Beautiful Gauge Field Equations in Clifforms

By combining the tetrads of unholonomic frames of spacetime with the Dirac matrices to a one-form , we can reformulate not only the Dirac equation, but also the Einstein equations and supergravity in a very concise form. These Clifforms also shed some light on the chiral decomposition à la Ashtekar, the role of the axion as a dynamical degree of freedom dual to the torsion of the Einstein—Cartan theory, and the role of the Seiberg—Witten equation for S-duality.     

S-duality in 3D gravity with torsion

The deformation of the connection in three spacetime dimensions by the kinematically equivalent coframe is shown to induce a duality between the (Lorentz-) rotational and translational field momenta, for which the coupling to the deformation parameter is inverted. This new kind of strong/weak duality, pertinent to 3D, is instrumental for studying exact solutions of the 3D Poincaré gauge field equations and the particle content of propagating modes on a background of constant curvature. For a topological Chern-Simons model of gravity, the propagating modes ‘living’ on an Anti-de Sitter (AdS) background correspond to real massive particles. Yang-Mills type generalizations and new cubic Lagrangians are found and completely classified in 3D. AdS or black hole type solutions with constant axial torsion emerge, also for these higher-order Lagrangians with new ‘exotic’ torsion-curvature couplings. Their pattern complies with our S-duality, with new repercussions for the field redefinition of the metric in 3D quantum gravity and the cosmological constant problem.     

Strong and weak chaos in nonlinear networks with time-delayed couplings

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.     

Substituent Effects on 31P and 13C Chemical Shifts of Substituted Diphenyl 1-anilino-1-arylmethanephosphonates and Their Anions

Abstract

For a series of 31 novel diphenyl 1-anilino-1-arylmethanephosphonates, substituted in the meta and para position of the anilino and/or the aryl ring, ³¹P chemical shifts show good linear correlation with Taft's [sgrave]° parameters, the ³¹P nucleus appearing better shielded in the case of electron-withdrawing substituents. This inverse relationship is due to a field effect of the substituent dipole which polarizes π-electron clouds in the molecule, resulting in a higher P=O double bond order, and thence better ³¹P shielding. A corresponding shift of π-electron density is likewise observed for the ¹³C resonances of the two diastereotopic phenoxy and the anilino or aryl rings, respectively, where-M ands-I substituents cause a downfield shift of para and meta, and an upfield shift of ortho and ipso carbon resonances.     

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.     

Synchronization scenarios of chimeras in multiplex networks

Complex networks consisting of several interacting layers allow for remote synchronization of distant layers via an intermediate relay layer. We extend the notion of relay synchronization to chimera states, and study the scenarios of relay synchronization in a three-layer network of FitzHugh–Nagumo (FHN) oscillators, where each layer has a nonlocal coupling topology. Varying the coupling strength and time delay in the inter-layer connections, we observe relay synchronization between chimera states, i.e., complex spatio-temporal patterns of coexisting coherent and incoherent domains, in the outer network layers. Special regimes where only the coherent domains of chimeras are synchronized, and the incoherent domains remain desynchronized, as well as transitions between different synchronization regimes are analyzed.