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At least 1,603 records · Page 89

Structural, Electronic, and Photophysical Insights into a Few Atom Copper-Sulfur Cluster in the Solid and Solution States

Coinage-metal chalcogenide clusters are widely studied for their attractive photoluminescence properties. Copper chalcogenides are especially promising, but are often confined to solid-state investigations due to their limited solution stability and the difficulty of synthesizing stable, well-defined clusters. Here, we investigate copper–sulfur clusters incorporating a small number of Cu atoms to elucidate fundamental atomic interactions, ground- and excited-state characteristics, and photophysical behavior in both solid and solution. We have synthesized the Cu6(4,6-dimethyl-2-mercaptopyrimidine)6 cluster in both neutral and charged states, Cu6 and Cu6-2H2+, respectively, by selective ligand protonation. The molecular structures are determined using single-crystal X-ray diffraction, while Cu K-edge X-ray absorption spectroscopy is used to probe Cu electronic structure differences arising from the ligand modification. Steady-state and pump-probe optical spectroscopy is used to investigate photophysical properties, interpreted using density functional theory methods. Both clusters exhibit good stability in the solid state and in solution and show characteristic near-infrared emission with microsecond lifetimes. Overall, the Cu6S6 clusters display favorable charge–transfer characteristics and show potential for further use in driving photochemical transformations.

Copper-sulfur clusters↗

Earthquake-induced impact of base-isolated buildings: theory, numerical modeling, and design solutions

Earthquake shaking more intense than that used to size the horizontal clearance between a base–isolated building and near–rigid perimeter moat wall will result in hard impact, producing high–frequency, high–amplitude acceleration response in the structure and supported equipment. Herein this paper provides a design solution for the damaging effects of hard impact by installing a compliant engineered element in the load path between the base–isolated building and the moat wall, resulting in soft impact and a much smaller acceleration response. The engineered element assumed herein is a commercial–off–the–shelf marine fender with mechanical properties determined by physical testing. The attachment of a flexible engineered element, with well–defined stiffness and damping, to a near–rigid moat wall, simplifies the numerical modeling of the building–moat wall system and eliminates the need to bound the lateral stiffness of the wall for impact calculations. The simple model of the engineered element can be implemented in commercial finite element codes. Theory is developed for two–sided impact of a single–degree–of–freedom oscillator. Analytical solutions are derived for the shifted first–mode frequency of the impacted oscillator and for its free–vibration response. The shifted first–mode frequency is a function of the composite lateral stiffness of the isolator–engineered element assembly and its earthquake–induced displacement. Local peaks in the spectral response of the impacted oscillator form at odd integer multiples of the shifted first–mode frequency. The analytical solutions can be used to verify, in part, the numerical model used for impact analysis.

42 ENGINEERING↗

Morphological Studies of Solution-Crystallized Thermoplastic Elastomers with Polyethylene Endblocks and a Random-Copolymer Midblock

Styrenic thermoplastic elastomers (TPEs) in the form of triblock copolymers possessing glassy endblocks and a rubbery midblock account for the largest global market of TPEs worldwide, and typically rely on microphase separation of the endblocks and the subsequent formation of rigid microdomains to ensure satisfactory network stabilization. In this work, the morphological characteristics of a relatively new family of crystallizable TPEs that instead consist of polyethylene endblocks and a random-copolymer midblock composed of styrene and (ethylene-co-butylene) moieties are investigated. Copolymer solutions prepared at logarithmic concentrations in a slightly endblock-selective solvent are subjected to crystallization under different time and temperature conditions to ascertain if copolymer self-assembly is directed by endblock crystallization or vice versa. According to transmission electron microscopy, semicrystalline aggregates develop at the lowest solution concentration examined (0.01 wt%), and the size and population of crystals, which dominate the copolymer morphologies, are observed to increase with increasing aging time. Real-space results are correlated with small- and wide-angle X-ray scattering to elucidate the concurrent roles of endblock crystallization and self-assembly of these unique TPEs in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fundamental Solutions for Two-Point Boundary Value Problems in Orbital Mechanics

We consider a two-point boundary value problem (TPBVP) in orbital mechanics involving a small body (e.g., a spacecraft or asteroid) and N larger bodies. The least action principle TPBVP formulation is converted into an initial value problem via the addition of an appropriate terminal cost to the action functional. The latter formulation is used to obtain a fundamental solution, which may be used to solve the TPBVP for a variety of boundary conditions within a certain class. In particular, the method of convex duality allows one to interpret the least action principle as a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. In the case where the time duration is less than a specific bound, there exists a unique critical point for the resulting differential game, which yields the fundamental solution given in terms of the solutions of associated Riccati equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On Nonuniqueness of Solutions of Hamilton–Jacobi–Bellman Equations

