Taut contact circles and bi-contact metric structures on three-manifolds

Geiges and Gonzalo (Invent. Math. 121:147–209 1995, J. Differ. Geom. 46:236–286 1997, Acta. Math. Vietnam 38:145–164 2013) introduced and studied the notion of taut contact circle on a three-manifold. In this paper, we introduce a Riemannian approach to the study of taut contact circles on three-manifolds. We characterize the existence of a taut contact metric circle and of a bi-contact metric structure. Then, we give a complete classification of simply connected three-manifolds which admit a bi-H-contact metric structure. In particular, a simply connected three-manifold admits a homogeneous bi-contact metric structure if and only if it is diffeomorphic to one of the following Lie groups: SU(2), \({\widetilde{SL}}(2,{\mathbb {R}})\), \({\widetilde{E}}(2)\), E(1, 1). Moreover, we obtain a classification of three-manifolds which admit a Cartan structure \((\eta _1,\eta _2)\) with the so-called Webster function \({\mathcal {W}}\) constant along the flow of \(\xi _1\) (equivalently \(\xi _2\)). Finally, we study the metric cone, i.e., the symplectization, of a bi-contact metric three-manifold. In particular, the notion of bi-contact metric structure is related to the notions of conformal symplectic couple (in the sense of Geiges (Duke Math. J. 85:701–711 1996)) and symplectic pair (in the sense of Bande and Kotschick (Trans. Am. Math. Soc. 358(4):1643–1655 2005)).     

Wealth-sensitive positional competition as a source of dynamic complexity in OLG models

This paper examines the interactions between economic activity and consumption externalities in an overlapping generations model. Existence of multiple steady states is studied from a global point of view, and possible mechanisms producing cycles and chaotic behavior are analyzed. Wealth-sensitive positionality is found to be able to generate persistent endogenous fluctuations, whereas wealth-neutral positionality doesn’t. Under wealth-sensitive positionality, the economy may moreover experience complex dynamics, with sensitivity to initial conditions, leading to poverty traps even when starting from relatively large endowments of capital assets.     

Factorization Properties in d-Dimensional Spin Glasses. Rigorous Results and Some Perspectives

In this paper we show that d-dimensional Gaussian spin glass models are strongly stochastically stable, fulfill the Ghirlanda-Guerra identities in distribution and the ultrametricity property.     

Analytic proof systems for λ-calculus: the elimination of transitivity, and why it matters

We introduce new proof systems G[β] and G _ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free derivations—of a number of well-known and central results concerning β- and βη-reduction. The latter include the Church–Rosser theorem for both reductions, the Standardization theorem for β- reduction, as well as the Normalization (Leftmost reduction) theorem and the Postponement of η-reduction theorem for βη-reduction      

Time Scales in Polymer Modified Asphalts

Historically, Maxwell was probably the first one who recognized the importance of time scales for understanding the mechanical response of asphalt. In instantaneous response asphalt behaves as an elastic, solid-like material, on the other hand its long time response is that of a viscous, fluid-like material. In the linear viscoelastic region asphalt behaves as a low molecular weight polymer. However, in the nonlinear region of high strains or rates of strain the behavior of some asphaltic systems can be rather complicated. In asphalts, asphaltenes, resins and alkanes compose a complex colloidal system, in which alkanes act as a solvent, asphaltenes as micelles and the polar resins as stabilizers. In order to enhance the mechanical properties of asphalts they are frequently modified by blending them with appropriate polymers. Changes in the impermanent network that can be formed in some of these blends can lead to an unexpected behavior of the steady shear viscosity function. Several different time scales emerge from this behavior. A possible relation of these “nonlinear” time scales to the linear viscoelastic time scales is discussed and examples of anomalous behavior of polymer-modified asphalts are given.     

Rotational Raman scattering dependence on pump polarization

The influence of the ellipticity degree of the pump radiation polarization on threshold energies and energy conversion efficiencies of stimulated rotational Raman scattering (SRRS) are investigated in H₂ with a XeCl excimer laser, by using different focusing geometries. For the first time, it is shown that the dependence of SRRS on pump radiation polarization is also affected by the focusing geometry, i.e. whether low- or high-angle focusing is applied. The experimentally determined threshold energies as a function of the pump radiation polarization are in accordance with theory mainly at high-angle focusing geometries. It is also shown for the first time that gain suppression effects on vibrational Raman scattering have to be considered in understanding the experimental results. Received: 5 January 1999 / Final version: 10 September 1999 / Published online: 8 March 2000     

A Fully Magnetizing Phase Transition

We analyze the Farey spin chain, a one-dimensional spin system with long-range multibody interactions. Using a polymer model technique, we show that when the temperature is decreased below the (single) critical temperature T _c=1/2, the magnetization jumps from zero to one.     

Contact metric manifolds whose characteristic vector field is a harmonic vector field

In this paper, contact metric manifolds whose characteristic vector field ξ is a harmonic vector field are called H-contact manifolds. We show that a (2n+1)-dimensional contact metric manifold is an H-contact manifold if and only if ξ is an eigenvector of the Ricci operator (J.C. González-Dávila and L. Vanhecke [J. Geom. 72 (2001) 65–76] proved this result for n=1). Consequently, the class of H-contact manifolds is very large. Moreover, we give some application about the topology of a compact H-contact manifold.     

AC losses and stability on large cable-in-conduit superconductors

The cable-in-conduit superconductors are preferred for applications where the AC losses and stability are a major concern, e.g., fusion magnets and SMES. A review of coupling currents loss results for both NbTi and Nb₃Sn cable-in-conduit conductors (CICC) is presented and the AC loss relevant features are listed, with special emphasis for the role of the interstrand resistance and strand coating. The transient stability approach for CICCs is discussed and the analytical models are quoted as well as the relevant experimental database. The likely spectrum of transient disturbance in CICC is reviewed and the need to account for interstrand current sharing in the design is outlined. Eventually a practical criterion for the interstrand resistance is proposed to link the stability and AC loss design.