Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

Surface free energies of styrene-acrylic acid copolymer plates prepared in various frames

Styrene (St)-acrylic acid (AA) copolymer plates were synthesized in the frames made of glass, aluminum (Al) and poly(difluoroethylene) (PDFE). Surface properties of the prepared copolymer plates were characterized with regard to critical surface tension ( _C ), chemical components by IR analysis and surface energies (total energy, _S ; dispersion force components, _S ^d ; polar component, _S ^p ; hydrogen bonding component, _S ^h ) and the following results were obtained.The _C values of the copolymer plates increased with AA content and also depended on the sort of the used frame. The increasing order of the _C values of the copolymer plates corresponded to those of the used frames, namely, PDFE frame < Al frame < Glass frame.The prepared copolymer plates with low AA contents (ca. 10 mol%) were enriched in the AA moiety in the surface layer regardless of the kind of the used frame.The total and the individual components of the surface free energies of the copolymer plates were largely affected by the property of the used frame. The glass frame gave the plate with higher _S ^h values suggesting preferential orientation of the polar site of AA component.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Relations between site percolation thresholds

By decomposing certain lattices into two sublattices, and examining at percolation threshold the structure of their infinite clusters, an approximate relation between p _c ⁰ , of the original lattice and p _c ¹ , of the sublattice is established: p _c ⁰ (p _c ¹ )^1/2. It is conjectured that an inequality always holds: p _c ⁰ (p _c ¹ )^1/2, and heuristic arguments are given to substantiate it. By similar considerations good estimates forp _c of certain correlated percolation problems are also obtained.     

Preparation and characterization of dendrimer-star PNIPAAM using dithiobenzoate-terminated PPI dendrimer via RAFT polymerization

Two dendritic reversible addition-fragmentation transfer (RAFT) agents with 8 and 16 terminal dithiobenzoate (DTB) groups on the surface of poly(propylene imine) (PPI) dendrimers (generation 2.0 and 3.0, respectively) were successively prepared, and they were used in the RAFT polymerization of N-isopropylacrylamide (NIPAAM). The polymerization kinetics was confirmed to pseudo-first-order behavior. The ¹H NMR and GPC analyses show that the dendrimer-star den (NIPAAM)_x (x = 8 or 16) prepared by RAFT method has well-defined structure, controlled molecular weight and low polydispersities (PDI < 1.3). The aqueous solution prepared from dendrimer-star PNIPAAM showed reversible changes in optical properties: transparent below a lower critical solution temperature (LCST) and opaque above the LCST.     

Effect of bovine serum albumin on the surface properties of ionic liquid-type Gemini surfactant

The effect of bovine serum albumin on the surface properties of IL-type gemini surfactant ([C₁₀-4-C₁₀im]Br₂), have been investigated by surface tension method. The critical micelle concentration (CMC) as a function of BSA concentrations at various temperatures was investigated. The CMC of [C₁₀-4-C₁₀im]Br₂ increases with increasing the concentration of BSA as well as the temperature of the system. The interfacial parameters viz; maximum surface excess concentration (Γ_max), the minimum area per molecule (A_min), and surface pressure at CMC (Π_cmc) were calculated. In addition, thermodynamic parameters of adsorption and micellization were evaluated by using surface tension data. The results indicated that the binding of [C₁₀-4-C₁₀im]Br₂ to BSA is spontaneous and exothermic in nature. The process is entropy driven and hydrophobic interactions are the major driving forces.     

Analysis of PCBs in Biotic Matrices by Two-Dimensional GC-ECD

Abstract

The suitability of three GC-ECD systems for the separation of a model mixture containing various congeners of PCBs together with persistent chlorinated aromatics (pesticides and their metabolites, industrial chemicals) was tested. Analyses were performed on two parallel capillaries, the stationary phase of one of them was always in routine practice very common 5% phenyl-methylpolysiloxane, the second one was either 50% phenylmethylpolysiloxane or 7% phenyl-7% cyanopropyl-methylpolysiloxane. The number of unresolved (coeluted) analytes was significantly reduced in these systems and thus unbiased quantitation of PCBs and other components used for regulation was possible. The utilization of this type of multidimensional chromatography for rapid and reliable analysis of real samples (fish oil, human fat) was documented.