An example of a nonunique solution of the Cauchy problem of Hamilton–Jacobi–Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t, x, p) is locally Lipschitz continuous with respect to all variables, convex in p and with linear growth with respect to p and x. The HJB equation possesses two distinct lower semicontinuous solutions with the same final conditions; moreover, one of them is the value function of the corresponding Bolza problem. The definition of lower semicontinuous solution was proposed by Frankowska (SIAM J. Control Optim. 31:257–272, 1993) and Barron and Jensen (Commun. Partial Differ. Equ. 15(12):1713–1742, 1990). Using the example an analysis and comparison of assumptions in some uniqueness results in HJB equations is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Structure of Methanol Solvated Iodozinc(II) Complexes in Solution

The structures of the solvated zinc ion and the solvated zinc–iodide complexes in methanol solution have been determined by EXAFS. The zinc ion is six-coordinated in an octahedral fashion with a mean Zn–O bond distance of 2.071(4) Å . According to the stability constants of the zinc–iodide system in methanol solution the first complex, ZnI + , is suppressed, which may indicate that a coordination change takes place at this step. On the other hand, the second complex, ZnI 2 , predominates at excess of iodide. The methanol solvated ZnI 2 complex has a tetrahedral structure with mean Zn–I and Zn–O bond distances of 2.55(1) and 1.99(1) Å , respectively. The mean Zn–I bond distance in a solution containing a maximal content of ZnI + , ca. 12%, strongly indicates that the first complex also has a tetrahedral structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543–1608, 2004), (Bull Inst Math Acad Sin 1:1–78, 2006), (Bull Inst Math Acad Sin 6:151–243, 2011) and Lee et al. (Commun Math Phys 269:17–37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices

In recent results on representation of the solutions of systems of delayed differential equations, the condition that the linear parts are given by pairwise permutable matrices was assumed. We show how this strong condition can be avoided and derive a representation of solutions of systems of differential equations with nonconstant coefficients and variable delays. The results are applied to a system with two constant delays. In addition, the nonexistence of blow-up solutions is proved for nonlinear systems.

97 MATHEMATICS AND COMPUTING↗

Qualitative Properties of Solutions to Elliptic Equations with Nonpower Nonlinearities in ℝ{sub n}

We consider a class of anisotropic elliptic equations with nonpower nonlinearities. We establish the existence of a solution in the local Sobolev–Orlicz spaces without conditions on the data growth at infinity. We find sufficient uniqueness conditions, obtain estimates characterizing the behavior of the solution at infinity, and prove the continuous dependence of the solution on the right-hand side of the equation.

97 MATHEMATICS AND COMPUTING↗

Lyapunov Characteristics of Oscillation, Rotation, and Wandering of Solutions of Differential Systems

A number of Lyapunov exponents are defined for solutions of linear systems on the half-line. These exponents are responsible for such properties of the solutions as oscillation, rotation, and wandering and are defined in terms of certain functionals applied to the solutions on finite intervals as a result of two operations: upper or lower averaging in time and minimization over all bases in the phase space. We consider important special cases of systems: those of a low order, autonomous systems, those associated with equations of an arbitrary order. We obtain a set of relations (equalities and inequalities) between the said exponents, together with their refined values in special cases. It is shown that this set is complete in the sense that it cannot be extended or strengthened by any other meaningful relation.

97 MATHEMATICS AND COMPUTING↗

Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation

We study solutions in integers of an implicit linear inhomogeneous first order difference equation bx{sub n+1} = ax{sub n} + f{sub n}. Based on the p-adic topology on the ring of integers, we obtain a criterion for the existence of solutions and show that for a = 1 a typical (in the natural topological sense) equation has no integer solutions.

97 MATHEMATICS AND COMPUTING↗

Physical Interpretation of Strict Solutions of Diffraction Problems by Heuristic Relations

We propose a new approach to construct heuristic relations describing solutions of diffraction problems. Those relations are based on physical principles and allow one to interpret mathematically strict solutions. Since the heuristic relations possess high performance and accuracy, they can also be used along with any strict approach or experimental results for a significant improvement of efficiency of solutions of practical problems related to applications of the diffraction theory.

