Introduction of Coupled Map Lattice and Its Application to Simulate the Complex Mechanism of Change from Fresh Cream to Butter via Whipped Cream

Abstract

Coupled map lattice (CML) is a powerful simulation approach that reproduces well complex and diverse patterns and motions in dynamical phenomena with spatial degrees of freedom (Kaneko and Tsuda, 2001). Indeed, CML has simulated various phenomena such as full range boiling (Yanagita, 1992), convection with turbulence transition (Yanagita and Kaneko, 1993), cloud formation predicting ʻguerrilla rainstormsʼ (Yanagita and Kaneko, 1997), and astronomical formation of grand-design spirals (Nozawa, 2020, 2030). We proposed a CML for simulating phase inversion processes (Fujita, 2006) from fresh cream to butter via whipped cream. It is one of complex systems approaches to the pattern formation and self-organization of diverse food textures appearing in the phase inversion processes. The proposed CML has three field variables, surface energy, cohesive energy, and velocity of the emulsion defined on a two-dimensional square lattice, and is constructed by the three simple procedures, whipping, coalescence, and flocculation, acting on the field variables. In the simulations, we have observed two different phase inversion processes at high and low whipping temperatures (WTs). The overrun and viscosity changes in these processes are consistent with those in experiments. The two processes give rise to distinctive spatial patterns of overrun (surface energy) and viscosity (cohesive energy), and are characterized on the viscosity-overrun plane which is one of the state diagrams, as the viscosity-dominant process at high WT and the overrun dominant process at low WT, respectively. The butters obtained in the two processes were of low overrun and viscosity and of high overrun and viscosity, respectively in the butter region, and had, so to say, soft & creamy and hard & f luf f y texture patterns. In the presentation, we will design a new texture (f luf f y & creamy with moderate firmness) by controlling the cooking parameters of the CML procedures based on the above texture difference.