Kinetics of methane and tar evolution during coal pyrolysis

The first objective of this work was to compare the pyrolysis behavior of coals coming from different geographic locations (South Africa, South America, Europe, Australia, and North America). This preliminary study was limited to the kinetics of methane and tar evolution, with data on additional species to be reported in a separate publication. The second objective was to examine the possible relationship between tar and methane evolution during pyrolysis. This study was done by employing a thermogravimetric analyzer coupled with a Fourier-transform infrared spectrometer (TG-FTIR). The evolution curves for 35 coals of different elemental compositions were measured at three different heating rates (10, 30, and 100 K/min). Pyrolysis kinetics were described using a simple first-order reaction model. The technique, first proposed by Kissinger, is based on the variation of the temperature at which a volatile species evolution rate is a maximum (T_max) as a function of the heating rate. The TG-FTIR data for tar evolution reveal a generally consistent behavior for coals from different parts of the world, showing increasing activation energies with increasing coal rank. The same correlation is also true for methane, although the slope of the activation energy versus carbon content curve is rather flat, at least up to about 90% carbon content. The values of activation energies for methane evolution were found to be lower in the case of the Argonne coals, as compared with the non-US coals. A study of the temperatures at which the evolution of methane and tar begins (T_ini), and the temperatures at which the evolution rates reach a maximum (T_max), reveals a correlation between the T_ini for methane and T_max for tar. This may be due to the fact that both tar and methane evolve as a result of similar reactions involved in the breakup and recombination of the coal macromolecular network.     

Optimal Trajectories for Spacecraft Rendezvous

The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space. The time-optimal case results in a two-subarc solution: a max-thrust accelerating subarc followed by a max-thrust braking subarc. The fuel-optimal case results in a four-subarc solution: an initial coasting subarc, followed by a max-thrust braking subarc, followed by another coasting subarc, followed by another max-thrust braking subarc. The time-optimal case with fuel given and the fuel-optimal case with time given result in two, three, or four-subarc solutions depending on the performance index and the constraints. Regardless of the number of subarcs, the optimal thrust distribution requires the thrust magnitude to be at either the maximum value or zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Yet another finding is that, depending on the performance index, constraints, and initial conditions, sometime the initial application of thrust must be delayed, resulting in an optimal rendezvous trajectory which starts with a coasting subarc. This research has been supported by NSF under Grant CMS-0218878.     

Two‐Photon‐Induced Fluorescence of Isomorphic Nucleobase Analogs

Five isomorphic fluorescent uridine mimics have been subjected to two‐photon (2P) excitation analysis to investigate their potential applicability as non‐perturbing probes for the single‐molecule detection of nucleic acids. We find that small structural differences can cause major changes in the 2P excitation probability, with the 2P cross sections varying by over one order of magnitude. Two of the probes, both thiophene‐modified uridine analogs, have the highest 2P cross sections (3.8 GM and 7.6 GM) reported for nucleobase analogs, using a conventional Ti:sapphire laser for excitation at 690 nm; they also have the lowest emission quantum yields. In contrast, the analogs with the highest reported quantum yields have the lowest 2P cross sections. The structure‐photophysical property relationship presented here is a first step towards the rational design of emissive nucleobase analogs with controlled 2P characteristics. The results demonstrate the potential for major improvements through judicious structural modifications.     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.     

Using kalman filter and finite difference techniques in default free bond pricing models

A model to price default free bonds, similar to ones developed by Cox, Ingersoll and Ross, Langetieg, and Richard, is empirically examined. Calculation of model prices involves three disjoint tasks: (1) estimation of the values of the real interest rate and the inflation rate (which we will refer to as state variables or sources of uncertainty) as well as the parameters of the state stochastic differential equations, (2) estimation of the market prices of risk associated with the two state variables, and (3) the solution of the valuation partial differential equation. Task 1 is accomplished by using a Kalman Filter algorithm, task 2 uses a Fama/MacBeth approach, and task 3 utilizes an Alternating Direction Implicit finite difference technique. Model prices are compared to actual prices. The model performs better during a period of relatively stable economic conditions compared to a period associated with more volatile conditions. Pricing errors are smaller at short maturities, and increase as time to maturity increases.     

Angle-of-incidence dependence in angle-resolved photoemission from chemisorbed molecules: c(2 × 2)O,c(2 × 2)5, and CO on Ni(100)

We have measured the angular distribution of photoemitted electrons from c(2 × 2)O, c(2 × 2)S, and CO adsorbed on a Ni(100) substrate for various independently set angles of incidence of unpolarized light at 21.2 eV. We have found that these systems have very different dependence on angle of incidence, depending upon which components of the vector potential of the light ($\text{A}$) are responsible for emission. Because the incident and reflected light combine to form a standing wave at a metal surface, the phase relationships between components of $\text{A}$ parallel and perpendicular to the surface play an important role in determining the effective orientation and magnitude of A at the emission site. We compare our measurements with macroscopic $\text{A}$ fields, calculated via the Fresnel relations, which lead to a general understanding of the effects. We further propose a method for expediting photoemission calculations by projecting out components of $\text{A}$ which preserve their phase relationships.