A simple proof of the stability criterion of Gray and Griffeath

Summary Gray and Griffeath studied attractive nearest neighbor spin systems on the integers having “all 0's” and “all 1's” as traps. Using the contour method, they established a necessary and sufficient condition for the stability of the “all 1's” equilibrium under small perturbations. In this paper we use a renormalized site construction to give a much simpler proof. Our new approach can be used in many situations as a substitute for the contour method. Partially supported by a grant from the National Science Foundation Partially supported by the Army Research Office through the Mathematical Sciences Institute at Cornell University     

An optoelectronic recirculating sorter based on CMOS/vertical cavity surface emitting laser smart pixel arrays; architecture and system demonstration

The architecture of an optoelectronic recirculating sorter based on the hybrid integration of CMOS logic circuitry, silicon detector/receivers and vertical cavity surface emitting lasers is presented along with the demonstration of the system.     

Evidence for vibrational excitation in H+ + CH4, CD4 collisions by means of a surface-hopping mechanism

The energy-loss spectra for H⁺ scattered at small angles from CH₄ and CD₄ display an unusual bimodal character and extremely large average excitation energies. We propose a potential energy surface-hopping mechanism to account for the novel features of this system.     

Simulations of proton order and disorder in ice Ih

Computer simulations of ice Ih with different proton orientations are presented. Simulations of proton disordered ice are carried out using a Monte Carlo method which samples over proton degree of freedom, allowing for the calculation of the dielectric constant and for the examination of the degree of proton disorder. Simulations are also presented for two proton ordered structures of ice Ih, the ferroelectric Cmc2(1) structure or ice XI and the antiferroelectric Pna2(1) structure. These simulations indicate that a transition to a proton ordered phase occurs at low temperatures (below 80 K). The symmetry of the ordered phase is found to be dependent on the water potential. The stability of the two proton ordered structures is due to a balance of short-ranged interactions which tend to stabilize the Pna2(1) structure and longer-range interactions which stabilize the Cmc2(1) structure.     

Cluster size selectivity in the product distribution of ethene dehydrogenation on niobium clusters

Ethene reactions with niobium atoms and clusters containing up to 25 constituent atoms have been studied in a fast-flow metal cluster reactor. The clusters react with ethene at about the gas-kinetic collision rate, indicating a barrierless association process as the cluster removal step. Exceptions are Nb8 and Nb10, for which a significantly diminished rate is observed, reflecting some cluster size selectivity. Analysis of the experimental primary product masses indicates dehydrogenation of ethene for all clusters save Nb10, yielding either Nb(n)C2H2 or Nb(n)C2. Over the range Nb-Nb6, the extent of dehydrogenation increases with cluster size, then decreases for larger clusters. For many clusters, secondary and tertiary product masses are also observed, showing varying degrees of dehydrogenation corresponding to net addition of C2H4, C2H2, or C2. With Nb atoms and several small clusters, formal addition of at least six ethene molecules is observed, suggesting a polymerization process may be active. Kinetic analysis of the Nb atom and several Nb(n) cluster reactions with ethene shows that the process is consistent with sequential addition of ethene units at rates corresponding approximately to the gas-kinetic collision frequency for several consecutive reacting ethene molecules. Some variation in the rate of ethene pick up is found, which likely reflects small energy barriers or steric constraints associated with individual mechanistic steps. Density functional calculations of structures of Nb clusters up to Nb(6), and the reaction products Nb(n)C2H2 and Nb(n)C2 (n = 1...6) are presented. Investigation of the thermochemistry for the dehydrogenation of ethene to form molecular hydrogen, for the Nb atom and clusters up to Nb6, demonstrates that the exergonicity of the formation of Nb(n)C2 species increases with cluster size over this range, which supports the proposal that the extent of dehydrogenation is determined primarily by thermodynamic constraints. Analysis of the structural variations present in the cluster species studied shows an increase in C-H bond lengths with cluster size that closely correlates with the increased thermodynamic drive to full dehydrogenation. This correlation strongly suggests that all steps in the reaction are barrierless, and that weakening of the C-H bonds is directly reflected in the thermodynamics of the overall dehydrogenation process. It is also demonstrated that reaction exergonicity in the initial partial dehydrogenation step must be carried through as excess internal energy into the second dehydrogenation step.     

Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. VII. Stress-birefringence relations

Crosslinks are introduced by γ irradiation into 1,2-polybutadiene while strained in uniaxial extension near T_g with stretch ratio λ₀, thereby trapping a proportion of the entanglements originally present. The stress at any subsequent strain λ is accurately given by the sum σ_N + σ_x, where σ_N is the stress contributed by a trapped entanglement network with λ = 1 as reference and a Mooney–Rivlin stress-strain relation, and σ_x is that contributed by a crosslink network with λ = λ₀ as reference and neo-Hookean stress-strain relation. The birefringence is accurately given as δn = ?_Nσ_N + ?_xσ_x, where the ?'s are the respective stress-optical coefficients. From measurements at λ = λ₀ where σ_x = 0, ?_N can be determined separately. For polymer with 88% 1,2 microstructure, ?_N and ?_x are nearly equal and independent of irradiation dose, though strongly dependent on temperature. For polymer with (95–96)% 1,2, ?_N and ?_x are different (even opposite in sign) and dependent on dose. This behavior is associated with a side reaction of cyclization by the γ irradiation, which is inhibited by the 1,4 moiety in the polymer with lesser 1,2 content. It is responsible for residual birefringence in the state of ease (λ = λ_s) where σ_N = –σ_x and the stress is zero.     

COPPER BENZOCHLORIN, A NOVEL PHOTOSENSITIZER FOR PHOTODYNAMIC THERAPY: EFFECTS ON A TRANSPLANTABLE UROTHELIAL TUMOR

Abstract— An iminum salt of octaethylbenzochlorin with copper in the aromatic ring, CDSI, was tested for its tumoricidal effects on theA–27 N-[4-(5-notro-2-furyl)-2-thiazoly] formamide tumor line. CDSI was found to be an effective photosensitiz4r in vivo when used in combination with either a xenon arc lamp or a pulsed alexandrite laser. Hemodynamically, CDSI and light caused a rapid decrease in tumor blood flow. skin photosensitization was found to be minimal when drug-injected mice werwe illuminated in a solar simulator.     

Nonlinear pedagogy: a constraints-led framework for understanding emergence of game play and movement skills

Team sport competition can be characterized as a complex adaptive system in which concepts from nonlinear dynamics can provide a sound theoretical framework to understand emergent behavior such as movement coordination and decision making in game play. Nonlinear Pedagogy is presented as a methodology for games teaching, capturing how phenomena such as movement variability, self-organization, emergent decision making, and symmetry-breaking occur as a consequence of interactions between agent-agent and agent-environment constraints. Empirical data from studies of basketball free-throw shooting and dribbling are used as task vehicles to exemplify how nonlinear phenomena characterize game play in sport. In this paper we survey the implications of these data for Nonlinear Pedagogy, focusing particularly on the manipulation of constraints in team game settings. The data and theoretical modeling presented in this paper provide a rationale in nonlinear dynamics for the efficacy of a prominent model of game play teaching, Teaching Games for Understanding approach.     

Evolution in predator–prey systems

We study the adaptive dynamics of predator–prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit long term prey coexistence and the trait of the resident prey type converges to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. In this case, depending on the parameters being varied, we see that (i) the number of coexisting predators remains tight and the differences in traits from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity, and we calculate the asymptotic rate at which the traits of the least and most “fit” predators in the population increase. This last result is obtained by comparison with a branching random walk killed to the left of a linear boundary and a finite branching–selection particle system.     

Combined Photoredox/Enzymatic C−H Benzylic Hydroxylations

Chemical transformations that install heteroatoms into C?H bonds are of significant interest because they streamline the construction of value‐added small molecules. Direct C?H oxyfunctionalization, or the one step conversion of a C?H bond to a C?O bond, could be a highly enabling transformation due to the prevalence of the resulting enantioenriched alcohols in pharmaceuticals and natural products,. Here we report a single‐flask photoredox/enzymatic process for direct C?H hydroxylation that proceeds with broad reactivity, chemoselectivity and enantioselectivity. This unified strategy advances general photoredox and enzymatic catalysis synergy and enables chemoenzymatic processes for powerful and selective oxidative transformations.