Stationary policies and Markov policies in Borel dynamic programming

Summary The question of the existence of good Markov [good stationary] policies is studied for a general class of Borel [stationary] dynamic programming models. It is shown, for example, that Markov [stationary] policies are uniformly adequate if every transition law is absolutely continuous with respect to a fixed measure [and the reward function is positive or the model satisfies certain compactness and continuity conditions].Research supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72Research supported by National Science Foundation Grant MCS 8100789     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

On the nature and origin of complexity in discrete,homogeneous, locally-interacting systems

The observed complexity of nature is often attributed to an intrinsic propensity of matter to self-organize under certain (e.g., dissipative) conditions. In order better to understand and test this vague thesis, we define complexity as logical depth, a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. We then assess the effects of dissipation, noise, and spatial and other symmetries of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems. We concentrate on discrete, spatially-homogeneous, locally-interacting systems such as kinetic Ising models and cellular automata.     

On the low temperature magnetic properties of some sulfites of divalent iron

Zero field Mössbauer spectra and powder susceptibility measurements show that the condensed, hydrogen bonded network compound FeSO₃ 3H₂O orders antiferromagnetically (T_Néel 9.5 K). The related anhydrous material FeSO₃ also shows antiferromagnetic exchange but no evidence of long range three-dimenstional magnetic order to as low as 1.4 K.Supported by the U.S. National Science Foundation Division of Materials Research—Solid State Chemistry Program Grant No. DMR 8313710.     

Thermodynamics of the dissociation of 2-aminopyridinium ion in synthetic seawater and a standard for pH in marine systems

Buffer solutions composed of 2-aminopyridinium chloride and 2-aminopyridine in synthetic seawater are useful as a supplement to buffers of Tris (pH 8.2) and Bis (pH 8.8) in standardizing measurements of hydrogen ion concentration (pm _H or pH(SWS)) in oceanography. The dissociation constant of 2-amino-pyridinium ion over the range of salinities (S) from 30 to 40 has now been determined from the emf of cells without liquid junction at eight temperatures (T) from 278.15 to 313.15 K. The results fit the equation pK=2498.31/T–15.3274+2.4050 lnT+S(0.012928–2.9417×10^–5T) with a standard deviation of 0.0023. Thermodynamic constants for the dissociation process and standard reference values of pm _H and pH(SWS) were derived from the data. The pm _H of the buffer consisting of 2-aminopyridinium chloride and 2-aminopyridine (each 0.04 molal) in synthetic seawater of salinity 35 varies from 7.356 at 278.15 K to 6.601 at 313.15 K.     

A Chiral Coordination Polymer of Silver(I) with Saccharinate and Pyridine: Synthesis,Spectral, Thermal,and Structural Characterization of [Ag(sac)(py)]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The first silver(I) complex of saccharinate (sac) with pyridine (py), [Ag(sac)(py)]_n has been synthesized and characterized by elemental analysis, IR spectroscopy and single crystal X-ray diffractometry. The complex crystallizes in chiral, trigonal space group P3₁21 (No. 152) with unit cell parameters of a = 11.2605(2) Å, c = 17.3300(4) Å, V = 1903.02(6) ų and Z = 6. [Ag(sac)(py)]_n contains monomeric [Ag(sac)(py)] units linked into infinite helices by way of Ag⋅sAg interactions [d(Ag⋅sAg) = 2.909(2) and 2.985(1) Å]. The distorted square-planar environment of Ag is completed by an N-bonded sac [Ag—N = 2.084(2) Å] and a py molecule [Ag—N = 2.116(2) Å]. The N_sac—Ag—N_py angle is 173.85(10)^∘. The one-dimensional chains are crosslinked by C—H⋅sO interactions involving the carbonyl and sulfonyl O atoms of sac and aromatic-ring hydrogen atoms of both sac and py. The thermal stability of the title complex was investigated using thermogravimetry and differential thermal analysis in a static atmosphere of air. The first decomposition stage between 90 and 160^∘C corresponds to removal of the py molecule in a single stage, while the degradation of the sac moiety occurs at two stages in the temperature range 370–515^∘C, giving an end product of metallic Ag.     

Direct dynamics trajectory study of the reaction of formaldehyde cation with D2: vibrational and zero-point energy effects on quasiclassical trajectories

Quasiclassical, direct dynamics trajectories have been used to study the reaction of formaldehyde cation with molecular hydrogen, simulating the conditions in an experimental study of H2CO+ vibrational effects on this reaction. Effects of five different H2CO+ modes were probed, and we also examined different approaches to treating zero-point energy in quasiclassical trajectories. The calculated absolute cross-sections are in excellent agreement with experiments, and the results provide insight into the reaction mechanism, product scattering behavior, and energy disposal, and how they vary with impact parameter and reactant state. The reaction is sharply orientation-dependent, even at high collision energies, and both trajectories and experiment find that H2CO+ vibration inhibits reaction. On the other hand, the trajectories do not reproduce the anomalously strong effect of nu2(+) (the CO stretch). The origin of the discrepancy and approaches for minimizing such problems in quasiclassical trajectories are discussed.     

Photosensitization of TiO2 colloids by Erythrosin B in acetonitrile

Photosensitization by Erythrosin B of a TiO₂ colloidal dispersion in acetonitrile has been studied by fast kinetic spectroscopy. The dye molecules adsorbed on the TiO₂ surface had a significantly shorter lifetime (2&#x0303; 250 ps) compared to those in homogeneous solution (≈ 1.6 ns) in acetonitrile. The photosensitization of TiO₂ occurred more efficiently from the singlet than from the triplet state of the dye.     

Polar substituent effects in the bicyclo[1.1.1]pentane ring system: acidities of 3-substituted bicyclo[1.1.1]pentane-1-carboxylic acids

Experimental gas-phase acidities are reported for a series of 3-substituted (X) bicyclo [1.1.1]pent-1-yl carboxylic acids (1, Y = COOH). A comparison with available calculated data (MP2/6-311++G**// B3LYP/6-311+G**) reveals good agreement. The relative substituent effects are shown to be adequately described by a much lower level of theory (B3LYP/6-31+G*). Various correlations are presented which clearly point to polar field effects as being the origin of the relative acidities.