A Classical Formulation of Quantum Theory?

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit.     

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.     

Reactivity of tetrahydrochromeno[2,3‐b]indoles: chromic indicators of cyanide

The synthesis and reactivity of a tetrahydrochromeno[2,3‐b]indoles are reported. Evidence for reversible ring‐opening is based on H/D exchange and trapping experiments. These compounds readily undergo reaction with tetra‐n‐butylammonium cyanide. The cyanide reaction is 10–100× faster when the solution is irradiated with 350 nm light. Reaction with trimethylsilyl cyanide occurs only with UV irradiation demonstrating photoreactivity. The rate of tetrahydrochromeno[2,3‐b]indole ring‐opening is greater for (i) Me substitution at the hemiaminal carbon (compared to Ph), and (ii) substitution of fluorine at the 9‐position of the indole. Under acidic conditions, the ring‐opened indolium ion is observed. Copyright © 2013 John Wiley & Sons, Ltd.     

Force-torque correlations

The equilibrium force-torque correlation ?Nf? is studied, first for a general fluid in which the intermolecular potential is expanded in generalized spherical harmonics, and then for the specific case of homonuclear diatomic molecules. If coordinate axes are taken with z axis parallel to the 12 intermolecular vector, it is shown that two (and only two) elements of the tensor are non-zero : ?n_x (12)f_y (12)? = -?n_y (12)f_x (12)?. For the linear molecule, these elements are evaluated in the limit of zero density for the atom-atom model of the potential. Example calculations are done, numerically for finite L (where L is the length of the diatomic molecule) and analytically in the limit of small L.     

On the validity and properties of the atom-atom potential as a function of intermolecular separation,configuration, and partial wave order

The intermolecular partial wave expansion of the atom-atom potential U is reviewed briefly and developed, by using results due to Sack, so that the radial components of the expansion can be evaluated to arbitrary accuracy for all relevant partial wave orders and values of the intermolecular distance r. These results are used to study the convergence of the partial wave expansion of U as a function of partial wave order, r, intermolecular orientation, and the anisotropy of the interacting molecules. In marked contrast to previous work it is found that many of the higher order partial wave components of U are important relative to the isotropic term even for the interaction of relatively spherical molecules and that the results obtained from a truncated partial wave expansion depend significantly upon the method of summation due to the generally poor convergence of the expansion. The validity of the atom-atom potential as a representation of the correct attractive intermolecular potential is also discussed in some detail. There are basic problems associated with the representations furnished by both the isotropic and the anisotropic parts of the atom-atom potential at intermediate and large r. The different convergence properties of the r ^-1 expansions of the partial wave expansions of U and of the correct potential for these values of r is illustrated by using model interactions. While it appears that it may be possible to obtain a qualitatively reasonable representation of the attractive part of an intermolecular potential over a useful range of r from atom-atom results, this apparently cannot be achieved for wider ranges of r or for the purely anisotropic part of the potential.     

Multi-photon vibrational resonances,with modulation effects,using HeXe,NeAr and NeXe as models

Model calculations are presented for the multi-photon vibrational spectra for the bound states of the (non-rotating) rare gas dimers HeXe, NeAr and NeXe. The results are used to discuss some of the features of electric dipole spectra that can occur due to the presence of non-zero diagonal dipole matrix elements and/or near-degenerate energy levels. These include multi-photon resonance profiles with oscillatory fringe patterns localized around the main resonance peaks and the possibility of shifts of resonance positions to low frequency relative to the weak field limit.     

An experimental and modeling study of the autoignition of 3-methylheptane

An experimental and kinetic modeling study of the autoignition of 3-methylheptane, a compound representative of the high molecular weight lightly branched alkanes found in large quantities in conventional and synthetic aviation kerosene and diesel fuels, is reported. Shock tube and rapid compression machine ignition delay time measurements are reported over a wide range of conditions of relevance to combustion engine applications: temperatures from 678 to 1356 K; pressures of 6.5, 10, 20, and 50 atm; and equivalence ratios of 0.5, 1.0, and 2.0. The wide range of temperatures examined provides observation of autoignition in three reactivity regimes, including the negative temperature coefficient (NTC) regime characteristic of paraffinic fuels. Comparisons made between the current ignition delay measurements for 3-methylheptane and previous results for n-octane and 2-methylheptane quantifies the influence of a single methyl substitution and its location on the reactivity of alkanes. It is found that the three C₈ alkane isomers have indistinguishable high-temperature ignition delay but their ignition delay times deviate in the NTC and low-temperature regimes in correlation with their research octane numbers. The experimental results are compared with the predictions of a proposed kinetic model that includes both high- and low-temperature oxidation chemistry. The model mechanistically explains the differences in reactivity for n-octane, 2-methylheptane, and 3-methylheptane in the NTC through the influence of the methyl substitution on the rates of isomerization reactions in the low-temperature chain branching pathway, that ultimately leads to ketohydroperoxide species, and the competition between low-temperature chain branching and the formation of cyclic ethers, in a chain propagating pathway.     

Piecewise optimal linearization method for nonlinear stochastic differential equations

A method for estimating the dynamical statistical properties of the solutions of nonlinear Langevin-type stochastic differential equations is presented. The non-linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval. The linearization procedure is optimal in the sense of the Chebyshev inequality. Long-term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals. The method is applied to a model nonlinear equation for which the exact time-dependent moments can be obtained by numerical methods. The calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium.Supported in part by the National Science Foundation under Grants CHE77-16307 and PHY76-04761.