Sensitivity of steady states in a degenerately damped stochastic Lorenz system

We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz ’63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant probability measure if and only if noise acts on the convection variable. On the other hand, if there is a positive growth term on the vertical temperature profile, we prove that there is no normalizable invariant state. Our approach relies on the derivation and analysis of nontrivial Lyapunov functions which ensure positive recurrence or null-recurrence/transience of the dynamics.

Secondary instability in thin film flows under an inclined plane: growth of lenses on spatially developing rivulets

The response of a thin film flowing under an inclined plane, modelled using the lubrication equation, is studied. The flow at the inlet is perturbed by the superimposition of a spanwise-periodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the so-called rivulets grow downstream and eventually reach a streamwise-invariant state, modulated along the direction perpendicular to the flow. The linearized dynamics in the presence of a time-harmonic inlet forcing shows the emergence of a time-periodic flow characterized by drop-like structures (so-called lenses) that travel on the rivulet. The spatial evolution is rationalized by a weakly non-parallel stability analysis. The occurrence of the lenses, their spacing and thickness profile, is controlled by the inclination angle, flow rate, and the frequency and amplitude of the time-harmonic inlet forcing. The faithfulness of the linear analyses is verified by nonlinear simulations. The results of the linear simulations with inlet forcing are combined with the computations of nonlinear travelling lenses solutions in a double-periodic domain to obtain an estimate of the dripping length, for a large range of conditions.

Uniform and Completely Nonequilibrium Invariant States for Weak Coupling Limit Type Quantum Markov Semigroups Associated with Eulerian Cycles

We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.

Multiwave pandemic dynamics explained: how to tame the next wave of infectious diseases

Pandemics, like the 1918 Spanish Influenza and COVID-19, spread through regions of the World in subsequent waves. Here we propose a consistent picture of the wave pattern based on the epidemic Renormalisation Group (eRG) framework, which is guided by the global symmetries of the system under time rescaling. We show that the rate of spreading of the disease can be interpreted as a time-dilation symmetry, while the final stage of an epidemic episode corresponds to reaching a time scale-invariant state. We find that the endemic period between two waves is a sign of instability in the system, associated to near-breaking of the time scale-invariance. This phenomenon can be described in terms of an eRG model featuring complex fixed points. Our results demonstrate that the key to control the arrival of the next wave of a pandemic is in the strolling period in between waves, i.e. when the number of infections grows linearly. Thus, limiting the virus diffusion in this period is the most effective way to prevent or delay the arrival of the next wave. In this work we establish a new guiding principle for the formulation of mid-term governmental strategies to curb pandemics and avoid recurrent waves of infections, deleterious in terms of human life loss and economic damage.

Multiwave pandemic dynamics explained: How to tame the next wave of infectious diseases

Pandemics, like the 1918 Spanish Influenza and COVID-19, spread through regions of the World in subsequent waves. Here we propose a consistent picture of the wave pattern based on the epidemic Renormalisation Group (eRG) framework, which is guided by the global symmetries of the system under time rescaling. We show that the rate of spreading of the disease can be interpreted as a time-dilation symmetry, while the final stage of an epidemic episode corresponds to reaching a time scale-invariant state. We find that the endemic period between two waves is a sign of instability in the system, associated to near-breaking of the time scale-invariance. This phenomenon can be described in terms of an eRG model featuring complex fixed points. Our results demonstrate that the key to control the arrival of the next wave of a pandemic is in the strolling period in between waves, i.e. when the number of infections grow linearly. Thus, limiting the virus diffusion in this period is the most effective way to prevent or delay the arrival of the next wave. In this work we establish a new guiding principle for the formulation of mid-term governmental strategies to curb pandemics and avoid recurrent waves of infections, deleterious in terms of human life loss and economic damage.