TY - GEN A1 - Bestehorn, Michael A1 - Bestehorn, Michael A1 - Michelitsch, Thomas M. A1 - Collet, Bernard A. A1 - Riascos, Alejandro P. A1 - Nowakowski, Andrzej. F. T1 - Simple model of epidemic dynamics with memory effects T2 - Physical Review E N2 - We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model. KW - Bifurcations KW - Diseases KW - Dynamics of networks KW - Patterns in complex systems KW - Nonlinear Dynamics KW - Interdisciplinary Physics KW - Biological Physics Y1 - 2022 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.024205 U6 - https://doi.org/10.1103/PhysRevE.105.024205 SN - 2470-0045 VL - 105 IS - 2 SP - 024205-1 EP - 024205-10 ER - TY - GEN A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael A1 - Sharma, Deewakar A1 - Amiroudine, Sakir T1 - Phase field modeling in liquid binary mixtures: isothermal and non-isothermal problems T2 - Physical Review Fluids N2 - The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached. KW - Binary fluids KW - Drop coalescence KW - Drop interactions KW - Drops & bubbles KW - Microfluidics Y1 - 2022 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.064005 U6 - https://doi.org/10.1103/PhysRevFluids.7.064005 SN - 2469-990X VL - 7 IS - 6 SP - 1 EP - 19 ER -