Neutron Diffraction Analysis of H3Co2[C5H2(t-Bu)3]2, a Molecule with a Triply Hydrogen-Bridged Metal–Metal Bond: Some Comments on Structural Patterns in M(μ-H)nM Systems (n=1, 2, 3, 4)

The structure of H₃Co₂[C₅H₂(t-Bu)₃]₂ has been analyzed by low-temperature single-crystal neutron diffraction techniques, and shown to consist of two CoCp moieties with three hydride ligands bridging the central Co–Co bond. Despite a fairly extensive twinning problem, the structure could be solved and successfully refined to a final R factor of 9.2% for 2024 reflections. Average molecular parameters in the H₃Co₂ core of the molecule are as follows: Co–Co=2.275(21) Å, Co–H=1.637(16) Å, HH=2.050(20) Å, Co–H–Co=88.0(9)°, H–Co–H=77.0(7)°. Also included in this paper is a discussion on the molecular dimensions of symmetric hydride-bridged dinuclear systems (M(-H)_nM, n=1, 2, 3, 4) that have been studied to date by neutron diffraction.     

Analytical solutions to Fisher’s equation with time-variable coefficients

This paper provides analytical solutions to the generalized Fisher equation with a class of time varying diffusion coefficients. To accomplish this we use the Painlevé property for partial differential equations as defined by Weiss in 1983 in “The Painlevé property for partial-differential equations”. This was first done for the variable coefficient Fisher’s equation by Ö?ün and Kart in 2007; we build on this work, finding additional solutions with a weaker restriction on the trial solution. We also use the same technique to find solutions to Fisher’s equation with time-dependent coefficients for both diffusion and nonlinear terms. Lastly we compute specific solutions to illustrate their behaviors.     

Ag2PbO2, Optimierung der Kristallzüchtung und Verfeinerung der Kristallstruktur

Ag₂PbO₂, Optimization of Crystal Growth and Crystal Structure Refinement Large single crystals of Ag₂PbO₂ (1×1×7 mm) suitable for measurements of anisotropic physical properties have been grown. The refinement of the crystal structure (I2/c; crystal size 0.08 × 0.08 × 0.31 mm; a = 6.0775(9), b = 8.704(1), c = 6.553(1) Å, β = 93.545(8)°; Z = 4; 1235 diffractometer data; R = 0.038) confirms the positions of the heavy atoms, and allows for an unambiguous determination of the oxygen coordinates.     

The q-deformed Bose gas: integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.     

Making thermodynamic models of mixtures predictive by machine learning: matrix completion of pair interactions

Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths from both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies, as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model.

Embedding matrix completion methods from machine learning in classical thermodynamic models creates powerful hybrid models for predicting properties of mixtures.     

Quantitative Fatou Theorems and Uniform Rectifiability

We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.

     

Spinodal decomposition in Monte Carlo simulations of a binary alloy

Recently Cahn's generalized diffusion equation theory of spinodal decomposition in binary alloys has been modified to include the effects of thermal fluctuations. This paper reports studies of a one-dimensional binary alloy system in which fluctuations can be observed on an atomic time scale. The system, a computer-simulated linear chain binary alloy which evolves from an initially random atomic arrangement through interchange of unlike nearest neighbors via the Monte Carlo technique, rapidly develops grains of two different concentrations and then slowly experiences coarsening. A numerical solution of the diffusion equation successfully predicts the development of grain structure, but only predicts coarsening to the extent present as fluctuations in the initial atomic arrangement. The simulated alloy coarsens further than the prediction of the diffusion equation because of thermal fluctuations which develop naturally during its evolution. This suggests that thermal fluctuations may play an important role in coarsening in real alloys.