System bandwidth and the existence of generalized shift-invariant frames

We consider the question whether, given a countable family of lattices ${({\mathrm{\Gamma }}_j)}_{j\in J}$ in a locally compact abelian group G, there exist functions ${(g_j)}_{j\in J}$ such that the resulting generalized shift-invariant system ${(g_j(??\gamma ))}_{j\in J,\gamma \in {\mathrm{\Gamma }}_j}$ is a tight frame of $L^2(G)$. This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system.     

A linear time algorithm for balance vertices on trees

The concept of balance vertices was first investigated by Reid (1999). For the main result “the balance vertices of a tree consist of a single vertex or two adjacent vertices”, Shan and Kang (2004) and Reid and DePalma (2005) improved the length and technique of the proof. In this paper we further discuss the balance vertices on trees in a generalization context. We do not only provide a simple efficient proof for the relevant result but also develop a linear time algorithm to find the set of balance vertices on the underlying tree.     

Mobility of Li+, Na+, and Cs+ cations in Nafion membrane,as studied by NMR techniques

The local mobility and diffusion of Li⁺, Na⁺, and Cs⁺ cations in Nafion 117 membrane were explored by ⁷Li, ²³Na, and ¹³³Cs spin relaxation and pulsed field gradient NMR techniques. It was shown that the macroscopic mass transfer of cations is controlled by ion motion near sulfonate groups. Lithium and sodium cations, whose hydrated energy is higher than the water hydrogen bond energy, are moving together with water molecules, but cesium cations possessing a low hydrated energy are jumping directly between the neighboring sulfonate groups.     

Innovative Electrochemical Strategies for Hydrogen Production: From Electricity Input to Electricity Output

Renewable H₂ production by water electrolysis has attracted much attention due to its numerous advantages. However, the energy consumption of conventional water electrolysis is high and mainly driven by the kinetically inert anodic oxygen evolution reaction. An alternative approach is the coupling of different half-cell reactions and the use of redox mediators. In this review, we, therefore, summarize the latest findings on innovative electrochemical strategies for H₂ production. First, we address redox mediators utilized in water splitting, including soluble and insoluble species, and the corresponding cell concepts. Second, we discuss alternative anodic reactions involving organic and inorganic chemical transformations. Then, electrochemical H₂ production at both the cathode and anode, or even H₂ production together with electricity generation, is presented. Finally, the remaining challenges and prospects for the future development of this research field are highlighted.     

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part II: A ChemTraYzer Study of Chlorinated Dibenzofuran Formation and Decomposition Processes

In our two-paper series, we first present the development of ReaxFF CHOCl parameters using the recently published ParAMS parametrization tool. In this second part, we update the reactive Molecular Dynamics – Quantum Mechanics coupling scheme ChemTraYzer and combine it with our new ReaxFF parameters from Part I to study formation and decomposition processes of chlorinated dibenzofurans. We introduce a self-learning method for recovering failed transition-state searches that improves the overall ChemTraYzer transition-state search success rate by 10 percentage points to a total of 48 %. With ChemTraYzer, we automatically find and quantify more than 500 reactions using transition state theory and DFT. Among the discovered chlorinated dibenzofuran reactions are numerous reactions that are new to the literature. In three case studies, we discuss the set of reactions that are most relevant to the dibenzofuran literature: (i) bimolecular reactions of the chlorinated-dibenzofuran precursors phenoxy radical and 1,3,5-trichlorobenzene, (ii) dibenzofuran chlorination and pyrolysis, and (iii) oxidation of chlorinated dibenzofurans.     

Torands Revisited: Metal Sequestration and Self‐Assembly of Cyclo‐2,9‐tris‐1,10‐phenanthroline Hexaaza Macrocycles

A series of novel toroidal cyclo‐2,9‐tris‐1,10‐phenanthroline macrocycles with an unusual hexaaza cavity are reported. Nickel‐mediated Yamamoto aryl–aryl coupling was found to be a versatile tool for the cyclotrimerization of functionalized 1,10‐phenathroline precursors. Due to the now improved processability, both liquid‐crystalline behavior in the bulk phase and two‐dimensional self‐assembly at the molecular level could be studied, for the first time, for a torand system. The macrocycles exhibited a strong affinity for the complexation of different metal cations, as evidenced by MALDI‐TOF analysis and spectroscopic methods. Experimental results were correlated to an extensive computational study of the cyclo‐2,9‐tris‐1,10‐phenanthroline cavity and its binding mode for metal cations. Due to the combination of several interesting features, toroidal macrocycles may find future applications in the field of ion and charge transport through molecular channels, as well as for chemical sensing and molecular writing in surface‐confined monolayers under STM conditions.     

