TEM characterization of chemically synthesized copper–gold nanoparticles

Dodecanethiol-capped Cu–Au nanoparticles, synthesized via a successive two-phase (water/toluene) and galvanic-exchange procedure, were characterized using transmission electron microscopy (TEM). The size range of the particles is around 1–7 nm. Electron-induced morphological evolution was observed under high resolution (HR) TEM. Cuboctahedral morphology was found to be thermodynamically stable. Electron-induced aggregation of two particles was also observed. Chemical ordering of cuboctahedral particles was studied by atomic-resolution high angle annular dark field (HAADF) imaging in scanning TEM (STEM) mode and energy dispersive X-ray (EDX) element mapping using a silicon drift detector (SDD). The particles were found to be Cu–Au mixed, and to be stable in air. Surface plasmon resonance (SPR), which is dependent on local structure and morphology, was investigated by electron energy loss spectroscopy (EELS).     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

A New Proof for the Convergence of an Individual Based Model to the Trait Substitution Sequence

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and the process is viewed in the timescale of mutations. Using averaging techniques due to Kurtz (in Lecture Notes in Control and Inform. Sci., vol. 177, pp. 186–209, 1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (in Trends in Ecology and Evolution 7(6), 198–202, 1992), first worked out by Dieckman and Law (in Journal of Mathematical Biology 34(5–6), 579–612, 1996) and rigorously proved by Champagnat (in Theoretical Population Biology 69, 297–321, 2006): rigging the model such that “invasion implies substitution”, we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population.     

Cubic symmetric polynomials yielding variations of the Erdős–Ginzburg–Ziv theorem

Let p be a prime and let $\varphi\in\mathbb{Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ be a symmetric polynomial, where  $\mathbb {Z}_{p}$ is the field of p elements. A sequence T in  $\mathbb {Z}_{p}$ of length p is called a φ-zero sequence if φ(T)=0; a sequence in $\mathbb {Z}_{p}$ is called a φ-zero free sequence if it does not contain any φ-zero subsequence. Motivated by the EGZ theorem for the prime p, we consider symmetric polynomials $\varphi\in \mathbb {Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ , which satisfy the following two conditions: (i) every sequence in  $\mathbb {Z}_{p}$ of length 2p?1 contains a φ-zero subsequence, and (ii) the φ-zero free sequences in  $\mathbb {Z}_{p}$ of maximal length are all those containing exactly two distinct elements, where each element appears p?1 times. In this paper, we determine all symmetric polynomials in $\mathbb {Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ of degree not exceeding 3 satisfying the conditions above.     

A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton–Jacobi equations

We investigate the large-time behavior of the value functions of the optimal control problems on the n-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of view of the study on partial differential equations, it is equivalent to consider viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations. The large-time behavior of viscosity solutions of this problem has been recently studied by the authors and Camilli, Ley, Loreti, and Nguyen for some special cases, independently, but the general cases remain widely open. We establish a convergence result to asymptotic solutions as time goes to infinity under rather general assumptions by using dynamical properties of value functions.     

Generalized Random Spectral Measures

In an attempt to examine the random version of the spectral theorem, the notion of random spectral measures and generalized random spectral measures are introduced and investigated. It is shown that each generalized random spectral measure on $(\mathbb C ,\mathcal{B}(\mathbb C ))$ admits a modification which is a random spectral measure.     

Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

     

Determination of sugar structures in solution from residual dipolar coupling constants: methodology and application to methyl beta-D-xylopyranoside

We have developed methodology for the determination of solution structures of small molecules from residual dipolar coupling constants measured in dilute liquid crystals. The power of the new technique is demonstrated by the determination of the structure of methyl beta-d-xylopyranoside (I) in solution. An oriented sample of I was prepared using a mixture of C(12)E(5) and hexanol in D(2)O. Thirty residual dipolar coupling constants, ranging from -6.44 to 4.99 Hz, were measured using intensity-based J-modulated NMR techniques. These include 15 D(HH), 4 (1)D(CH), and 11 (n)D(CH) coupling constants. The accuracy of the dipolar coupling constants is estimated to be < +/- 0.02 Hz. New constant-time HMBC NMR experiments were developed for the measurement of (n)D(CH) coupling constants, the use of which was crucial for the successful structure determination of I, as they allowed us to increase the number of fitted parameters. The structure of I was refined using a model in which the directly bonded interatom distances were fixed at their ab initio values, while 16 geometrical and 5 order parameters were optimized. These included 2 CCC and 6 CCH angles, and 2 CCCC and 6 CCCH dihedral angles. Vibrationally averaged dipolar coupling constants were used during the refinement. The refined solution structure of I is very similar to that obtained by ab initio calculations, with 11 bond and dihedral angles differing by 0.8 degrees or less and the remaining 5 parameters differing by up to 3.3 degrees . Comparison with the neutron diffraction structure showed larger differences attributable to crystal packing effects. Reducing the degree of order by using dilute liquid crystalline media in combination with precise measurement of small residual dipolar coupling constants, as shown here, is a way of overcoming the limitation of strongly orienting liquid crystals associated with the complexity of (1)H NMR spectra for molecules with more than 12 protons.     

Diffusion of non-volatile phenolic compounds in zeolite beta and silicalite in liquid phase

The present study aims to systematically investigate the adsorption kinetics of “non-volatile” phenolic compounds with different critical diameters (p-coumaric acid, ferulic acid, sinapinic acid, p-hydroxybenzoic acid, vanillic acid, syringic acid, and vanillin) onto zeolite beta and silicalite in several solvents. In the aqueous phase, the corrected diffusivity of non-volatile phenolic compounds is 2–5 orders of magnitude smaller than that of volatile aromatic compounds with the same critical diameter. On the other hand, the corrected diffusivity in zeolite beta is on the same order of magnitude among non-volatile phenolic compounds, despite the significant difference in critical diameter of the adsorbate. This suggests that the intracrystalline diffusivity of the non-volatile adsorbate is strongly affected by its original molecular immobility, rather than by the size (narrowness) of the adsorbate and micropore aperture. Non-volatility is considered to remarkably lower the molecular mobility of adsorbate on the surface of zeolite, even in the liquid phase. In addition, the intracrystalline diffusivity of non-volatile adsorbate is strongly affected by the type of solvent, and a close correlation was found between intracrystalline diffusivity and adsorption affinity. Revelations as to the kinetic behavior of non-volatile adsorbate in zeolite are expected to supply more information on the kinetic separation of compounds in the liquid phase. The significant difference in diffusivity among non-volatile and volatile adsorbates in zeolite leads to the possibility of kinetic separation among these adsorbates.