5 problems

Consider a finite multi-floor TASEP with $c\ge 1$ floors and attempted particle arrival and departure rates $\alpha>0$ and $\beta>0$. Let … and let … Assume condition (a): $L^*$ co…

Let a Hamiltonian dynamical system exhibit mixed chaos, with chaotic trajectories and islands of regularity in its phase space. Suppose the system is weakly coupled to a thermal ba…

Let $N$ particles occupy a volume $V$, with density $d=N/V$. Let $\m_{\d,T}$ be the SRB distribution of the reversible Gaussian-thermostatted model at kinetic-energy parameter $T$,…

Continuum rotating-states conjecture. For every sufficiently large $\beta$, there exists $N=N(\beta)$ such that, for every $N\geq N(\beta)$ and every $d>0$, the driven $N$-clock mo…

Rotating-state conjecture. For every $N\geq\bar N$ and $\beta>\beta_N^{cr}$, there exists a critical drift $d_{cr}(\beta,N)>0$ such that, if $|d|<d_{cr}(\beta,N)$, then…