Solving Differential Equations in R: Package deSolve

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR), DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1) to demonstrate the potential of using R for dynamic modeling, (2) to highlight typical uses of the different methods implemented and (3) to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to RâÂÂs high-level procedures. deSolve is the successor of package odesolve which will be deprecated in the future; it is free software and distributed under the GNU General Public License, as part of the R software project.

Investigating Varied Pedagogical Approaches for Problem-Based Learning in a Fire Safety Engineering Course

Fire safety engineering is a critical component of a well-rounded engineering undergraduate curriculum but is understudied in the context of engineering education literature. Guided by previous work in problem-based learning, we conducted a multiple case study structured around three sections of a fire safety engineering course for students across engineering programmes. Our goal was to develop a better understanding of the impact of different pedagogical approaches on students. These approaches were chosen for study because they align with predominating approaches to industry practice in fire safety engineering. Classroom observations and student coursework from each of the three sections were used to evaluate the different approaches: (A) controlling (the specialist approach), (B) student autonomy (the generalist approach), and (C) combination strategy (autonomous/generalist and controlling/specialist). Findings confirm more autonomous/generalist approaches foster positive student experiences and outcomes, but a balance of instructional techniques is still needed. It is clear that more work needs to be done to explore engineering education in the context of fire safety engineering, and this study provides preliminary results that suggest areas for future scholarship

Efficacy of localized chemical treatments for Cryptotermes brevis (Isoptera: Kalotermitidae) in naturally infested lumber.

Localized injection of insecticides into termite galleries in infested wood represents an alternative to whole-structure fumigation for drywood termite control. The efficacy of this method is limited, however, by the use of repellant insecticides and the difficulty of locating drywood termite colonies. The present study addressed both issues by the use of an experimental acoustic emissions (AE) detector to assist in location of termite infestations in naturally infested shipping pallets, and application of the non-repellant insecticide spinosad (Dow AgroSciences). Chlorpyrifos 0.5% aerosol, 15% aqueous disodium octaborate tetrahydrate (DOT), resmethrin 0.25% aerosol, distilled water (control) and two treatments of 0.5% spinosad suspension concentrate (one with the injection site based on visual evidence and the other on acoustic evidence) were injected into boards in hardwood shipping pallets naturally infested with the drywood termite Cryptotermes brevis Walker. Termite mortality was greatest with spinosad treatments, although variability was high due to the continued difficulty of identifying and treating all separate areas of infestation in the boards

Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure

Annual Survey of Virginia Law: Planning, Zoning and Subdivision Law

In recent years, a debate has sharpened in Virginia concerning the limits of public power over private property and the determination of which arm of the government will exercise the public\u27s power in land use matters. This debate has continued into 1990 and 1991

Geology and Ground-Water Resources of Wichita and Greeley Counties, Kansas

This report describes the geography, geology, and ground-water resources of Wichita and Greeley counties in western Kansas. The area consists of a flat to gently rolling plain, which slopes eastward [at] about 15 feet per mile. A short reach of Ladder Creek (Beaver) is the only perennially flowing stream in the two counties. Ephemeral streams, which flow only during and after heavy rains, are White Woman and Sand Creeks and the western reach of Ladder Creek. The climate is semiarid, the normal annual precipitation being about 17 inches in Wichita County and 16 inches in Greeley County. Agriculture is the principal occupation in the area, and wheat is the most important crop. A considerable area is irrigated; sugar beets and sorghums are the principal irrigated crops. The outcropping rocks range in age from late Cretaceous to Recent; the Smoky Hill chalk member of the Niobrara formation, which is exposed along White Woman Creek in western Greeley County, is the oldest. The Niobrara is almost everywhere overlain by the Ogallala formation of Pliocene age. Generally the Ogallala is overlain by windblown silt of the Pleistocene Sanborn formation, but in places it is exposed along streams. The most recent deposits are dune sand and the alluvium along the streams. The Dakota formation, which is an important aquifer in parts of Kansas, is 300 to 450 feet beneath the Niobrara formation. The ground water that is available to wells in Wichita and Greeley counties is derived entirely from precipitation in the area or in areas immediately west and north. Ground water moves in a generally easterly direction with a gradient that varies inversely with the permeability of the water-bearing beds. The ground-water reservoir is recharged principally by precipitation within the area or within adjacent areas, Ground-water discharge takes place principally by pumping from wells, subsurface outflow, and evaporation and transpiration. Most of the domestic, stock, public, and irrigation supplies are obtained from wells. It is estimated that probably more than 2 billion gallons of water is pumped annually from wells in the area. Since 1947, ground-water recharge has been about equal to ground-water discharge. The use of ground water for irrigation has increased greatly since 1946 and indications are that many more wells may be drilled and pumped without dangerously lowering the water table. Approximately 11,000 to 12,000 acres were irrigated in 1951. A map showing the thickness of water-bearing materials indicates that although much of the area has enough water-bearing material to support irrigation wells, parts of Wichita and Greeley counties have little or none. The Ogallala is the principal water-bearing formation in the area. Small amounts of water may also be obtained locally from alluvial deposits and from cracks in the Niobrara formation. Two deep test wells to the Dakota formation have been drilled but, because of the poor quality of the water, have never been used. The ground water in Wichita and Greeley counties, though hard, is suitable for most purposes. Water from the Ogallala is generally high in fluoride and in some cases may be injurious to the teeth of children. Water from the Dakota, though soft, is unfit for irrigation because of a high content of sodium. The field data upon which most of this report is based are given in tables; they include records of 417 wells, chemical analyses of 31 samples of water, and logs of 57 test holes and wells

Nonparametric Inference for Multivariate Data: The R Package npmv

We introduce the R package npmv that performs nonparametric inference for the comparison of multivariate data samples and provides the results in easy-to-understand, but statistically correct, language. Unlike in classical multivariate analysis of variance, multivariate normality is not required for the data. In fact, the different response variables may even be measured on different scales (binary, ordinal, quantitative). p values are calculated for overall tests (permutation tests and F approximations), and, using multiple testing algorithms which control the familywise error rate, significant subsets of response variables and factor levels are identified. The package may be used for low- or highdimensional data with small or with large sample sizes and many or few factor levels