New models for a class of adhesive grippers. The hemivariational inequality approach

Summary A hemivariational inequality model for adhesive grasping problems is proposed and studied in this paper. The unilateral frictionless and frictional contact effects between the fingertips and the grasping object that lead to linear complementarity problems with singular matrices for the study of static equilibrium of the gripper-object system are generalized here to cover adhesive multifingered grippers. Adhesive effects are modelled by appropriately defined, generally nonconvex, yield sets in the space of contact stresses, friction stresses, gaps or frictional slips and their combinations. The hemivariational inequality problem that arises may involve copositive plus, symmetric matrices and nonempty closed sets for the frictionless gripper problem and copositive plus, nonsymmetric matrices with starshaped sets for the frictional case. Solvability conditions that guarantee the existence of a solution to the gripper problem are given. They specify the conditions which are required to hold between external forces, fingertip mechanical behavior and finger placement in order to solve the gripper problem.     

Phase field dependent viscoplastic behaviour of solder alloys

A phase field model is presented to describe the mechanical behaviour of microstructure dependent materials, which is demonstrated by applying it to eutectic tin–lead solder. This solder material is known to be heavily influenced by its continuously evolving microstructure. For the constitutive behaviour of the different phases the elasto-viscoplastic Perzyna model has been used. It is coupled to the phase field model through the constitutive parameters which are taken dependent on the mass fraction field resulting from the solution of the phase field equations.     

On internal dissipation inequalities and finite strain inelastic constitutive laws: Theoretical and numerical comparisons

Internal dissipation always occurs in irreversible inelastic deformation processes of materials. The internal dissipation inequalities (specific mathematical forms of the second law of thermodynamics) determine the evolution direction of inelastic processes. Based on different internal dissipation inequalities several finite strain inelastic constitutive laws have been formulated for instance by Simo [Simo, J.C., 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 99, 61–112]; Simo and Miehe [Simo, J.C., Miehe, C., 1992. Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering 98, 41–104]; Lion [Lion, A., 1997. A physically based method to represent the thermo-mechanical behavior of elastomers. Acta Mechanica 123, 1–25]; Reese and Govindjee [Reese, S., Govindjee, S., 1998. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455–3482]; Lin and Schomburg [Lin, R.C., Schomburg, U., 2003. A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects. Computer Methods in Applied Mechanics and Engineering 192, 1591–1627]; Lin and Brocks [Lin, R.C., Brocks, W., 2004. On a finite strain viscoplastic theory based on a new internal dissipation inequality. International Journal of Plasticity 20, 1281–1311]; and Lin and Brocks [Lin, R.C., Brocks, W., 2005. An extended Chaboche’s viscoplastic law at finite strains: theoretical and numerical aspects. Journal of Materials Science and Technology 21, 145–147]. These constitutive laws are consistent with the second law of thermodynamics. As the internal dissipation inequalities are described in different configurations or coordinate systems, the related constitutive laws are also formulated in the corresponding configurations or coordinate systems. Mathematically, these constitutive laws have very different formulations. Now, a question is whether the constitutive laws provide identical constitutive responses for the same inelastic constitutive problems. In the present work, four types of finite strain viscoelastic and endochronically plastic laws as well as three types of J₂-plasticity laws are formulated based on four types of dissipation inequalities. Then, they are numerically compared for several problems of homogeneous or complex finite deformations. It is demonstrated that for the same inelastic constitutive problem the stress responses are identical for deformation processes without rotations. In the simple shear deformation process with large rotation, the presented viscoelastic and endochronically plastic laws also show almost identical stress responses up to a shear strain of about 100%. The three laws of J₂-plasticity also produce the same shear stresses up to a shear strain of 100%, while different normal stresses are generated even at infinitesimal shear strains. The three J₂-plasticity laws are also compared at three complex finite deformation processes: billet upsetting, cylinder necking and channel forming. For the first two deformation processes similar constitutive responses are obtained, whereas for the third deformation process (with large global rotations) significant differences of constitutive responses can be observed.