This paper explores the dynamic properties of price-based policies in a model of competition between two jurisdictions. Jurisdictions invest over time in infrastructure to increase the quality of the environment, a global public good. They are identical in all respects but one: initial stocks of infrastructure. This is a dynamic type of heterogeneity that disappears in the long run. Therefore, ...

For Diesel engines, the determination of the exit conditions of the injector nozzle flow is of great importance because it greatly influences the spray development inside the combustion chamber and hence the combustion process. In addition, it is relevant to know the flow conditions to provide the initial conditions for spray models. Since the possibility of experimentally observing and measuri...

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end we impose a pressure and gap-dependent thermal boundary condition. This condition, known as the Barber condition, couples the thermal and elastic problems....

We study an elementary two-player card game where in each round players compare cards and the holder of the card with the smaller value wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn randomly. We obtain an exact solution for arbitrary initial conditions. In general, the game approaches a steady state where the card value densities o...

We have developed a set of numerical tools for the quantitative analysis of defect dynamics in quasiperiodic structures. We have applied these tools to study dislocation motion in the dynamical equation of Lifshitz and Petrich [Phys. Rev. Lett. 79 (1997) 1261] whose steady state solutions include a quasiperiodic structure with dodecagonal symmetry. Arbitrary dislocations, parameterized by the h...

Hall magnetohydrodynamics (MHD) properties near a two-dimensional (2D) X-type magnetic neutral line in the steady state are considered. Upon considering the steady-state as the asymptotic limit of the corresponding time-dependent problem and using a rigorous development, Hall effects are shown to be or not to be able to sustain the hyperbolicity of the magnetic field (and hence a more open X-po...

The proportionality between raindrop-driven soil erosion delivery and area of soil exposed to raindrops under a uniform precipitation rate was investigated in terms of individual size classes using laboratory flume experiments. In particular, we examined the dependence of soil erosion on the area exposed to raindrop detachment. Twelve experiments were performed on the same laboratory flume, fil...

The Ehrenfest urn is a model for the diffusion of gases between two chambers. Classic research deals with this system as a Markovian model with a fixed number of balls, and derives the steady-state behavior as a binomial distribution (which can be approximated by a normal distribution). We study the gradual change for an urn containing n (a very large number) balls from the initial condition to...

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the infinite-size limit). Consequently, empirical studies also seek to verify the steady-state prediction in real data. The caveat concomitant with confining the analysis ...

This paper contains rigorous results for a simple stochastic model of heat conduction similar to the KMP (Knipnis–Marchiori–Presutti) model but with possibly energydependent interaction rates. We prove the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, and exponential convergence to steady states from suitable initial conditions.