Roy-Steiner equations for pion-nucleon scattering

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high-energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the $\pi\pi\to\bar NN$ partial waves into the form of a Muskhelishvili-Omn\`es problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.Comment: 106 pages, 18 figures; version published in JHE

Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion

How ice grows from premelting films and water droplets

Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.Comment: 32 pages, 10 figure

The Spin Foam Approach to Quantum Gravity

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.Comment: To appear in Living Reviews in Relativit

Revealing the ductility of nanoceramic MgAl2O4

Ceramics are strong but brittle. According to the classical theories, ceramics are brittle mainly because dislocations are suppressed by cracks. Here, the authors report the combined elastic and plastic deformation measurements of nanoceramics, in which dislocation-mediated stiff and ductile behaviors were detected at room temperature. In the synchrotron-based deformation experiments, a marked slope change is observed in the stress-strain relationship of MgAl2O4 nanoceramics at high pressures, indicating that a deformation mechanism shift occurs in the compression and that the nanoceramics sample is elastically stiffer than its bulk counterpart. The bulk-sized MgAl2O4 shows no texturing at pressures up to 37 GPa, which is compatible with the brittle behaviors of ceramics. Surprisingly, substantial texturing is seen in nanoceramic MgAl2O4 at pressures above 4 GPa. The observed stiffening and texturing indicate that dislocation-mediated mechanisms, usually suppressed in bulk-sized ceramics at low temperature, become operative in nanoceramics. This makes nanoceramics stiff and ductile

Revealing the ductility of nanoceramic MgAl2O4

Ceramics are strong but brittle. According to the classical theories, ceramics are brittle mainly because dislocations are suppressed by cracks. Here, the authors report the combined elastic and plastic deformation measurements of nanoceramics, in which dislocation-mediated stiff and ductile behaviors were detected at room temperature. In the synchrotron-based deformation experiments, a marked slope change is observed in the stress-strain relationship of MgAl2O4 nanoceramics at high pressures, indicating that a deformation mechanism shift occurs in the compression and that the nanoceramics sample is elastically stiffer than its bulk counterpart. The bulk-sized MgAl2O4 shows no texturing at pressures up to 37 GPa, which is compatible with the brittle behaviors of ceramics. Surprisingly, substantial texturing is seen in nanoceramic MgAl2O4 at pressures above 4 GPa. The observed stiffening and texturing indicate that dislocation-mediated mechanisms, usually suppressed in bulk-sized ceramics at low temperature, become operative in nanoceramics. This makes nanoceramics stiff and ductile