Extremal Coupled Map Lattices

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and power law distributions.Comment: 4 RevTeX pages, 3 eps figures. Uses psfig.sty. To be published in The European Physical Journal B (1999

New vector bosons and the diphoton excess

We consider the possibility that the recently observed diphoton excess at $\sim 750$ GeV can be explained by the decay of a scalar particle ($\varphi$) to photons. If the scalar is the remnant of a symmetry-breaking sector of some new gauge symmetry, its coupling to photons can be generated by loops of the charged massive vectors of the broken symmetry. If these new $W^\prime$ vector bosons carry color, they can also generate an effective coupling to gluons. In this case the diphoton excess could be entirely explained in a simplified model containing just $\varphi$ and $W^\prime$. On the other hand if $W^{\prime}$ does not carry color, we show that, provided additional colored particles exist to generate the required $\varphi$ to gluon coupling, the diphoton excess could be explained by the same $W^{\prime}$ commonly invoked to explain the diboson excess at $\sim 2$ TeV. We also explore possible connections between the diphoton and diboson excesses with the anomalous $t\bar{t}$ forward-backward asymmetry.Comment: Latex 8 pages, 1 figure. Extended discussion, new references. Matches published versio

The Riccati System and a Diffusion-Type Equation

We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered.Comment: 11 pages, no figure

On The Harmonic Oscillator Group

We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. A six parameter family of the square integrable oscillator wave functions, which seems cannot be obtained by the standard separation of variables, is presented as an example. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.Comment: 11 pages, no figure

Electrochemical comparison and deposition of lithium and potassium from phosphonium- and ammonium-tfsi ionic liquids

In this work, ionic liquids (ILs) were investigated for use as battery electrolytes. The ILs were synthesized from quaternary ammonium and phosphonium salts and TFSI-. A dendrite free lithium metal anode was demonstrated by deposition of a lithium-potassium alloy. Several phosphonium ILs were synthesized using the TFSI- and PF6- anions until a room temperature IL was obtained. The smaller size, highly symmetric PF6- anion yielded high melting point salts, while TFSI- yielded much lower melting point ILs. When a room temperature IL, Bu3HexP+TFSI-, was obtained the analogous ammonium IL, Bu3HexP+TFSI-, was synthesized and compared. The phosphonium-based ionic liquid showed improved stability and physical properties compared to the analogous ammonium-based IL. The phosphonium-based IL had higher conductivity, 0.43 mS/cm, than the ammonium-based IL, 0.28 mS/cm. The addition of LiTFSI to both ILs led to a decrease in conductivity and increase in viscosity. The lower viscosity and higher stability of the phosphonium-based IL led to higher current density and stability for electrodeposited lithium metal. IL reduction interfered with lithium deposition reflecting lower coulombic efficiencies and giving the appearance of an unstable lithium couple. An optimum deposition potential was found which was bounded by the electrochemical stability of each IL. The stability of lithium in the ILs increased at lower temperature due to slower reactivity with the IL. Addition of higher quantities of lithium ions caused a higher fraction of the cathodic current going to lithium deposition that was reoxidized. The stability of lithium in the ILs increased at lower temperature due to slower reactivity with the IL. The electrodeposition and reoxidation of potassium was also demonstrated. Deposition of a lithium-potassium alloy caused slight increases in the cathodic and anodic currents along with higher coulombic efficiencies. Also, it was found that a lithium-potassium alloy could be deposited at high current for long times without the occurrence of dendrites.M.S.Committee Chair: Paul Kohl; Committee Member: Jiri Janata; Committee Member: Tom Fulle