Instabilities and Non-Reversibility of Molecular Dynamics Trajectories

The theoretical justification of the Hybrid Monte Carlo algorithm depends upon the molecular dynamics trajectories within it being exactly reversible. If computations were carried out with exact arithmetic then it would be easy to ensure such reversibility, but the use of approximate floating point arithmetic inevitably introduces violations of reversibility. In the absence of evidence to the contrary, we are usually prepared to accept that such rounding errors can be made small enough to be innocuous, but in certain circumstances they are exponentially amplified and lead to blatantly erroneous results. We show that there are two types of instability of the molecular dynamics trajectories which lead to this behavior, instabilities due to insufficiently accurate numerical integration of Hamilton's equations, and intrinsic chaos in the underlying continuous fictitious time equations of motion themselves. We analyze the former for free field theory, and show that it is essentially a finite volume effect. For the latter we propose a hypothesis as to how the Liapunov exponent describing the chaotic behavior of the fictitious time equations of motion for an asymptotically free quantum field theory behaves as the system is taken to its continuum limit, and explain why this means that instabilities in molecular dynamics trajectories are not a significant problem for Hybrid Monte Carlo computations. We present data for pure $SU(3)$ gauge theory and for QCD with dynamical fermions on small lattices to illustrate and confirm some of our results.Comment: 28 pages latex with 19 color postscript figures included by eps

Non-Reversibility of Molecular Dynamics Trajectories

We study the non-reversibility of molecular dynamics trajectories arising from the amplification of rounding errors. We analyse the causes of such behaviour and give arguments, indicating that this does not pose a significant problem for Hybrid Monte Carlo computations. We present data for pure SU(3) gauge theory and for QCD with dynamical fermions on small lattices to illustrate and to support some of our ideas.Comment: 3 pages LATEX, 4 color figures included using epsf. Talk presented at LATTICE96(algorithms

The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation

We analyze the autocorrelations for the LHMC algorithm in the context of free field theory. In this case this is just Adler's overrelaxation algorithm. We consider the algorithm with even/odd, lexicographic, and random updates, and show that its efficiency depends crucially on this ordering of sites when optimized for a given class of operators. In particular, we show that, contrary to previous expectations, it is possible to eliminate critical slowing down (z[int]=0) for a class of interesting observables, including the magnetic susceptibility: this can be done with lexicographic updates but is not possible with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the dynamical critical exponent z[int] for integrated autocorrelations rather than for the exponential autocorrelation time; this is reasonable because it is the integrated autocorrelation which determines the cost of a Monte Carlo computation.Comment: LaTeX, 33 pages, 3 postscript figure

Safer selection and use of pesticides: Integrating risk assessment, monitoring and management of pesticides

Crop Production/Industries,

Testing the hypothesis that variations in atmospheric water vapour are the main cause of fluctuations in global temperature

A hypothesis that the increasing application of both surface and ground water for irrigation of crops is a significant source of anthropogenic global warming is tested. In climate models, water is already assigned a major secondary amplifying role in warming, solely as a positive feedback from an atmosphere previously warmed by other GHGs. However, this conclusion ignores the direct anthropogenic forcing from increasing use of water in dry regions to grow crops for the human population. The area irrigated worldwide increased by around 1.5% annually between 1960 and 2000, almost trebling in magnitude. Importantly, though only a small proportion of the Earth’s surface, this additional water vapour is dynamically focussed on dry land, intensifying its potential to elevate the troposphere and reduce the regional OLR. Our modelling analysis suggests that the increase in atmospheric water vapour from irrigation could be significantly more than 1% by 2050 compared to 1950, imposing a global forcing exceeding 1.0 W/m2. Fortunately, this hypothesis can be tested, for example, using the satellite data on OLR acquired since the 1970s, relating this to local trends of increasing irrigation or major floods in arid regions. If found consistent with the data, current proposals to mitigate climate change by limiting combustion of fossil fuels may prove less effective. This prediction regarding the warming effect of increasing irrigation is tested using NCAR reanalysis data made possible by the natural experiments of the periodic flooding of Lake Eyre in Australia's semi-arid interior. It is recommended that this hypothesis be tested using data from local studies in irrigated regions such as changes in outgoing longwave radiation and in increased absorption of incoming shortwave radiation in air

