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Register a new userQuasistatic rheology of soft cellular systems using Cellular Potts Model
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Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model. The accuracy of the method is tested by simulating the quasistatic strain 2D dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular systems.
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The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in the scientific literature to evolve this model preserves connectivity of cells on a limited range of simulation temperature only. We present a new algorithm in which cell fragmentation is forbidden for all simulation temperatures. This allows to significantly enhance realism of the simulated patterns. It also increases the computational efficiency compared with the standard CPM algorithm even at same simulation temperature, thanks to the time spared in not doing unrealistic moves. Moreover, our algorithm restores the detailed balance equation, ensuring that the long-term stage is independent of the chosen acceptance rate and chosen path in the temperature space.
Many systems, including biological tissues and foams, are made of highly packed units having high deformability but low compressibility. At two dimensions, these systems offer natural tesselations of plane with fixed density, in which transitions from ordered to disordered patterns are often observed, in both directions. Using a modified Cellular Potts Model algorithm that allows rapid thermalization of extensive systems, we numerically explore the order-disorder transition of monodisperse, two-dimensional cellular systems driven by thermal agitation. We show that the transition follows most of the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory developed for melting of 2D solids, extending the validity of this theory to systems with many-body interactions. In particular, we show the existence of an intermediate hexatic phase, which preserves the orientational order of the regular hexagonal tiling, but looses its positional order. In addition to shedding light on the structural changes observed in experimental systems, our study shows that soft cellular systems offer macroscopic systems in which KTHNY melting scenario can be explored, in the continuation of Braggs experiments on bubble rafts.
We study the rheology of a soft particulate system where the inter-particle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions ($phi$), attraction strengths ($u$) and imposed shear-rates ($dot{gamma}$). In striking contrast to repulsive systems, we find that at small shear-rates generically a fragile isostatic solid is formed even if we go to $phi ll phi_J$. Further, with increasing shear-rates, even at these low $phi$, non-monotonic flow curves occur which lead to the formation of persistent shear-bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough $phi$, we also observe structural changes via the interplay of low shear-rates and attraction with the formation of micro-clusters and voids. Finally, we characterize the properties of the emergent shear bands and thereby, we find surprisingly small mobility of these bands, leading to prohibitely long time-scales and extensive history effects in ramping experiments.
We present the first experimental realization of a ratchet cellular automaton (RCA) which has been recently suggested as an alternative approach for performing logical operations with interacting (quasi) particles. Our study was performed with interacting colloidal particles which serve as a model system for other dissipative systems i.e. magnetic vortices on a superconductor or ions in dissipative optical arrays. We demonstrate that noise can enhance the efficiency of information transport in RCA and consequently enables their optimal operation at finite temperatures.
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added onto a site. Whenever the local energy content of a site reaches a fixed threshold $E_{c1}$, energy will be dissipated. Dissipation of energy propagates to the neighboring sites provided that the energy contents of those sites are greater than or equal to another fixed threshold $E_{c2} (leq E_{c1})$. Under such dynamics, the system evolves into three different types of states depending on the values of $E_{c1}$ and $E_{c2}$ as reflected in their dissipation size distributions, namely: localized peaks, power laws, or exponential laws. This model is able to describe the behaviors of various physical systems including the statistics of burst sizes and burst rates in type-I X-ray bursters. Comparisons between our model and the famous forest-fire model (FFM) are made.
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