Four‐Center Oxidation State Combinations and Near‐Infrared Absorption in [Ru(pap)(Q)2]n (Q=3,5‐Di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine,pap=2‐Phenylazopyridine)

The complex series [Ru(pap)(Q)₂]ⁿ ([ 1 ]ⁿ–[ 4 ]ⁿ; n=+2, +1, 0, ?1, ?2) contains four redox non‐innocent entities: one ruthenium ion, 2‐phenylazopyridine (pap), and two o‐iminoquinone moieties, Q=3,5‐di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine (aryl=C₆H₅ ( 1⁺ ); m‐(Cl)₂C₆H₃ ( 2⁺ ); m‐(OCH₃)₂C₆H₃ ( 3⁺ ); m‐(tBu)₂C₆H₃ ( 4 ⁺)). A crystal structure determination of the representative compound, [ 1 ]ClO₄, established the crystallization of the ctt‐isomeric form, that is, cis and trans with respect to the mutual orientations of O and N donors of two Q ligands, and the coordinating azo N atom trans to the O donor of Q. The sensitive C? O (average: 1.299(3) Å), C? N (average: 1.346(4) Å) and intra‐ring C? C (meta; average: 1.373(4) Å) bond lengths of the coordinated iminoquinone moieties in corroboration with the N?N length (1.292(3) Å) of pap in 1 ⁺ establish [Ru^III(pap⁰)(Q^.?)₂]⁺ as the most appropriate electronic structural form. The coupling of three spins from one low‐spin ruthenium(III) (t_2g⁵) and two Q^.? radicals in 1 ⁺– 4 ⁺ gives a ground state with one unpaired electron on Q^.?, as evident from g=1.995 radical‐type EPR signals for 1 ⁺– 4 ⁺. Accordingly, the DFT‐calculated Mulliken spin densities of 1 ⁺ (1.152 for two Q, Ru: ?0.179, pap: 0.031) confirm Q‐based spin. Complex ions 1 ⁺– 4 ⁺ exhibit two near‐IR absorption bands at about λ=2000 and 920 nm in addition to intense multiple transitions covering the visible to UV regions; compounds [ 1 ]ClO₄–[ 4 ]ClO₄ undergo one oxidation and three separate reduction processes within ±2.0 V versus SCE. The crystal structure of the neutral (one‐electron reduced) state ( 2 ) was determined to show metal‐based reduction and an EPR signal at g=1.996. The electronic transitions of the complexes 1 ⁿ– 4 ⁿ (n=+2, +1, 0, ?1, ?2) in the UV, visible, and NIR regions, as determined by using spectroelectrochemistry, have been analyzed by TD‐DFT calculations and reveal significant low‐energy absorbance (λ_max>1000 nm) for cations, anions, and neutral forms. The experimental studies in combination with DFT calculations suggest the dominant valence configurations of 1 ⁿ– 4 ⁿ in the accessible redox states to be [Ru^III(pap⁰)(Q^.?)(Q⁰)]²⁺ ( 1 ²⁺– 4 ²⁺)→[Ru^III(pap⁰)(Q^.?)₂]⁺ ( 1 ⁺– 4 ⁺)→[Ru^II(pap⁰)(Q^.?)₂] ( 1 – 4 )→[Ru^II(pap^.?)(Q^.?)₂]^? ( 1 ^?– 4 ^?)→[Ru^III(pap^.?)(Q^2?)₂]^2? ( 1 ^2?– 4 ^2?).     

A detailed insight into the optimization of plate and frame heat exchanger design by comparing old and new generation metaheuristics algorithms

The voluminous utilization and application of plate and frame heat exchangers (PFHE) in many industries has accelerated the consumer and designer both to optimize exchanger total cost. Over the last few years, several old and new generation algorithms were employed and exploited to optimize PFHE cost. This study explores the application and performance of three new-generation algorithms Big Bang-Big Crunch (BBBC), Grey Wolf Optimizer (GWO), and Water Evaporation Optimization (WEO) in designing optimally PFHE. Besides, this study also compares the performance of three well-established old generations algorithms namely genetic algorithm (genetics and natural selection), particle swarm optimization (animals behaviour), and differential evolution (population-based) with the above three new algorithms in the optimization of PFHE.Seven design factors are chosen for PFHE optimization: exchanger length on hot and cold sides, height and thickness of fin, length of the fin-strip, fin frequency, and the number of hot side layers. The applicability of the suggested algorithms is assessed using a case study based on published research. Though DE performs the best in this study of design optimization concerning total cost and computational time, the three new-generation meta-heuristic algorithms BBBC, GWO, and WEO also provide the novel scope of application in heat exchanger design optimization and successfully finding the cost of the heat exchanger. According to this study, capital costs increase by 19.5% for BBBC, 24% for GWO, and 7.6% for GWO, but operational costs fall by 9.5% for BBBC and GWO when compared to the best performing algorithm (DE). On the other hand, WEO shows an increase of 32.6% in operational costs. Aside from that, a full analysis of the computing time for each algorithm is also provided. The DE has the quickest run time of 0.09 ?s, while the PSO takes the longest at 33.97 ?s. The rest of the algorithms have nearly identical values. As a result, a good comparison is established in this study, offering an excellent platform for designers and customers to make selections. Additionally, the three new generations algorithms mentioned here were not used earlier for optimization of PFHE and the comparative study illustrates that each of them possesses eat potential for cost optimization and also solving other complex problems.     

