We describe the asymptotic behaviour of entropy solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the forcing. We obtain as a corollary a new result on the flow of the associated Hamiltonian system.

[1] Quasi‐equilibrium (QE) closure is an approximation that is expected to apply to a large ensemble of clouds under slowly changing weather conditions. It breaks down under rapidly changing conditions or when the domain size is too small to provide an adequate sample of the cloud field. We explore fluctuations about an equilibrium state as simulated by a three‐dimensional cloud‐resolving model...

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...

We present a technique for coding sets “into K,” where K is the core model below a strong cardinal. Specifically, we show that if there is no inner model with a strong cardinal then any X ⊂ ω1 can be made ∆3 (in the codes) in a reasonable and stationary preserving set generic extension.

We use model theoretic forcing to study and generalize the construction of (K ,≤)-generic models introduced by Kueker and Laskowski. We characterize the (K ,≤)-generic models in terms of forcing and introduce a more general class of models, called essential forcing generics, which have many of the same properties.

We introduce and study the first-order Generic Vopěnka’s Principle, which states that for every definable proper class of structures C of the same type, there exist B 6= A in C such that B elementarily embeds into A in some set-forcing extension. We show that, for n ≥ 1, the Generic Vopěnka’s Principle fragment for Πn-definable classes is equiconsistent with a proper class of n-remarkable cardi...

We present some results about generics for computable Mathias forcing. The n-generics and weak n-generics in this setting form a strict hierarchy as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing relation, and show that if G is any n-generic with n ≥ 3 then it satisfies the jump property G(n−1) = G′ ⊕ ∅(n). We prove that every such G has generalized high degree, ...

Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to א1. Later we give applications, among them the c...

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the fe...

Influences of the Earth’s astronomical forcing on the evolution of East Asian monsoon have been demonstrated with various geological records and climate models. Here, we present time series of climatic proxies from the Chinese Loess Plateau and Sanbao/Hulu caves and the winter/summer monsoon intensity index from a long-term transient climate model simulation. Both the observations and modelling...