Soils developed on Quaternary fluvial fill terraces in the humid tropics of Costa Rica display progressive changes in mineral assemblage, chemical composition and particle size with age. Clay minerals from B horizons of active floodplains are predominantly smectite with lesser amounts of disordered kaolinite. B horizons in 5 to 10 ka soils consist of sub-equal amounts of smectite and disordered kaolinite, and soils on 37–125 ka terraces consist of disordered kaolinite with only traces of smectite. The composition of the smectite, as determined by EDX scans of smectite-rich pore space, is [(Mg0.2,Ca0.1)(Fe0.6Al1.4)(Si3.6Al0.4)O10(OH)2], consistent with ferruginous beidellite.

Bulk mineral assemblage varies from a smectite-plagioclase-augite-quartz-magnetite assemblage in ⩽ 10 ka terrace soils to a disordered kaolinite-goethite-hematite-quartz-magnetite assemblage in ⩾37 ka terrace soils. Leaching results in rapid loss of soluble base cations and residual concentration of Ti and Zr indicates mass losses of ∼50% by chemical denudation by 125 ka. Plots of terrace age vs. various measures of clay mineralogy, chemical composition, and particle size produce parabolic curves consistent with rapid chemical weathering pre-37 ka and slower to imperceptible rates of change from 37 to 125 ka. For some pedogenic properties, particularly particle size and concentrations of base cations and Zr, soils appear to reach steady-state conditions within 37 ka.

These results were applied to interpretation of landscape evolution in this tectonically active region by: (1) facilitating identification of two Holocene (5 ka and 10 ka) terraces on the Esterillos Block 5–30 m above sea level (masl), and two Pleistocene terraces ⩾ 125 ka on the Parrita Block 30 masl, and, in turn, (2) documenting uplift rates as high as 4.4 m/ka between 37 and 10 ka on the Esterillos Block, and as low as 0.1 m/ka over the past 125 ka on the adjacent Parrita Block. These findings are consistent with previous work indicating that the subduction of anomalous bathymetric features at the Middle America Trench is having a significant impact on fore-arc dynamics and topography over relatively short geological time periods and spatial scales.

We study weighted ensemble, an interacting particle method for sampling distributions of Markov chains that has been used in computational chemistry since the 1990s. Many important applications of weighted ensemble require the computation of long time averages. We establish the consistency of weighted ensemble in this setting by proving an ergodic theorem for time averages. As part of the proof, we derive explicit variance formulas that could be useful for optimizing the method.

We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size $b-1$ with $b=O(\sqrt{\log N})$, i.e. a server can have at most one job in service and $b-1$ jobs queued. We focus on the steady-state performance of load-balancing algorithms in the heavy traffic regime such that the load of the system is $\lambda = 1 - \gamma N^{-\alpha}$ for $0<\alpha<0.5$ and $\gamma > 0,$ which we call the sub-Halfin–Whitt regime ($\alpha=0.5$ is the so-called Halfin–Whitt regime). We establish a sufficient condition under which the probability that an incoming job is routed to an idle server is 1 asymptotically (as $N \to \infty$) at steady state. The class of load-balancing algorithms that satisfy the condition includes join-the-shortest-queue, idle-one-first, join-the-idle-queue, and power-of-d-choices with $d\geq \frac{r}{\gamma}N^\alpha\log N$ (r a positive integer). The proof of the main result is based on the framework of Stein’s method. A key contribution is to use a simple generator approximation based on state space collapse.

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence rate. They take advantage of the properties of hyperbolic partial differential equations (PDEs) and try to cover a family of characteristics of the corresponding Hamilton-Jacobi equation in a certain direction simultaneously in each sweeping order. Different from other fast sweeping methods, fixed-point iterative sweeping methods have the advantages such as that they have explicit forms and do not involve inverse operation of nonlinear local systems. In principle, it can be applied in solving very general equations using any monotone numerical fluxes and high order approximations easily. In this paper, based on the recently developed fifth order WENO schemes which improve the convergence of the classical WENO schemes by removing slight post-shock oscillations, we design fifth order fixed-point sweeping WENO methods for efficient computation of steady state solution of hyperbolic conservation laws. Especially, we show that although the methods do not have linear computational complexity, they converge to steady state solutions much faster than regular time-marching approach by stability improvement for high order schemes with a forward Euler time-marching.

We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild space-time, and we introduce a version of the finite volume method which is formulated from the geometric formulation (and thus takes the geometry into account at the discretization level) and is well-balanced, in the sense that it preserves steady solutions to the Euler equations on the curved geometry under consideration. In order to formulate our method, we first derive a closed formula describing all steady and spherically symmetric solutions to the Euler equations posed on Schwarzschild spacetime. Second, we describe a geometry-preserving, finite volume method which is based from the family of steady solutions to the Euler system. Our scheme is second-order accurate and, as required, preserves the family of steady solutions at the discrete level. Numerical experiments are presented which demonstrate the efficiency and robustness of the proposed method even for solutions containing shock waves and nonlinear interacting wave patterns. As an application, we investigate the late-time asymptotics of perturbed steady solutions and demonstrate its convergence for late time toward another steady solution, taking the overall effect of the perturbation into account.

