Constrained sampling methods

The penalty approach corresponds to augmenting the energy surface with a biasing potential U, for example a harmonic function centred at position to with a suitable width ku. 

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The decision on the sampling method to use is constrained by the type of information needed to answer a specific hypothesis and by the available resources (both logistical and financial). Instantaneous or time-integrated, whole water, or dissolved (filtered), one sample or replicates, and how much and what types of quality control measures will be used are all options that need to be considered as part of the sample collection plan (Alvarez and Jones-Lepp, 2010). The development of a sound sampling plan will help eliminate problems in the field and ensure a representative sample will be collected to meet the needs of the study. 

Elucidation of degradation kinetics for the reactive extrusion of polypropylene is constrained by the lack of kinetic data at times less than the minimum residence time in the extruder. The objectives of this work were to develop an experimental technique which could provide samples for short reaction times and to further develop a previously published kinetic model. Two experimental methods were examined the classical "ampoule technique" used for polymerization kinetics and a new method based upon reaction in a static mixer attached to a single screw extruder. The "ampoule technique was found to have too many practical limitations. The "static mixer method" also has some difficult aspects but did provide samples at a reaction time of 18.6 s and is potentially capable of supplying samples at lower times with high reproducibility. Kinetic model improvements were implemented to remove an artificial high molecular weight tail which appeared at high initiator concentrations and to reduce step size sensitivity. 

One reason for the inefficiencies of constraint methods is that they may prevent an efficient sampling of the set (x) = . This is illustrated by Fig. 4.2. It is common that many pathways separated by high energy barriers exist to go from A to B. In constrained simulation, the system can get trapped in one of the pathways. In the most serious cases, this leads to quasi-nonergodic effect where only a part of the set (x) is effectively explored. In less serious cases, the convergence is quite slow. 

Cross-linking constrains the conformational flexibility of biopolymers and, as a rule, stabilizes their secondary, tertiary, and quaternary structures against the denaturing effects of high temperatures.29 We used differential scanning calorimetry (DSC) to compare the heat-induced conformational transitions of selected RNase A samples that were characterized in Figure 15.2. A brief introduction to DSC is provided in Section 15.15.1 for those readers unfamiliar with this biophysical method. Trace 1 in Figure 15.3a is the heat absorption... 

Crosslinked polymer networks formed from multifunctional acrylates are completely insoluble. Consequently, solid-state nuclear magnetic resonance (NMR) spectroscopy becomes an attractive method to determine the degree of crosslinking of such polymers (1-4). Solid-state NMR spectroscopy has been used to study the homopolymerization kinetics of various diacrylates and to distinguish between constrained and unconstrained, or unreacted double bonds in polymers (5,6). Solid-state NMR techniques can also be used to determine the domain sizes of different polymer phases and to determine the presence of microgels within a poly multiacrylate sample (7). The results of solid-state NMR experiments have also been correlated to dynamic mechanical analysis measurements of the glass transition (1,8,9) of various polydiacrylates. 

Analysis time is typically of the order of minutes to hours depending on the sample. Normally the time spent in actual AMS analysis is not the constraining factor, but rather sample purification prior to the spectrometric analysis. Accelerator mass spectrometers are space demanding facilities that typically occupy hundreds of square meters. Normally, dedicated personnel operate the device. Considerable effort is directed into refining the methods to allow operation by smaller, less costly facilities. 

Local sensitivity analysis is of limited value when the chemical system is non-linear. In this case global methods, which vary the parameters over the range of their possible values, are preferable. Two global uncertainty methods have been used in this work, a screening method, the so-called Morris One-At-A-Time (MOAT) analysis and a Monte Carlo analysis with Latin Hypercube Sampling (Saltelli et al., 2000 Zador et al., submitted, 20041). The analyses were performed by varying rate parameters, branching ratios and constrained concentrations within their uncertainty interval,... 

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