Glassy states and microphase separation in cross-linked homopolymer blends

The physical properties of blends of distinct homopolymers, cross-linked beyond the gelation point, are addressed via a Landau approach involving a pair of coupled order-parameter fields: one describing vulcanisation, the other describing local phase separation. Thermal concentration fluctuations, present at the time of cross-linking, are frozen in by cross-linking, and the structure of the resulting glassy fluctuations is analysed at the Gaussian level in various regimes, determined by the relative values of certain physical length-scales. The enhancement, due to gelation, of the stability of the blend with respect to demixing is also analysed. Beyond the corresponding stability limit, gelation prevents complete demixing, replacing it by microphase separation, which occurs up to a length-scale set by the rigidity of the network, as a simple variational scheme reveals.Comment: 7 pages, 6 figure

Variational approach to gravitational theories with two independent connections

A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the dependence upon one of the connections is left completely unspecified. When the variation is applied to the Einstein-Hilbert action the Einstein field equations are recovered. However when applied to $f(R)$ and Scalar-Tensor theories, it yields gravitational field equations which differ from their equivalents obtained with a metric or Palatini variation and reduce to the former ones only when no connections appear in the matter action.Comment: 11 pages, no figure

Galileon gravity and its relevance to late time cosmic acceleration

We consider the covariant galileon gravity taking into account the third order and fourth order scalar field Lagrangians L_3(\pi) and L_4(\pi) consisting of three and four $\pi$'s with four and five derivatives acting on them respectively. The background dynamical equations are set up for the system under consideration and the stability of the self accelerating solution is demonstrated in general setting. We extended this study to the general case of the fifth order theory. For spherically symmetric static background, we spell out conditions for suppression of fifth force effects mediated by the galileon field $\pi$. We study the field perturbations in the fixed background and investigate conditions for their causal propagation. We also briefly discuss metric fluctuations and derive evolution equation for matter perturbations in galileon gravity.Comment: 11 pages, no figure, minor clarifications and few refs added, to appear in pr

Unifying Einstein and Palatini gravities

We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, C-theories include completely new physically distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$, C-theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show that C-theories have a scalar-tensor formulation, which in some special cases reduces to simple Brans-Dicke-type gravity. If matter fields couple to the connection, the conservation laws in C-theories are modified. The stability of perturbations about flat space is determined by a simple condition on the lagrangian.Comment: 17 pages, no figure

The New Brazilian Arbitration Law

This article selects four landmark events: the enactment of Law No. 9.307 on Sept. 23, 1996 (the “1996 Arbitration Law”); (ii) the recognition of the constitutionality of such law by the Supreme Court in 2001; (iii) the ratification of the New York Convention on the Recognition and Enforcement of Foreign Arbitral Awards in 2002; and (iv) the enactment of Law No. 13.129 on May 26, 2015 (the “Amendment”). The first three events are analyzed jointly with the fourth event, in order to identify novel important legal issues involving arbitration in Brazil: (a) subject arbitrability concerning state and state entities; (b) the compromise between institutional rules and parties’ choice by means of changes at the roster of arbitrators and multiparty arbitration, focused at reduction of arbitral awards annulment risks; (c) the amendment of arbitration agreement by using terms of reference, which adjusts limitation periods by the exact date of its interruption; (d) the annulment of arbitral awards and its application in precedents; (e) the provision concerning foreign awards recognition and enforcement, which is closely identified with the New York Convention on the Recognition and Enforcement of Arbitral Awards (“NYC”), strictly interpreted by the Superior Court of Justice in several foreign arbitral decisions recognition precedents; (f) the ‘arbitral letter’, also included and provided as a mechanism of cooperation between arbitrators and courts; finally, (g) the inclusion of arbitration agreements in bylaws of Brazilian corporations, in order to face the growing disputes involving companies since the enactment of the Constitution in 1988

Black holes in scalar-tensor gravity

Hawking has proven that black holes which are stationary as the endpoint of gravitational collapse in Brans--Dicke theory (without a potential) are no different than in general relativity. We extend this proof to the much more general class of scalar-tensor and f(R) gravity theories, without assuming any symmetries apart from stationarity.Comment: v1: 4 pages; v2: typos corrected, published versio

The New Brazilian Arbitration Law

This article selects four landmark events: the enactment of Law No. 9.307 on Sept. 23, 1996 (the “1996 Arbitration Law”); (ii) the recognition of the constitutionality of such law by the Supreme Court in 2001; (iii) the ratification of the New York Convention on the Recognition and Enforcement of Foreign Arbitral Awards in 2002; and (iv) the enactment of Law No. 13.129 on May 26, 2015 (the “Amendment”). The first three events are analyzed jointly with the fourth event, in order to identify novel important legal issues involving arbitration in Brazil: (a) subject arbitrability concerning state and state entities; (b) the compromise between institutional rules and parties’ choice by means of changes at the roster of arbitrators and multiparty arbitration, focused at reduction of arbitral awards annulment risks; (c) the amendment of arbitration agreement by using terms of reference, which adjusts limitation periods by the exact date of its interruption; (d) the annulment of arbitral awards and its application in precedents; (e) the provision concerning foreign awards recognition and enforcement, which is closely identified with the New York Convention on the Recognition and Enforcement of Arbitral Awards (“NYC”), strictly interpreted by the Superior Court of Justice in several foreign arbitral decisions recognition precedents; (f) the ‘arbitral letter’, also included and provided as a mechanism of cooperation between arbitrators and courts; finally, (g) the inclusion of arbitration agreements in bylaws of Brazilian corporations, in order to face the growing disputes involving companies since the enactment of the Constitution in 1988

Glassy correlations and microstructures in randomly crosslinked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of crosslinking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellae or random structures with a unique wavelength, can be energetically favorable.Comment: 19 pages, 10 figures. Submitted to the Journal of Chemical Physics (http://jcp.aip.org

Rigidly Rotating Strings in Stationary Spacetimes

In this paper we study the motion of a rigidly rotating Nambu-Goto test string in a stationary axisymmetric background spacetime. As special examples we consider the rigid rotation of strings in flat spacetime, where explicit analytic solutions can be obtained, and in the Kerr spacetime where we find an interesting new family of test string solutions. We present a detailed classification of these solutions in the Kerr background.Comment: 19 pages, Latex, 9 figures, revised for publication in Classical and Quantum Gravit