This paper provides an analysis on a discrete version of the Ornstein-Uhlenbeck (OU) process which reflects the small discrete movements caused by the tick size effect. This discrete OU process is derived from matching the first two moments to those of the standard OU process in an infinitesimal sense. We discuss the distributional convergence from the discrete to the continuous processes, and show that the convergence speed is in the second order of the step (tick) size. We also provide some analytical results for the proposed discrete OU process itself, including the closed-form formula of the moment generating function and a full characterisation of the steady state distribution. These results enable us to examine the convergence order explicitly.

Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workload and the numbers of customers present in the systems as well as the distributions of the lengths of busy and idle periods. Moreover, we use the duality approach to study finite capacity storage systems with general state-dependent outflow rates. Here our duality leads to a Markovian finite storage system with state-dependent jump sizes whose content level process can be analyzed using level crossing techniques. We also derive a connection between the steady-state densities of the non-Markovian continuous-time content level process of the G/M/1 finite storage system with state-dependent outflow rule and the corresponding embedded sequence of peak points (local maxima).

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and co-workers [A. M. Berezhkovskii, C. Sample and S. Y. Shvartsman, “How long does it take to establish a morphogen gradient?” Biophys. J. 99 (2010) L59–L61] rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single-species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalize the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications, for example the analysis of models describing coupled chemical decay and cell differentiation processes.

We describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that this interface can be viewed as a square root of a polynomial of degree at most 6. We solve this equation using an original method. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results, which can predict the occurrence of a full film with respect to physical parameters (fluxes, shear velocity, viscosities). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters. Moreover, we give some indications for a better understanding of the multi-fluid case.

The kinetics of granular gases, including both freely cooling and steadily driven systems, is studied experimentally in quasi-two-dimensional cells. Under microgravity conditions achieved inside an aircraft flying parabolic trajectories, the frictional force is reduced. In both the freely cooling and steadily driven systems, we confirm that the velocity distribution function has the form exp(−α|v|β). The value of exponent β is close to 1.5 for the driven system in a highly excited case, which is consistent with theory derived under the assumption of the existence of the white-noise thermostat (van Noije & Ernst, Gran. Mat., vol. 1, 1998, p. 5764). In the freely cooling system, the value of β evolves from 1.5 to 1 as the cooling proceeds, and the system's energy decays algebraically (Tg = T0(1 + t/τ)−2), agreeing with Haff's law (Haff, J. Fluid Mech., vol. 134, 1983, p. 401430).

The integration to steady state of many initial value ODEs and PDEs using the forward Euler methodcan alternatively be considered as gradient descent for an associated minimization problem.Greedy algorithms such as steepest descent for determining the step size are asslow to reach steady state as is forward Euler integration with the best uniform step size.But other, much faster methods using bolder step size selection exist.Various alternatives are investigated from both theoretical and practical points of view.The steepest descent method is also known for the regularizing or smoothing effect that thefirst few steps have for certain inverse problems,amounting to a finite time regularization. We further investigate the retention of thisproperty using the faster gradient descent variants in the context of two applications.When the combination of regularization and accuracy demands more than a dozen or so steepestdescent steps, the alternatives offer an advantage, even though (indeed because)the absolute stability limit of forward Euler is carefully yet severely violated.

This paper explores the possible real effects of inflation within a two-sector neoclassical growth model of the Heckscher–Ohlin type with a cash-in-advance constraint on the purchases of consumption goods. The main findings are that the relative prices of both factors and of both goods, which are linked via a Stolper–Samuelson relation, depend only on the rate of time preference, not on any monetary variable; that the steady-state level of total capital can be influenced by inflation if the capital intensities and the cash requirements in both sectors differ, leading to Tobin effects or reversed Tobin effects; and that higher inflation unambiguously reduces total labor supply and leads to a reversed Tobin effect in most cases if the labor/leisure choice is endogenized.

Species-area relationships (SPARs) dictate a sea change in the strategies of biodiversity conservation. SPARs exist at three ecological scales: Sample-area SPARs (a larger area within a biogeographical province will tend to include more habitat types, and thus more species, than a smaller one), Archipelagic SPARs (the islands of an archipelago show SPARs that combine the habitat-sampling process with the problem of dispersal to an island), and Interprovincial SPARs (other things being equal, the speciation rates of larger biogeographical provinces are higher and their extinction rates are lower, leading to diversities in proportion to provincial area). SPARs are the products of steady-state dynamics in diversity, and such dynamics appears to have characterized the earth for most of the last 500 million years. As people reduce the area available to wild species, they impose a linear reduction of the earth's species diversity that will follow the largest of these scales, i.e. each 1% reduction of natural area will cost about 1% of steady-state diversity. Reserving small tracts of wild habitat can only delay these reductions. But we can stop most of them by redesigning anthropogenic habitats so that their use is compatible with use by a broad array of other species. That is reconciliation ecology. Many pilot projects, whether intentionally or inadvertently espousing reconciliation ecology, are demonstrating that it can be done.

We investigate the steady state behavior of an M/G/1 queue with modified Bernoulli schedule server vacations. Batches of variable size arrive at the system according to a compound Poisson process. However, all arriving batches are not allowed into the system. The restriction policy differs when the server is available in the system and when he is on vacation. We obtain in closed form, the steady state probability generating functions for the number of customers in the queue for various states of the server, the average number of customers as well as their average waiting time in the queue and the system. Many special cases of interest including complete admissibility, partial admissibility and no server vacations have been discusssed. Some known results are derived as particular cases of our model.