate velocity fluctuations on scales that are smaller than the size of the averaging window. The results show very good agreement between the exact stress and its closed form approximation.