Three Bis‐BODIPY Analogous Diruthenium Redox Series: Characterization and Electronic Structure Analysis

The dianion derived from (2Z,6Z)‐3,7‐diphenyl‐N2,N6‐di(pyridin‐2‐yl)pyrrolo[2,3‐f]indole‐2,6(1H,5H)‐diimine (H₂BL), a modified BODIPY ligand precursor, is shown to be capable of bridging two metal complex fragments RuL₂, L=2,4‐pentanedionato (acac^?), 2,2’‐bipyridine (bpy) or 2‐phenylazopyridine (pap) in [Ru(acac)₂Ru(μ‐BL)Ru(acac)₂] ( 1 / 2 ), [Ru(bpy)₂Ru(μ‐BL)Ru(bpy)₂](ClO₄)₂ ([ 3 ](ClO₄)₂) and [Ru(pap)₂Ru(μ‐BL)Ru(pap)₂](ClO₄)₂ ([ 4 ](ClO₄)₂). The compounds, including a diastereoisomeric pair 1 (meso) and 2 (rac) were spectroscopically and structurally characterized. Reversible electron transfers as revealed by cyclic and differential pulse voltammetry allowed for an EPR and UV‐vis‐NIR spectroelectrochemical investigation of several neighboring charge states. Together with susceptibility measurements and TD‐DFT calculations the assignment of oxidation states reveals that 1 , 2 are diruthenium(III) species which can be oxidized or reduced by one electron whereas 3 ²⁺ and 4 ²⁺ contain ruthenium(II) and get reduced or oxidized mainly at the dianionic bridge ( 3 ²⁺) or are reduced at the ancillary ligands pap ( 4 ²⁺).     

η-π0 mixing and ψ′ → ψπ0 decay

The ψ′ → ψπ⁰ decay rate is studied in a chiral symmetry breaking scheme by including effects from π⁰-η mixing only. The result obtained is in very good agreement with the experiment.     

Strong phase separation in a model of sedimenting lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.     

On results of G. Brosch and T.C. Alzahary

We prove a uniqueness theorem for two non-constant meromorphic functions sharing three values which improves a recent result of T.C. Alzahary. As a consequence of our main result we also improve a theorem of G. Brosch.     

Effect of polarization on two-dimensional carrier distribution in nitride quantum wells

Wide band-gap group-III nitrides are important for the design of optical devices in the blue and blue–green region. Owing to their wurtzite structure, these materials have a strong inherent polarization field that affects carrier distribution, exciton stability and hence influences the optical properties of the devices. So far, carriers have been assumed to have a sheet-like character. In this paper a non sheet-like distribution function for these quasi two-dimensional carriers is proposed that incorporates the effect of the polarization field. Here GaN/InGaN/GaN and AlGaN/GaN/AlGaN quantum wells have been studied. The polarization field causes the electron and hole wave functions to separate out, thus causing decrease of emission strength and strong reduction of exciton binding energy. This treatment explains well the qualitative nature of carrier distribution in the well. The polarization field changes with GaN mole fraction present in the tertiary nitride layer. The effect of mole fraction on carrier distribution has also been studied. It is found that, inside the well, the hole distribution changes a little more with change in mole fraction than the electron distribution, but for all practical purposes the net change in the distribution pattern is negligible.     

Analysis of Ti:LiNbO3 zero-gap directional coupler for wavelength division multiplexer/demultiplexer

For the purpose of multichannel integrated-optical wavelength division MUX/DEMUX design, the wavelength tuning method of Ti:LiNbO₃ zero-gap directional coupler is analysed by effective-index based matrix method (EIMM). In this method, first, the 2D refractive index profile of the Ti:LiNbO₃ zero-gap directional coupler is transformed into lateral 1D effective-index profile by WKB method. Finally, matrix method is applied to this effective-index profile and the propagation constants are computed from the resonance peaks of the excitation efficiency versus propagation constant characteristics. It has been shown that the channel wavelength tuning can be achieved by varying the Y-branching angle at the input and output of the device or by a slight variation of two-mode-section length. The method of electro-optic fine tuning of the channel wavelength and channel separation of the device has also been investigated. A cascaded structure with proper parameters for four-channel application is also simulated and the results are presented.