A new approach in modeling of constant temperature boundary condition in thermal lattice‐Boltzmann method

The lattice‐Boltzmann method is being applied to a diversity of fluid flow and heat transfer problems nowadays. Because of its microscale nature, strict attention should be paid when introducing macroscopic inputs to the model. One of the challenging issues dealing with macroscale and microscale treatment is the implementation of boundary conditions. In this regard constant‐temperature boundaries are frequently used in energy transfer problems. Such boundaries are simply modeled in Navier–Stokes based solvers, but they are not so harnessed in lattice‐Boltzmann models. One of the problems is that the calculated tangential heat flux is not zero along such boundaries in most of the previous models. In the present paper, a model has been developed, which has the capability of controlling tangential heat flux along the constant‐temperature boundaries. It aims to set the heat flux nearly zero along the boundary in midplane grid schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Higgs–Dilaton cosmology: Are there extra relativistic species?

Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs–Dilaton cosmological model predicts the existence of a massless particle – the dilaton – associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs–Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation.     

Light‐Driven Coordination‐Induced Spin‐State Switching: Rational Design of Photodissociable Ligands

The bistability of spin states (e.g., spin crossover) in bulk materials is well investigated and understood. We recently extended spin‐state switching to isolated molecules at room temperature (light‐driven coordination‐induced spin‐state switching, or LD‐CISSS). Whereas bistability and hysteresis in conventional spin‐crossover materials are caused by cooperative effects in the crystal lattice, spin switching in LD‐CISSS is achieved by reversibly changing the coordination number of a metal complex by means of a photochromic ligand that binds in one configuration but dissociates in the other form. We present mathematical proof that the maximum efficiency in property switching by such a photodissociable ligand (PDL) is only dependent on the ratio of the association constants of both configurations. Rational design by using DFT calculations was applied to develop a photoswitchable ligand with a high switching efficiency. The starting point was a nickel–porphyrin as the transition‐metal complex and 3‐phenylazopyridine as the photodissociable ligand. Calculations and experiments were performed in two iterative steps to find a substitution pattern at the phenylazopyridine ligand that provided optimum performance. Following this strategy, we synthesized an improved photodissociable ligand that binds to the Ni–porphyrin with an association constant that is 5.36 times higher in its trans form than in the cis form. The switching efficiency between the diamagnetic and paramagnetic state is efficient as well (72 % paramagnetic Ni–porphyrin after irradiation at 365 nm, 32 % paramagnetic species after irradiation at 440 nm). Potential applications arise from the fact that the LD‐CISSS approach for the first time allows reversible switching of the magnetic susceptibility of a homogeneous solution. Photoswitchable contrast agents for magnetic resonance imaging and light‐controlled magnetic levitation are conceivable applications.     

PROTONATION CONSTANTS AND SOLVENT DEPENDENT SPIN-CROSSOVER BEHAVIOUR OF IRON(II)-2-(2′-PYRIDYL)BENZIMIDAZOLE COMPLEXES

Abstract

2-(2′-Pyridyl)benzimidazole (pybzim = LH) coordinates to iron(II) as a bidentate and forms the tris-ligated complex, [Fe(pybzim)₃]²⁺ as isolated in the solid. Titration of [Fe(pybzim)₃]²⁺ with base demonstrates the successive deprotonation of the imino hydrogens of the coordinated ligands. Protonation constants for the free ligand, pybzim (Iog₁₀ K ^H = 11.33) and the complex, [Fe(pybzim)₃]²⁺ (log₁₀ K ^H ₁ = 9.58, log₁₀ K ^H ₂ = 8.13 and log₁₀ K ^H ₃ = 6.97) were measured in 30% (v/v) H₂O/EtOH. Results show that coordination to iron(II) increases the acidity of the imino hydrogen of the ligand. Spin-crossover behaviour of the complex were studied in different solvents ME, AC, AN, NM, NB, DMF, DMSO and ANL. The complex shows strong spin-crossover behaviour which is solvent dependent. Values of the spin-equilibrium constant (K _sc) and the associated thermodynamic parameters (ΔH _sc = 18.1–21.3 kJ mol^?1 and δS _sc = 69.6–84.4JK^?1 mol^?1) were calculated. An increase of the enthalpy is observed with increasing donor number (DN) of the solvent.     

The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

Accuracy of high‐order density‐based compressible methods in low Mach vortical flows

At low Mach numbers, Godunov‐type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov‐type methods for simulations involving low Mach numbers by utilising a new, well‐posed, two‐dimensional, two‐mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second‐order and fifth‐order accurate Godunov‐type methods show that the vortex‐pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange‐remap method, a fifth‐order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth‐order spatial and third‐order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT , in solving low Mach flows is also demonstrated for the two time‐stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange‐remap approach, where dissipation is independent of Mach number. © 2013 Crown copyright. International Journal for Numerical Methods in Fluids. © 2013 John Wiley & Sons, Ltd.     

Nondimensional frequency scaling of aerodynamically-tensioned membranes

Membrane wings have applications that involve low Reynolds number flyers such as micro air vehicles. The time-averaged and time-dependent deformations of the membrane affect the aerodynamic characteristics of the wing, primarily in the region beyond the maximum aerodynamic efficiency of the wing. This paper investigates an appropriate nondimensional vibration frequency scaling of a spanwise tensioned membrane with free (unattached) leading and trailing edges at low Reynolds numbers relative to nondimensional aeroelastic parameters. Silicone rubber membranes with varying spanwise pre-tension, aerodynamic tension (due to wing angle-of-attack and flow dynamic pressure), modulus of elasticity, span, and thickness are studied. Experimental results are compared to a proposed scaling that simplifies the aerodynamic loading as a uniform pressure distribution acting on the membrane. Data is further compared and discussed relative to previous published results of membrane wings with finite wing spans (three-dimensional flow) and fixed (rigid) leading edges.