Kalman Filter Harmonic Bank for Vostok Ice Core Data Analysis and Climate Predictions

The Vostok ice core data cover 420,000 years indicating the natural regularity of Earth’s surface temperature and climate. Here, we consider four major cycles of similar duration, ranging from 86,000 to 128,000 years, comprising 15% of periods for the warming interglacials compared to some 85% of cooling periods. Globally, we are near the peak of a rapid warming period. We perform a detailed frequency analysis of temperature and CO2 cycles, as a primary stage in building a logical Climate Prediction Engine (CPE), illustrated with specific harmonics. This analysis can be repeated for all harmonics and various cycle combinations. Our time correlation estimates the CO2 time lag for temperature at 400–2300 years, depending on the cycle, longer on average than previously concluded. We also perform Fast-Fourier transform analysis, identifying a full harmonic spectrum for each cycle, plus an energy analysis to identify each harmonic amplitude − to achieve further prediction analysis using a Kalman filter harmonic bank. For Vostok data we can use combinations of different cycles compared to the most recent for learning and then the current ongoing cycle for testing. Assuming causal time regularity, more cycles can be employed in training, hence reducing the prediction error for the next cycle. This results in prediction of climate data with both naturally occurring as well as human forced CO2 values. We perform this detailed time and frequency analysis as a basis for improving the quality of our climate prediction methodologies, with particular attention to testing alternative hypotheses of the possible causes of climate change. These include the effect on albedo of suspended dust and increasing water vapor with temperature in initiating interglacial warming, the effect of temperature and pH values of surface water on ambient level of CO2 in the atmosphere and finding a larger latent heat capacity in the atmosphere required to sustain its circulatory motions, leading to friction and turbulent release of heat in boundary layer. All these potentials can be examined in an effective CPE

A Global Fit to Extended Oblique Parameters

The STU formalism of Peskin and Takeuchi is an elegant method for encoding the measurable effects of new physics which couples to light fermions dominantly through its effects on electroweak boson propagation. However, this formalism cannot handle the case where the scale of new physics is not much larger than the weak scale. In this case three new parameters (V, W and X) are required. We perform a global fit to precision electroweak data for these six parameters. Our results differ from what is found for just STU. In particular we find that the preference for S < 0 is not maintained.Comment: Plain TeX, 11 pages, one figure (ps file enclosed), (replaced version corrects minor TeX problem, text unchanged) UdeM-LPN-TH-93-166, McGill-93/24, OCIP/C-93-

Time and frequency analysis of Vostok ice core climate data

The periodicity of Vostok ice core climate temperature and gas concentration data indicate inherent long term past regularity of Earth’s climate, with a period of around 100,000 years, warming around 15,000 and cooling of around 85,000 years. At this point we are at the top of one of the warming periods. Vostok data cover around 430,000 years, ie 4 climate cycles (warming-cooling), of similar but not quite the same duration. In this paper we perform a detailed time and frequency analysis of these data for each of the cycles as well as their various combinations, including a full tested period of 430,000 years. Time correlation analysis allows for more accurate time lag estimate in each cycle already noted between temperature change and carbon dioxide content. We estimate these lags to lie between 1000-2500 years, longer than previously concluded. On the frequency side we perform Fast Fourier Analysis and identify full spectrum of harmonics for various cycles, and then perform energy analysis to identify which of the harmonics contributes the most. The idea is to reduce the computational load for further modeling and analysis using Kalman Filter based prediction method. Once the prediction model is defined (a follow up paper) data will be split into two segments, Learning and Testing, in preparation of a Machine Learning fine tunning methodology. We can use last three or last two or even just last cycle to learn on, and then the current on going cycle to test on. This will result in real time prediction of relevant climate data. Assuming causal time regularity, more of these cycles are employed in training, more the prediction error for the next cycle should be reduced. Hence it is critical to perform very detailed time and frequency analysis of Vostok data as a solid data base for the prediction model to follow