Characterization of the terminal iron(IV) imides [[PhBP(t)(Bu)2(pz')]Fe(IV)NAd]+

New hybrid bis(phosphine)(pyrazole)borate tripodal ligands ([PhBPtBu2(pz')]-) are reported that support pseudotetrahedral iron in the oxidation states +1, +2, +3, and +4. The higher oxidation states are stabilized by a terminal FeNR linkage. Of particular interest is the generation and thorough characterization of an S = 1 FeIVNR+ imide cation using this new ligand system. The latter species can be observed electrochemically and spectroscopically, and its solid-state crystal structure is reported.     

On the block counting process and the fixation line of the Bolthausen–Sznitman coalescent

The block counting process and the fixation line of the Bolthausen–Sznitman coalescent are analyzed. It is shown that these processes, properly scaled, converge in the Skorohod topology to the Mittag-Leffler process and to Neveu’s continuous-state branching process respectively as the initial state tends to infinity. Strong relations to Siegmund duality, Mehler semigroups and self-decomposability are pointed out. Furthermore, spectral decompositions for the generators and transition probabilities of the block counting process and the fixation line of the Bolthausen–Sznitman coalescent are provided leading to explicit expressions for functionals such as hitting probabilities and absorption times.     

Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles

We consider spin dynamics for implementation in an atomistic framework and we address the feasibility of capturing processes in the femtosecond regime by inclusion of moment of inertia. In the spirit of an s-d-like interaction between the magnetization and electron spin, we derive a generalized equation of motion for the magnetization dynamics in the semiclassical limit, which is nonlocal in both space and time. Using this result we retain a generalized Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and demonstrate how the exchange interaction, damping, and moment of inertia, all can be calculated from first principles.     

Water adsorption on clay minerals as a function of relative humidity: application of BET and Freundlich adsorption models

Water adsorption on kaolinite, illite, and montmorillonite clays was studied as a function of relative humidity (RH) at room temperature (298 K) using horizontal attenuated total reflectance (HATR) Fourier transform infrared (FTIR) spectroscopy equipped with a flow cell. The water content as a function of RH was modeled using the Brunauer, Emmett, and Teller (BET) and Freundlich adsorption isotherm models to provide complementary multilayer adsorption analysis of water uptake on the clays. A detailed analysis of model fit integrity is reported. From the BET fit to the experimental data, the water content on each of the three clays at monolayer (ML) water coverage was determined and found to agree with previously reported gravimetric data. However, BET analysis failed to adequately describe adsorption phenomena at RH values greater than 80%, 50%, and 70% RH for kaolinite, illite, and montmorillonite clays, respectively. The Freundlich adsorption model was found to fit the data well over the entire range of RH values studied and revealed two distinct water adsorption regimes. Data obtained from the Freundlich model showed that montmorillonite has the highest water adsorption strength and highest adsorption capacity at RH values greater than 19% (i.e., above ML water adsorption) relative to the kaolinite and illite clays. The difference in the observed water adsorption behavior between the three clays was attributed to different water uptake mechanisms based on a distribution of available adsorption sites. It is suggested that different properties drive water adsorption under different adsorption regimes resulting in the broad variability of water uptake mechanisms.     

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP\mathcal{CP} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.     

Absence of vacuum induced Berry phases without the rotating wave approximation in cavity QED

We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a nontrivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the rotating wave approximation (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semiclassical energy surfaces which in a simple way brings out the phase-space dynamics. With the RWA, a conical intersection between the surfaces emerges and encircling it gives rise to the Berry phase. Without the RWA, the conical intersection is absent and therefore the Berry phase vanishes. It is believed that this is a first example showing how the application of the RWA in the Jaynes-Cummings model may lead to false conclusions, regardless of the mutual strengths between the system parameters.     

Dynamic properties of water in silicalite-1 powder

Self-diffusion of D₂O in partially filled silicalite-1 crystals was studied at 25°C by ²H nuclear magnetic resonance (NMR) with bipolar field gradient pulses and longitudinal Eddy-current-delay. For the first time, reliable experimental diffusion data for this system were obtained. Analysis of NMR diffusion decays revealed the presence of a continuous distribution of apparent self-diffusion coefficients (SDCs) of water, ranging from 10⁻⁷ to ∼10⁻¹⁰ m²/s, which include values much higher and lower than that of bulk water (∼10⁻⁹ m²/s) in liquid phase. The observed distribution of SDC changes with variation of the diffusion time in the range of 10–200 ms. A two-site Kärger exchange model was successfully fitted to the data. Finally, the water distribution and exchange in silicalite-1 pores were described by taking into account (a) a gas-like phase in the zeolite pores, a gas-like phase in mesopores and an intercrystalline gas-like phase and (b) intercrystalline liquid droplets with intermediate exchange rate with the other phases. The other phases experience fast exchange on the NMR diffusion time scale. Diffusion coefficients and mean residence times of water in some of these states were estimated.     

Endogenous contrast blood flow imaging in embryonic hearts using hemoglobin contrast subtraction angiography

The genetic basis of congenital heart disease is yet to be defined, and the interactions between the malformed heart and biomechanical cardiac performance remain poorly understood. Functional optical imaging enables detailed biomechanical phenotyping of cardiac dysfunction in small animal models, which in turn enables specific gene-phenotype relationship. We have developed a new microangiography technique based on flow imaging using endogenous hemoglobin contrast enabling in vivo assessment and biomechanical phenotyping of Xenopus tropicalis embryonic heart. We demonstrated that hemoglobin contrast angiography can be used to quantify physiological response to treatment with well-established cardioactive drugs.     

Towards Recyclable NAD(P)H Regeneration Catalysts

Rh(III)-TsDPEN, an immobilized analog of the well-known [Cp*Rh(bpy)(H₂O)]²⁺ was evaluated as a heterogeneous, recyclable regeneration catalyst for reduced oxidoreductase cofactors [NAD(P)H]. Repeated use of this catalyst was established and the catalytic properties were initially investigated. Apparently, Rh(III)-TsDPEN is prone to severe diffusion limitations, necessitating further developments. Overall, a promising concept for chemoenzymatic redox catalysis is proposed, which may overcome some of the current limitations such as catalyst cost and incompatibility of Rh with some biocatalysts.     

Explicit expression for powers of tridiagonal 2-Toeplitz matrix of odd order

In this paper, we give the eigenvalue decomposition for odd order tridiagonal 2-Toeplitz matrix and derive the explicit expression for integer powers of such matrix.