Pythagoras’s oxen revisited

it is said that when Pythagoras discovered his famous theorem, in a right-angled triangle the squares of the smaller sides sum up to the square of the hypoteneuse, he sacrificed a hundred oxen to thank the gods.     

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

原子尺度上的异质催化

现实中的催化剂是个相当复杂的系统体系，且为粉末状，限制了多种表面科学表征手段的应用,科学家通过建立简化的催化剂模型，充分利用目前多种有力的科技分析手段，如扫描隧道显微镜（STM）、透射电镜（TEM）、光电子能谱（XPS）、傅里叶变换红外吸收谱（FTIR）、电子能量损失谱（EELS）等，直观地在原子尺度上研究催化反应的机理，从而使得人们能够设计出选择性能更高、催化性能更好的催化剂．     

Characterization of a Pd-Fe bimetallic model catalyst

Small bimetallic Pd-Fe particles supported on a well ordered alumina film grown on NiAl (1 1 0) were studied focusing on the geometric, electronic, adsorption, as well as magnetic properties. The morphology, growth mode and surface composition were investigated by combining scanning tunneling microscopy (STM), temperature-programmed desorption (TPD) and infrared spectroscopy (IRAS) using CO as a probe molecule. Information on the electronic properties of the bimetallic systems was obtained by means of X-ray photoelectron spectroscopy (XPS). These measurements were amended by in situ ferromagnetic resonance spectroscopy to address the magnetic properties of the bimetallic particles. The subsequent deposition of the metals at 300 K varying the order of metal deposition resulted in two distinct bimetallic systems. Pd deposited on existing Fe particles forms a shell, however, FMR and XPS suggest that intermixing of Pd and Fe occurs to some extent. For the reverse order, a larger amount of Fe is required to coat Pd particles, due to the strong tendency of Pd to segregate to the surface of the particles.     

Track Extensions of Categories and Cohomology

We introduce the notion of n-fold track extensions of a category C by a natural system D and prove that such extensions represent classes in the cohomology of C with coefficients in D introduced by Baues–Wirsching. This generalizes a result of Huebschmann on the cohomology of groups.