Related papers: Non-determinism in the limit of nonsmooth dynamics
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
Two coupled, interpenetrating fluids suffer instabilities beyond certain critical counterflows. For ideal fluids, an energetic instability occurs at the point where a sound mode inverts its direction due to the counterflow, while dynamical…
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
This study is motivated by two different, yet, connected, motivations. The first one follows the observation that the classical definition of derivatives involves prospective (or forward) difference quotients, not known whenever the time is…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
This paper provides a formal econometric framework behind the newly developed difference-in-discontinuities design (DiDC). Despite its increasing use in applied research, there are currently limited studies of its properties. We formalize…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences…
We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…