R. D. Levine

The Maximum Entropy Formalism.

An exchangeable or removable nozzle arrangement for use in a fluidized bed furnace is movable and in sealing contact with a surrounding sleeve at one end of the nozzle and may be withdrawn from the sleeve through a valve at the other end of the sleeve. An inlet to the space between the sleeve and the nozzle is connected to a source of pressurized fluidizing gas. Upon removal of a nozzle, while the furnace is under load, the bed is maintained in its fluidized state.

DNA computing circuits using libraries of DNAzyme subunits

Biological systems that are capable of performing computational operations could be of use in bioengineering and nanomedicine, and DNA and other biomolecules have already been used as active components in biocomputational circuits. There have also been demonstrations of DNA/RNA-enzyme-based automatons, logic control of gene expression, and RNA systems for processing of intracellular information. However, for biocomputational circuits to be useful for applications it will be necessary to develop a library of computing elements, to demonstrate the modular coupling of these elements, and to demonstrate that this approach is scalable. Here, we report the construction of a DNA-based computational platform that uses a library of catalytic nucleic acids (DNAzymes), and their substrates, for the input-guided dynamic assembly of a universal set of logic gates and a half-adder/half-subtractor system. We demonstrate multilayered gate cascades, fan-out gates and parallel logic gate operations. In response to input markers, the system can regulate the controlled expression of anti-sense molecules, or aptamers, that act as inhibitors for enzymes.

An Algorithm for Finding the Distribution of Maximal Entropy

Abstract An algorithm for determining the distribution of maximal entropy subject to constraints is presented. The method provides an alternative to the conventional procedure which requires the numerical solution of a set of implicit nonlinear equations for the Lagrange multipliers. Here they are determined by seeking a minimum of a concave function, a procedure which readily lends itself to computational work. The program also incorporates two preliminary stages. The first verifies that the constraints are linearly independent and the second checks that a feasible solution exists.

Vibrational energy transfer in molecular collisions: An information theoretic analysis and synthesis

State‐to‐state rate constants for vibrational energy transfer (both V–V and V–T) are characterized using an ’’exponential gap’’ representation. The collisions analyzed include experimental results for both V–T and V–V transfer rates, trajectory computations for V–T transfer rates (via both inelastic and reactive, atom exchange, collisions) and quantal computations for V–V transfer rates. The results are analyzed in terms of the surprisal, a measure of deviation of the actual rate from the prior (or reference) rate. The prior rates are computed on the basis of the assumption that (at a given collision energy) all final states are equally probable. For almost all cases the surprisal could be characterized by a single parameter. The magnitude of this parameter (and its temperature dependence) could be predicted using bulk averages only. Such predictions are demonstrated for both experimental and trajectory computed rates. The link between the microscopic dynamics and macroscopic kinetics is forged by the use...

A unified algebraic model description for interacting vibrational modes in ABA molecules

A simple yet realistic model Hamiltonian which describes the essence of many aspects of the interaction of vibrational modes in polyatomics is discussed. The general form of the Hamiltonian is that of an intermediate case between the purely local mode and purely normal mode limits. Resonance interactions of the Fermi and Darling–Dennison types are shown to be special cases. The classical limit of the Hamiltonian is used to provide a geometrical content for the model and to illustrate the ‘‘phase‐like’’ transition between local and collective (i.e., normal) mode behavior. Such transitions are evident as the coupling parameters in the Hamiltonian are changed and also for a given Hamiltonian as the energy is changed. Applications are provided to higher lying vibrational states of specific molecules (H2O, O3, SO2, C2H2, and C2D2).

Energy, entropy and the reaction coordinate: thermodynamic-like relations in chemical kinetics☆

Abstract A simple thermodynamic-like interpretation of the relation between the kinetic and the thermodynamic parameters of chemical reactions (“linear free energy relations”) is discussed and applied. The central concept is the introduction of mixing (or configurational) entropy to account for the activation barrier of chemical reactions.

Collision induced dissociation: A statistical theory

A statistical theory of collision induced dissociation using the three body angular momentum introduced by Delves and Smith is presented. A distinction is made between direct dissociation (no two body intermediates) and indirect processes, due to the formation of quasibound diatoms (of either the chaperon or the energy transfer type). The post‐threshold energy dependence in the statistical theory is of the type A(E−E0)n/Etr where E is the total energy and Etr the translational energy. (n ≈ 2 or 1.5 for direct and indirect processes.) The threshold energy, Eo, can be determined by a suitably linearized plot without a prior determination of n. Following a series of diagnostic calculations for the reaction He+H2+(ν)→ He+H++H, the experimental results are simulated via the introduction of a nonstatistical (i.e., selective) bias by representing the dependence of A on the initial vibrational energy in the form A ∝ exp(−λ fν) where fv is the fraction of enegy in the vibration.

Entropy and chemical change. III. The maximal entropy (subject to constraints) procedure as a dynamical theory

An equivalence between the dynamical (equations of motion) and the information theoretic (maximal entropy) approaches to collision phenomena is established. The connection is demonstrated in both directions. The variational procedure of maximal entropy is shown to converge to an exact solution of the equations of motion (be they classical or quantal) throughout the collision. In particular, a stationary precollision state is proved to be a state of maximal entropy (subject to constants of the unperturbed motion) and to remain a state of maximal entropy throughout the collision. Conversely, the exact solution of the equations of motion is shown to be of maximal entropy. In this fashion one obtains an algebraic procedure for the specification of the constraints which determine (via the procedure of maximal entropy) an exact solution of the equations of motion. Surprisal analysis does not require the solution of differential equations. These must be solved to determine the magnitude of the Lagrange parameter...

Mode Selective Chemistry

Selectivity of product formation in activated chemical reactions can be accomplished by the control of energy acquisition, storage and disposal in the molecular system. This goal can be achieved by ‘passive control’ via energy acquisition, i.e., selecting the initial conditions and letting the system evolve under its own Hamiltonian, and by the ‘active control’ of energy storage and disposal, i.e., modifying the equations of motion by imposing external, additional terms in the Hamiltonian. We discuss the possibility and conditions for non-statistical reaction dynamics in molecules, van der Waals molecules, clusters, surfaces, condensed phases and biophysical systems, which result in selective chemistry.

Energy transfer to a morse oscillator

Abstract The vibrational excitation of a Morse oscillator in a collinear collision is determined analytically using a new dynamical algebra. The dependence of V → T processes on the initial vibrational state is examined. At finite coupling strengths the decline of P n → n−1 / n with n is faster than that derived for weak coupling.