97 MATHEMATICS AND COMPUTING↗

Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities

The resonant nonlinear Schrödinger equation in three dimensions featuring both the Kerr and parabolic law nonlinearities has been considered in this paper due to its vital role in the propagation of solitons in optical fibers. Optical soliton solutions to this important model consisting of dark, singular and combo solitons alongside various periodic solutions that are new and more general to the lately devised solutions have been presented. We also reported the constraint conditions that guarantee the survival of these solitons and depicted certain results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Heteronuclear complexation in the system 1-hydroxyethylidenediphosphonic acid—manganese(II)—gadolinium(III) in aqueous solution

pH-Potentiometric method in combination with mathematical modeling was used to study the system manganese(II)—gadolinium(III)—1-hydroxyethylidenediphosphonic acid (HEDP, H{sub 4}L). When both cations simultaneously are present in the solution, the accumulation of heteronuclear forms with the ratio of Gd: Mn: HEDP equal to 1: 1: 1, 1: 1: 2, and 1: 1: 3 was observed already in the strongly acidic pH region, while from homonuclear forms only five complexes were detected in the solution, namely, MnL{sub 2}{sup 6–}, GdH{sub 4}L{sub 2}{sup –}, GdH{sub 2}L{sup +}, KGd{sub 2}HL{sub 2}↓, and K{sub 3}Gd{sub 2}L{sub 2}(OH)↓. It was concluded that heteronuclear complexes are much stronger and replace homonuclear forms in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Kinetic Model for Dissolution of Zinc Oxide Powder Obtained from Waste Alkaline Batteries in Sodium Hydroxide Solutions

The determination of individual dissolution behaviors of zinc and manganese in waste alkaline battery powders is an important subject from the points of the leaching yield, design of leaching reactor, and separation and recovery steps of hydrometallurgical process. In the current study, we investigated the dissolution kinetics of zinc oxide powder. Zinc oxide was obtained from waste alkaline batteries, and sodium hydroxide solutions were used as solvent. In the experiments, the effects of solution concentration, reaction temperature, stirring speed, solid-to-liquid ratio, and particle size on the dissolution of zinc oxide were investigated. It was demonstrated that the dissolution increased with the increasing concentration, reaction temperature, and stirring speed, and with the decreasing solid-to-liquid ratio and particle size. In consequence of the kinetic analysis performed, it was found that the dissolution kinetics of zinc powder obeyed the Avrami model. Activation energy for the process was determined to be 19.42 kJ/mol. Zinc ions in the resulting solution after dissolution process was recovered in the form of hydroxy-carbonate product by precipitation method. Zinc oxide was produced by isothermal decomposition of hydroxy-carbonate product.

36 MATERIALS SCIENCE↗

Corrosion Behavior of Sm{sub y}(Fe{sub x}Ni{sub 1−x}){sub 4}Sb{sub 12} (0.40 ≤ x ≤ 0.80) in NaCl Solutions Studied by Electron Microscopy and ICP-AES

Filled skutterudites are currently studied as thermoelectric materials to be used in the automotive and nautical field; the study of their resistance to a saline environment is therefore mandatory. To this purpose, the corrosion behavior of several compositions belonging to the Sm{sub y}(Fe{sub x}Ni{sub 1−x}){sub 4}Sb{sub 12} skutterudites system was investigated by immersing samples in differently concentrated (0.1 and 0.5 M) NaCl solutions. The effect of the treatment was analyzed both by SEM–EDS on the sample surface and at fixed times by ICP-AES on the solution. The formation of an oxide layer was observed on the surface of all the samples: the film results uniformly grown on specimens treated in NaCl at the lower concentration, while it is cracked and not spread over the whole surface in the other samples. Relying on the oxide layer thickness, the oxidation resistance results to increase with increasing the Fe content; correspondingly, the Sb concentration in the more diluted solution decreases at each time considered with increasing the Fe amount, pointing at a strict correlation between the cationic release and the oxide formation, and suggesting a possible mechanism for the growth of the protective film.

36 MATERIALS SCIENCE↗

Effect of Solution pH on Layered Double Hydroxide Formation on Electrogalvanized Steel Sheets

The effect of solution pH on layered double hydroxide (LDH) formation on electrogalvanized steel sheets (EG steel) was investigated in this study. EG steel with a Zn coating weight of 64 g/m{sup 2} was used as a substrate and was immersed in a 0.25 M Na{sub 2}Al{sub 2}O{sub 4}-based solution having several pH values to form a Zn-Al-based LDH conversion coating. After rinsing and drying, corrosion resistance was evaluated by EIS. It was found that corrosion resistance increased with increasing pH up to pH 12.6. However, above this pH, corrosion resistance tended to display a sharp decrease. To understand this trend, the conversion coating was characterized by FT-IR, XRD and GDOES. The conversion coating was found to consist mainly of Zn{sub 2}Al(OH){sub 6}(CO{sub 3}){sub 0.5}·xH{sub 2}O crystals (an LDH). The thickness of the conversion coating layer increased with increasing pH up to pH 12.4, but above this pH, its thickness tended to decrease due to the formation of ZnO. The reason for the dependence of corrosion resistance on solution pH is discussed from the viewpoints of the thickness and changes in the microstructure of the conversion coating layer, including its crystal size, density and uniformity, which could vary during the initial formation of ZnO at pH values above 12.6.

36 MATERIALS SCIENCE↗