Elements of Applied Stochastic Processes

Journal of the Operational Research Society -     

Enthalpies of reaction of bis(triphenylphosphine)(trans-stilbene)platinum(0) with diphenylcyclopropenone and benzocyclobutenedione

Enthalpies, ΔH(1) ?94.8 ± 6.0 and ΔH(6) ?57.1 ± 5.1 kJ mol^?1, of the following reactions have been measured calorimetrically [Pt(trans-stilbene)(PPh₃)₂](s) + dpcp(g) → (PPh₃)₂Pt(dpcb)(s) + trans-stilbene(g) (1) [Pt(trans-stilbene)(PPh₃)₂](s) + bcbd(g) → (PPh₃)₂Pt(bcpd)(s) + trans-stilbene (g) (6) where dpcp is diphenylcyclopropenone, (PPh₃)₂Pt(dpcb) is (1,1-bistriphenylphosphine)platinadiphenylcyclobutenone, (PPh₃)₂$\text{PtC(Ph)C(Ph)C}$O, bcbd is benzocyclobutene-1,2-dione and (PPh₃)₂Pt(bcpd) is (1,1-bistriphenylphosphine)platinabenzocyclopentanedione,

. It is concluded that the five-membered platinacyclo ring system in (PPh₃)₂Pt(dpcb) is not heavily strained.     

Analysis of Enzyme Structure and Activity by Protein Engineering

Structure-activity relationships of enzymes can now be analyzed for the first time by the systematic alteration of protein structure. Recent developments in the chemical synthesis of DNA fragments and recombinant DNA technology enable the facile modification of proteins by highly specific mutagenesis of their genes. Kinetic analysis of the mutant enzymes combined with high-resolution structural data from protein X-ray crystallography allow direct measurements on the relationships between structure and function. In particular, the strength and nature of enzyme-substrate interactions and their detailed roles in catalysis and specificity can now be studied. We have developed such analysis of enzyme structure-function by site-directed mutagenesis of the tyrosyl-tRNA synthetase from Bacillus stearothermophilus, concentrating so far on the subtle role of hydrogen bonding in both substrate specificity and catalysis. We find that the energetics of tyrosine and ATP binding must be analyzed in terms of an exchange reaction with solvent water. Based on this idea and structural data, we have engineered an enzyme of improved enzyme-substrate affinity, and there thus appear to be real prospects of engineering proteins of new specificities, activities, and structural properties. We are also using protein engineering to gather direct information on the nature of enzyme catalysis. For example, we find the catalysis of formation of Tyr-AMP from Tyr and ATP is due largely to electrostatic and hydrogen bonding interactions that are stronger in the transition state than in the ground state—a “strain” mechanism rather than acid-base or covalent catalysis.     

Staggered ladder spectra

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd- and even-parity states. The ladders are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation corresponds, in the limit of weak damping, to a generalized Ornstein-Uhlenbeck process where the random force depends upon position as well as time. The process describes damped stochastic acceleration, and exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.     

Perturbation Theory for a Stochastic Process with Ornstein-Uhlenbeck Noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.     

A pulsed, optically-pumped rubidium laser at high pump intensity

A rubidium laser operating at 795 nm is optically pumped by a pulsed titanium sapphire laser to investigate the dynamics of Diode Pumped Alkali Lasers (DPALs). Linear scaling of output intensity for longitudinal excitation at intensities of 1.3-43 kW/cm² and as much as 32 times threshold is observed. The slope efficiency depends directly on the number of absorbed photons for alkali concentrations of 0.8-2.0 × 10¹³ atoms/cm³ with no evidence for second order kinetics. The effective absorption cross section is reduced in part by the broad spectral width of the pump source relative to the pressure broadened lineshape. Spin orbit relaxation between the pumped and upper laser levels is sufficiently fast at 550 Torr of methane to prevent bottlenecking at all but the highest intensities. Comparison of laser characteristics with a quasi-two level analytic model suggests performance near the ideal steady-state limit, with the exception of modest mode matching.