On the origins of approximations for stochastic chemical kinetics

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies

On the dynamic response of pressure transmission lines in the research of helium-charged free piston Stirling engines

In free piston Stirling engine research the integrity of both amplitude and phase of the dynamic pressure measurements is critical to the characterization of cycle dynamics and thermodynamics. It is therefore necessary to appreciate all possible sources of signal distortion when designing pressure measurement systems for this type of research. The signal distortion inherent to pressure transmission lines is discussed. Based on results from classical analysis, guidelines are formulated to describe the dynamic response properties of a volume-terminated transmission tube for applications involving helium-charged free piston Stirling engines. The scope and limitations of the dynamic response analysis are considered

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques

Observations of MMOD Impact Damage to the ISS

This paper describes meteoroid and orbital debris (MMOD) damage observations on the International Space Station (ISS). Several hundred MMOD damage sites on ISS have been documented using imagery taken from ISS windows. MMOD damage sites visible from ISS windows are typically larger approximately 5mm diameter and greater due to the larger viewer-to-surface distance. Closer inspection of these surfaces by astronauts during spacewalks reveals many smaller features that are typically less distinct. Characterization of these features as MMOD or non- MMOD is difficult, but can be partially accomplished by matching physical characteristics of the damage against typical MMOD impact damage observed on ground-based impact tests. Numerous pieces of space-exposed ISS hardware were returned during space shuttle missions. Subsequent ground inspection of this hardware has also contributed to the database of ISS MMOD impact damage. A handful of orbital replacement units (ORUs) from the ISS active thermal control and electrical power subsystems were swapped out and returned during the Space Shuttle program. In addition, a reusable logistics module was deployed on ISS for a total 59.4 days on 11 shuttle missions between 2001 and 2011 and then brought back in the shuttle payload bay. All of this returned hardware was subjected to detailed post-flight inspections for MMOD damage, and a database with over 1,400 impact records has been collected. A description of the largest observed damage features is provided in the paper. In addition, a discussion of significant MMOD impact sites with operational or design aspects is presented. MMOD impact damage to the following ISS modules/subsystems is described: (1) Solar Arrays, (2) US and Russian windows, (3) Extravehicular Activity (EVA) handrails, (4) Radiators, and (5) Russian Functional Cargo Block (FGB) module

Two classes of quasi-steady-state model reductions for stochastic kinetics

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case

The stochastic quasi-steady-state assumption: Reducing the model but not the noise

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution

Comparison of Risk from Orbital Debris and Meteoroid Environment Models on the Extravehicular Mobility Unit (EMU)

A well-known hazard associated with exposure to the space environment is the risk of failure from an impact from a meteoroid and orbital debris (MMOD) particle. An extravehicular mobility unit (EMU) spacesuit impact during a US extravehicular activity (EVA) is of great concern as a large leak could prevent an astronaut from safely reaching the airlock in time resulting in a loss of life. A risk assessment is provided to the EVA office at the Johnson Space Center (JSC) by the Hypervelocity Impact Technology (HVIT) group prior to certification of readiness for each US EVA. Need to understand the effect of updated meteoroid and orbital debris environment models to EMU risk

The Influence of Federal Laboratory R&D on Industrial Research

Over the past 60 years the United States has created the world's largest system of government laboratories. The impact of the laboratories on the private economy has been little studied though their research accounts for 14% of total U.S. R&D, more than the R&D of all colleges and universities combined. In this paper we study the influence of federal laboratory R&D on industrial research using a sample of industrial laboratories. In head-to-head comparisons with alternative measures, we find that Cooperative Research and Development Agreements or CRADAs, are the primary channel by which federal laboratories increase the patenting and R&D of industrial laboratories. With a CRADA industrial laboratories patent more, spend more on company-financed R&D and spend more of their own money on federal laboratories. Without a CRADA patenting stays about the same and only federally funded R&D increases, mostly because of direct subsidies by government. These results are consistent with the literature on endogenous R&D spillovers, which emphasizes that knowledge spills over when recipients work at making it spill over. CRADAs are legal agreements between federal laboratories and firms to work together on joint research. They are backed by real budgets and accompanied by cost sharing that could bind the parties together in joint research. Moreover, the CRADA instrument is the main form of such agreements. Thus, both in theory and in fact CRADAs may be more beneficial to firms than other public- private interactions, precisely because of the mutual effort that they require of firms and government laboratories.

Economics of Using On-farm Reservoirs to Distribute Diverted Surface Water to Depleted Ground Water Areas of the Southern Mississippi Valley Region

Rapid ground water depletion has become a significant problem for parts of the Southern Mississippi River Valley. In 1997, the Arkansas Soil and Water Conservation Commission (ASWCC) declared six counties in the Grand Prairie of Arkansas critical ground water areas. A proposed solution to the ground water depletion problem in this region is to divert surplus flows from the White River by a canal system to the farmer stakeholders. To make the system work, on-farm reservoirs will be needed to store and manage the diverted surface water for crop irrigation use during the growing season