The method of ascending symmetry for irreducible characters of finite groups

The irreducible characters of a finite group are determined uniquely by those of a minimal set of maximal subgroups. The method is based on the construction of all class functions which are irreducible characters on every maximal subgroup. These are generalized characters by a theorem of Brauer, so that the irreducible characters are obtained by checking the norm. An alternative characterization of irreducible characters, the Maximum Mixing Rule, works for all point symmetry groups, and its physical significance is discussed. As an example, the character tables for all point symmetry groups and crystal double-groups are constructed in this way.Bat-Sheva de Rothschild fellow for 1985     

Influence of diffusion on the kinetics of excited-state association--dissociation reactions: comparison of theory and simulation

Several recent theories of the kinetics of diffusion influenced excited-state association--dissociation reactions are tested against accurate Brownian dynamics simulation results for a wide range of parameters. The theories include the relaxation time approximation (RTA), multiparticle kernel decoupling approximations and the so-called kinetic theory. In the irreversible limit, none of these theories reduce to the Smoluchowski result. For the pseudo-first-order target problem, we show how the RTA can be modified so that the resulting formalism does reduce correctly in the irreversible limit. We call this the unified Smoluchowski approximation, because it unites modern theories of reversible reactions with Smoluchowski's theory of irreversible reactions.     

A bond-order analysis of the mechanism for hydrated proton mobility in liquid water

Bond-order analysis is introduced to facilitate the study of cooperative many-molecule effects on proton mobility in liquid water, as simulated using the multistate empirical valence-bond methodology. We calculate the temperature dependence for proton mobility and the total effective bond orders in the first two solvation shells surrounding the H(5)O(2) (+) proton-transferring complex. We find that proton-hopping between adjacent water molecules proceeds via this intermediate, but couples to hydrogen-bond dynamics in larger water clusters than previously anticipated. A two-color classification of these hydrogen bonds leads to an extended mechanism for proton mobility.     

Crosslinked colloids with cyclopropenium cations

Chemical crosslinkers are commonly used to stabilize both natural and synthetic macromolecules, while providing opportunities to install functionality and modulate polymer architecture. Here, we introduce the aromatic cyclopropenium cation as a tri-functional crosslinker of secondary amine-containing polymers. The one-step crosslinking reaction is rapid and requires no subsequent purification. When dispersed in aqueous media, the crosslinked polymers form spherical nanoparticles with highly positive charge that is maintained even in alkaline conditions. This synthetic strategy will enable the incorporation of cyclopropenium into a wide variety of macromolecules. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2641–2645     

Adaptively refined dynamic program for linear spline regression

The linear spline regression problem is to determine a piecewise linear function for estimating a set of given points while minimizing a given measure of misfit or error. This is a classical problem in computational statistics and operations research; dynamic programming was proposed as a solution technique more than 40 years ago by Bellman and Roth (J Am Stat Assoc 64:1079–1084, 1969). The algorithm requires a discretization of the solution space to define a grid of candidate breakpoints. This paper proposes an adaptive refinement scheme for the grid of candidate breakpoints in order to allow the dynamic programming method to scale for larger instances of the problem. We evaluate the quality of solutions found on small instances compared with optimal solutions determined by a novel integer programming formulation of the problem. We also consider a generalization of the linear spline regression problem to fit multiple curves that share breakpoint horizontal coordinates, and we extend our method to solve the generalized problem. Computational experiments verify that our nonuniform grid construction schemes are useful for computing high-quality solutions for both the single-curve and two-curve linear spline regression problem.     

A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment

We consider a random walk on $\mathbb{Z }^d,\ d\ge 2$ , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from $x\in \mathbb{Z }^d$ to nearest neighbor $x+e$ is the same as to nearest neighbor $x-e$ . Assuming that the environment is genuinely $d$ -dimensional and balanced we show a quenched invariance principle: for $P$ almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler’s uniformly elliptic result (Comm Math Phys, 87(1), pp 81–87, 1982/1983) and Guo and Zeitouni’s elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments.     

Deactivation mechanism of the green fluorescent chromophore

We report time-resolved fluorescence data for the anion of p-hydroxybenzylidene dimethylimidazolinone (p-HBDI), a model chromophore of the green fluorescence protein, in viscous glycerol-water mixtures over a range of temperatures, T. The markedly nonexponential decay of the excited electronic state is interpreted with the aid of an inhomogeneous model possessing a Gaussian coordinate-dependent sink term. A nonlinear least-squares fitting routine enables us to achieve quantitative fits by adjusting a single activation parameter, which is found to depend linearly on 1/T. We derive an analytic expression for the absolute quantum yield, which is compared with the integrated steady-state fluorescence spectra. The microscopic origins of the model are discussed in terms of two-dimensional dynamics, coupling the phenyl-ring rotation to a swinging mode that brings this flexible molecule to the proximity of a conical intersection on its multidimensional potential energy surface.     

Heat-Treated Aerogel as a Catalyst for the Oxygen Reduction Reaction

Aerogels are fascinating materials that can be used for a wide range of applications, one of which is electrocatalysis of the important oxygen reduction reaction. In their inorganic form, aerogels can have ultrahigh catalytic site density, high surface area, and tunable physical properties and chemical structures—important features in heterogeneous catalysis. Herein, we report on the synthesis and electrocatalytic properties of an iron–porphyrin aerogel. 5,10,15,20-(Tetra-4-aminophenyl)porphyrin (H₂TAPP) and Fe^II were used as building blocks of the aerogel, which was later heat-treated at 600 °C to enhance electronic conductivity and catalytic activity, while preserving its macrostructure. The resulting material has a very high concentration of atomically dispersed catalytic sites (9.7×10²⁰ sites g⁻¹) capable of catalyzing the oxygen reduction reaction in alkaline solution (E_onset=0.92 V vs. RHE, TOF=0.25 e⁻ site⁻¹ s⁻¹ at 0.80 V vs. RHE).     

Heat‐Treated Aerogel as a Catalyst for the Oxygen Reduction Reaction

Aerogels are fascinating materials that can be used for a wide range of applications, one of which is electrocatalysis of the important oxygen reduction reaction. In their inorganic form, aerogels can have ultrahigh catalytic site density, high surface area, and tunable physical properties and chemical structures—important features in heterogeneous catalysis. Herein, we report on the synthesis and electrocatalytic properties of an iron–porphyrin aerogel. 5,10,15,20‐(Tetra‐4‐aminophenyl)porphyrin (H₂TAPP) and Fe^II were used as building blocks of the aerogel, which was later heat‐treated at 600 °C to enhance electronic conductivity and catalytic activity, while preserving its macrostructure. The resulting material has a very high concentration of atomically dispersed catalytic sites (9.7×10²⁰ sites g^?1) capable of catalyzing the oxygen reduction reaction in alkaline solution (E_onset=0.92 V vs. RHE, TOF=0.25 e^? site^?1 s^?1 at 0.80 V vs. RHE).