Theoretical study of the visible photodissociation spectrum of Ar 3 +

The photodissociation of Ar ₃ ⁺ is studied following a consistent theoretical approach from the Potential Energy Surfaces to the dynamics. Six P.E.S. are computed according to a D.I.M.-like model Hamiltonian. Transition dipole moments are determined using a similar method. The 4-D dynamics of this system is obtained with the H.W.D. method (Hemiquantal dynamic with the Whole DIM basis). All the 4 nuclear degrees of freedom and all the 6 electronic states are involved in the dynamical calculations, allowing for very general investigations. The main theoretical results are:

1. the spectrum essentially results from a Σ → Σg transition to the second excited electronic state along with a symmetric stretching motion
2. excited Ar ₃ ⁺ molecules almost all dissociate in Ar⁺ + 2 Ar
3. dissociation in Ar ₂ ⁺ + Ar requires special conditions such as low laser excitation and is predicted to increase with a specific excitation of the bending mode
4. the dominant symmetric stretching motion induces a bimodal kinetic energy distribution of the fragments.

All these points are in close agreement with experimental results.     

Mass spectra of the coordination compounds of nickel with the tetradentate Schiff bases of S-substituted thiosemicarbazides with 2,4-pentanedione and 3-oxo-2,4-pentanedione

The mass spectra of the coordination compounds of nickel(II) with the bis-S-substituted thiosemicarbazones of 2,4-pentanedione (R₂H₂L) with the general formula [NiR₂HL]X and of 3-oxo-2,4-pentanedione (H₂R₂LO) with the general formula NiR₂LO were studied. A distinguishing feature of the mass spectra of [NiR₂HL]X is the absence of molecular ion peaks. The initial point of fragmentation is the [M - HX] ions. The strongest lines in spectra of NiR₂LO are those due to the elimination of R and R-H. At the first stage the fragmentation of all the investigated compounds takes place mainly through only one of the thiosemicarbazide residues. At the second stage the 2,4-pentanedione (3-oxo-2,4-pentanedione) residue is eliminated, after which the remaining thiosemicarbazide part dissociates. A significant part of the fragmentation paths was confirmed by the peaks of the metastable ions and also by the mass spectra of the deuterated analogs.Institute of Chemistry, Academy of Sciences of the Moldavian SSR, Kishinev. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 2, 205–211, March–April, 1991. Original article submitted August 19, 1986.     

A proposal for the molecular basis of μ and δ opiate receptor differentiation based on modeling of two types of cyclic enkephalins and a narcotic alkaloid

Summary The molecular basis underlying the divergent receptor selectivity of two cyclic opioid peptides Tyr-c[N -d-Orn²-Gly-Phe-Leu-] (c-ORN) and [d-Pen², l-Cys⁵]-enkephalinamide (c-PEN) was investigated using a molecular modeling approach. Ring closure and conformational searching procedures were used to determine low-energy cyclic backbone conformers. Following reinsertion of amino acid side chains, the narcotic alkaloid 7-[(1R)-1-methyl-1-hydroxy-3-phenylpropyl]-6,14-endoethenotetrahydro oripavine (PEO) was used as a flexible template for bimolecular superpositions with each of the determined peptide ring conformers using the coplanarity and cocentricity of the phenolic rings as the minimum constraint. A vector space of PEO, accounting for all possible orientations for the C₂₁-aromatic ring of PEO served as a geometrical locus for the aromatic ring of the Phe⁴ residue in the opioid peptides. Although a vast number of polypeptide conformations satisfied the criteria of the opiate pharmacophore, they could be grouped into three classes differing in magnitude and sign of the torsional angle values of the tyrosyl side chain. Only class III conformers for both c-ORN and c-PEN, having tyramine dihedral angles ₁ =–150° ± 30° and ₂=–155° ± 20°, had significant structural and conformational properties that were mutually compatible while respecting the PEO vector space. Comparison of these properties in the context of the divergent receptor selectivity of the studied opioid peptides suggests that the increased distortion of the peptide backbone in the closure region of c-PEN together with the pendant ,-dimethyl group, combine to generate a steric volume which is absent in c-ORN and that may be incompatible with a restrictive topography of the receptor. The nature and stereo-chemistry of substituents adjacent to the closure region of the peptides could also modulate receptor selection by interacting with a charged () or neutral () subsite.     

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework,a volume distribution of holes

This paper treats the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of ³ and are located at the nodes of a regular mesh of size .) A suitable extension of the pressure is used to prove the convergence of the homogenization process to a Brinkman-type law (in which a linear zero-order term for the velocity is added to a Stokes or Navier-Stokes equation).     

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes

This paper is devoted to the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. For obstacles of critical size it was established in Part I that the limit problem is described by a law of Brinkman type. Here we prove that for smaller obstacles, the limit problem reduces to the Stokes or Navier-Stokes equations, and for larger obstacles, to Darcy's law. We also apply the abstract framework of Part I to the case of a domain containing tiny obstacles, periodically distributed on a surface. (For example, in three dimensions, consider obstacles of size ², located at the nodes of a regular plane mesh of period .) This provides a mathematical model for fluid flows through mixing grids, based on a special form of the Brinkman law in which the additional term is concentrated on the plane of the grid.     

An Ω(n 4/3) lower bound on the randomized complexity of graph properties

We improve King's (n ^5/4) lower bound on the randomized decision tree complexity of monotone graph properties to (n ^4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .