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.

The development of a finite elements based springback compensation tool for sheet metal products

Springback is a major problem in the deep drawing process. When the tools are released after the forming stage, the product springs back due to the action of internal stresses. In many cases the shape deviation is too large and springback compensation is needed: the tools of the deep drawing process are changed so, that the product becomes geometrically accurate after springback. In this paper, two different ways of geometric optimization are presented, the smooth displacement adjustment (SDA) method and the surface controlled overbending (SCO) method. Both methods use results from a finite elements deep drawing simulation for the optimization of the tool shape. The methods are demonstrated on an industrial product. The results are satisfactory, but it is shown that both methods still need to be improved and that the FE simulation needs to become more reliable to allow industrial application

Springback Compensation: Fundamental Topics and Practical Application

Now that the simulation of deep drawing processes has become more reliable the virtual\ud compensation of the forming tools has become reality. In literature, the Displacement Adjustment (DA)\ud algorithm has proved to be most effective. In this article it is shown how the compensation factor, required for\ud (one-step) DA depends on material, process and geometrical parameters. For this an analytical bar stretchbending\ud model was used. A compensation factor is not required when DA is applied iteratively and the\ud products geometrical accuracy is improved further. This was demonstrated on an industrial part. The\ud compensation varies over the product, leading to a reduction in shape deviation of 90% and more, a result that\ud could not have been achieved with one-step compensatio

Diffuse reflection of ultracold neutrons from low-roughness surfaces

We report a measurement of the reflection of ultracold neutrons from flat, large-area plates of different Fermi potential materials with low surface roughness. The results were used to test two diffuse reflection models, the well-known Lambert model and the micro-roughness model which is based on wave scattering. The Lambert model fails to reproduce the diffuse reflection data. The surface roughness b and correlation length w , obtained by fitting the micro-roughness model to the data are in the range 1$\le$ b $\le$3 nm and 10$\le$ w $\le$120 nm, in qualitative agreement with independent measurements using atomic force microscop

Testing isotropy of the universe using the Ramsey resonance technique on ultracold neutron spins

Physics at the Planck scale could be revealed by looking for tiny violations of fundamental symmetries in low energy experiments. In 2008, a sensitive test of the isotropy of the Universe using has been performed with stored ultracold neutrons (UCN), this is the first clock-comparison experiment performed with free neutrons. During several days we monitored the Larmor frequency of neutron spins in a weak magnetic field using the Ramsey resonance technique. An non-zero cosmic axial field, violating rotational symmetry, would induce a daily variation of the precession frequency. Our null result constitutes one of the most stringent tests of Lorentz invariance to date.Comment: proceedings of the PNCMI2010 conferenc

A next generation measurement of the electric dipole moment of the neutron at the FRM II

In this paper we discuss theoretical motivations and the status of experimental searches to find time-reversal symmetry-violating electric dipole moments (EDM). Emphasis is given to a next generation search for the EDM of the neutron, which is currently being set up at the FRM II neutron source in Garching, with an ultimate sensitivity goal of 5 × 10−28 cm (3σ). The layout of the apparatus allows for the detailed investigation of systematic effects by combining various means of magnetic field control and polarized UCN optics. All major components of the installations are portable and can be installed at the strongest available UCN beam

Demonstrations of Sustainable Vegetable Pest and Crop Management: Fresh Market Sweet Corn

NYS IPM Type: Project ReportFour sweet corn pest and crop management systems (organic, IPM/Present, IPM/Future, and conventional) were defined and implemented on grower farms and on a university research farm. The first years results showed differences among the four systems in terms of economics, pest control efficacy and environmental impact. Generally the conventional and IPM systems were the most profitable while the organic system showed the least environmental impact. Information on the comparisons was disseminated to growers and other food industry personnel. In cooperation with Wegmans supermarkets consumers were informed of IPM practices on sweet corn which were documented by growers. Fifteen growers participated in documenting IPM practices and in many cases have reduced pesticide use. Five of the fifteen growers were among the nine involved in the demonstrations conducted in this project