A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Mesh-free simulation of complex LCD geometries

We use a novel mesh-free simulation approach to study the post aligned bistable nematic (PABN) cell. By employing the Qian-Sheng formalism for liquid crystals along with a smooth representation of the surface posts, we have been able to identify two distinct stable configurations. The three-dimensional order field configurations of these states and their elastic free energies are consistent with both experimental results and previous simulation attempts. However, alternative states suggested in previous studies do not appear to remain stable when finite post curvature is considered.</p

Binary Decision Diagrams: from Tree Compaction to Sampling

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities

Motivated by recent theoretical and experimental works, we study the statistical fluctuations of the parametric derivative of the transmission T and reflection R coefficients in ballistic chaotic cavities in the presence of absorption. Analytical results for the variance of the parametric derivative of T and R, with and without time-reversal symmetry, are obtained for both asymmetric and left-right symmetric cavities. These results are valid for arbitrary number of channels, in completely agreement with the one channel case in the absence of absorption studied in the literature.Comment: Modified version as accepted in PR

Global Atmospheric Change and Its Effect on Managed Grassland Systems

Key points 1. Increasing atmospheric CO2 concentration and a trend to warmer mean temperatures are the most reliable aspects of global atmospheric change. Projections of the extent of climate change and the frequency of extreme weather conditions remain uncertain. 2. Research has considerably reduced the uncertainty about effects of global atmospheric change on physiology of plants, productivity and species composition of plant communities. 3. Other factors (e.g. nutrient availability, soil type) and long-term adaptation of the ecosystem (e.g. nutrient cycling and sequestration) influence the response of plant communities to global atmospheric change. Generalisation is not possible with respect to the response of different pasture and rangeland systems. 4. In temperate grasslands with regular fertilisation and defoliation, the effects of elevated CO2 may be smaller than those of climate and/or management. Adaptations in management can help to mitigate effects of global atmospheric change

The Influence of Rising Atmospheric CO\u3csub\u3e2\u3c/sub\u3e on Grassland Ecosystems

Increasing atmospheric CO2 concentrations and climatic change will have significant effects on the ecology of grasslands. This paper evaluates results from four CO2 enrichment studies in contrasting grasslands. A Swiss study investigates the effects of elevated CO2 (600 μL L-1 CO2) on perennial ryegrass (Lolium perenne L.) and white clover (Trifolium repens L), a New Zealand study examines how elevated CO2 (475 μL L-1 CO2) affects a botanically diverse pasture, and studies in the Kansas tallgrass prairie and the Colorado shortgrass steppe investigate the effects of an approximate doubling of CO2 in native grasslands. Productivity in all four grasslands was enhanced at elevated CO2, with the largest relative increases occurring in dry years on the shortgrass steppe (71%) and on the tallgrass prairie (36%). Nitrogen additions, whether from fertilizer or legumes, enhanced the capability of these grasslands to respond to CO2, and legumes were among the most competitive plant types in the Swiss and New Zealand grasslands under elevated CO2. No evidence was found to support the notion that C3 grasses were more competitive under elevated CO2 compared to C4 grasses. The results suggest that CO2 enrichment and global warming will have important impacts on grasslands

Texas Guide for Controlling Insects and Diseases on Fruits and Nuts.

7 p

Formalism for obtaining nuclear momentum distributions by the Deep Inelastic Neutron Scattering technique

We present a new formalism to obtain momentum distributions in condensed matter from Neutron Compton Profiles measured by the Deep Inelastic Neutron Scattering technique. The formalism describes exactly the Neutron Compton Profiles as an integral in the momentum variable $y$. As a result we obtain a Volterra equation of the first kind that relates the experimentally measured magnitude with the momentum distributions of the nuclei in the sample. The integration kernel is related with the incident neutron spectrum, the total cross section of the filter analyzer and the detectors efficiency function. A comparison of the present formalism with the customarily employed approximation based on a convolution of the momentum distribution with a resolution function is presented. We describe the inaccuracies that the use of this approximation produces, and propose a new data treatment procedure based on the present formalism.Comment: 11 pages, 8 figure