Electrification in granular gases leads to constrained fractal growth

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas -- a model representative of the above physical processes -- have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the system obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy $\mathcal{B}(t)\le 1$. This constraint on the collective evolution of charged clusters is confirmed both by the theory and the detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanism, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems

Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes

We review our work on generalisations of the Becker-Doring model of cluster-formation as applied to nucleation theory, polymer growth kinetics, and the formation of upramolecular structures in colloidal chemistry. One valuable tool in analysing mathematical models of these systems has been the coarse-graining approximation which enables macroscopic models for observable quantities to be derived from microscopic ones. This permits assumptions about the detailed molecular mechanisms to be tested, and their influence on the large-scale kinetics of surfactant self-assembly to be elucidated. We also summarise our more recent results on Becker-Doring systems, notably demonstrating that cross-inhibition and autocatalysis can destabilise a uniform solution and lead to a competitive environment in which some species flourish at the expense of others, phenomena relevant in models of the origins of life

Kinetic Intersections as a Source of Information on Rate Coefficients

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Multi-Scale Mathematical Modeling of Prion Aggregate Dynamics and Phenotypes in Yeast Colonies

Prion diseases are a multi-scale biological phenomenon that requires understanding intracellular processes as well as how cells interact with each other and their environment. In mammals, prion diseases are progressive, untreatable, and fatal. Yeast prion phenotypes are harmless and reversible, which suggests a deep understanding of the reversal of prion phenotypes in yeast may be informative to mammalian diseases. In yeast, the loss of some prion phenotypes appears to be stochastic and spatially dependent, suggesting a cell-based model of yeast prion dynamics would be a powerful tool for comparisons with experimental results and hypothesis generation. In this work, we consider the components necessary to develop such a model that depicts both the biochemical-, intracellular-, and colony-level scales in yeast prion phenotypes. We first review the literature of mathematical models of the intracellular processes of prion disease. We then review common approaches to cell-based modeling of multicellular systems and how they have led to biological insights in other systems. This chapter ends with a discussion of future studies aimed at motivating how these two types of models can be coupled to produce multi-scale models of prion phenotypes

Multi-Scale Fluctuations in Non-Equilibrium Systems: Statistical Physics and Biological Application

Understanding how fluctuations continuously propagate across spatial scales is fundamental for our understanding of inanimate matter. This is exemplified by self-similar fluctuations in critical phenomena and the propagation of energy fluctuations described by the Kolmogorov-Law in turbulence. Our understanding is based on powerful theoretical frameworks that integrate fluctuations on intermediary scales, as in renormalisation group or coupled mode theory. In striking contrast to typical inanimate systems, living matter is typically organised into a hierarchy of processes on a discrete set of spatial scales: from biochemical processes embedded in dynamic subcellular compartments to cells giving rise to tissues. Therefore, the understanding of living matter requires novel theories that predict the interplay of fluctuations on multiple scales of biological organisation and the ensuing emergent degrees of freedom. In this thesis, we derive a general theory of the multi-scale propagation of fluctuations in non-equilibrium systems and show that such processes underlie the regulation of cellular behaviour. Specifically, we draw on paradigmatic systems comprising stochastic many-particle systems undergoing dynamic compartmentalisation. We first derive a theory for emergent degrees of freedom in open systems, where the total mass is not conserved. We show that the compartment dynamics give rise to the localisation of probability densities in phase space resembling quasi-particle behaviour. This emergent quasi-particle exhibits fundamentally different response kinetics and steady states compared to systems lacking compartment dynamics. In order to investigate a potential biological function of such quasi-particle dynamics, we then apply this theory to the regulation of cell death. We derive a model describing the subcellular processes that regulate cell death and show that the quasi-particle dynamics gives rise to a kinetic low-pass filter which suppresses the response of the cell to fast fluituations in cellular stress signals. We test our predictions experimentally by quantifying cell death in cell cultures subject to stress stimuli varying in strength and duration. In closed systems, where the total mass is conserved, the effect of dynamic compartmentalisation depends on details of the kinetics on the scale of the stochastic many-particle dynamics. Using a second quantisation approach, we derive a commutator relation between the kinetic operators and the change in total entropy. Drawing on this, we show that the compartment dynamics alters the total entropy if the kinetics of the stochastic many-particle dynamics violate detailed balance. We apply this mechanism to the activation of cellular immune responses to RNA-virus infections. We show that dynamic compartmentalisation in closed systems gives rise to giant density fluctuations. This facilitates the emergence of gelation under conditions that violate theoretical gelation criteria in the absence of compartment dynamics. We show that such multi-scale gelation of protein complexes on the membranes of dynamic mitochondria governs the innate immune response. Taken together, we provide a general theory describing the multi-scale propagation of fluctuations in biological systems. Our work pioneers the development of a statistical physics of such systems and highlights emergent degrees of freedom spanning different scales of biological organisation. By demonstrating that cells manipulate how fluctuations propagate across these scales, our work motivates a rethinking of how the behaviour of cells is regulated

Models for Metal Hydride Particle Shape, Packing, and Heat Transfer

A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric model is presented that replicates features of particle size and shape distributions observed experimentally that result from cyclic hydride decreptitation. The quasi-static dense packing of a sample set of these particles is simulated via energy-based structural optimization methods. These particles jam (i.e., solidify) at a density (solid volume fraction) of 0.665+/-0.015 - higher than prior experimental estimates. Effective thermal conductivity of the jammed system is simulated and found to follow the behavior predicted by granular effective medium theory. Finally, a theory is presented that links the properties of bi-porous cohesive powders to the present systems based on recent experimental observations of jammed packings of fine powder. This theory produces quantitative experimental agreement with metal hydride powders of various compositions.Comment: 12 pages, 12 figures, 2 table

Electrification in granular gases leads to constrained fractal growth

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas – a model representative of the above physical processes – have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the granular temperature of the cluster population, the charge variance of the cluster population and the number density of the cluster population evolve in such a way that their non-dimensional combination obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy. This constraint on the collective evolution of charged clusters is confirmed both by our theory and our detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanisms, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems