Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods

Polydispersity is believed to have important effects on the formation of liquid crystal phases in suspensions of rod-like particles. To understand such effects, we analyse the phase behaviour of thin hard rods with length polydispersity. Our treatment is based on a simplified Onsager theory, obtained by truncating the series expansion of the angular dependence of the excluded volume. We describe the model and give the full phase equilibrium equations; these are then solved numerically using the moment free energy method which reduces the problem from one with an infinite number of conserved densities to one with a finite number of effective densities that are moments of the full density distribution. The method yields exactly the onset of nematic ordering. Beyond this, results are approximate but we show that they can be made essentially arbitrarily precise by adding adaptively chosen extra moments, while still avoiding the numerical complications of a direct solution of the full phase equilibrium conditions. We investigate in detail the phase behaviour of systems with three different length distributions: a (unimodal) Schulz distribution, a bidisperse distribution and a bimodal mixture of two Schulz distributions which interpolates between these two cases. A three-phase isotropic-nematic-nematic coexistence region is shown to exist for the bimodal and bidisperse length distributions if the ratio of long and short rod lengths is sufficiently large, but not for the unimodal one. We systematically explore the topology of the phase diagram as a function of the width of the length distribution and of the rod length ratio in the bidisperse and bimodal cases.Comment: 18 pages, 16 figure

Vacuum energy and spectral function sum rules

We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of conditions on the spectrum of the fundamental theory. We specialize the approach to both Minkowski and de Sitter space-times and investigate some examples.Comment: 11 pages, revtex4, no figures, version to be published on PR

Triggering rogue waves in opposing currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity, $U_0$, and the wave group velocity, $c_g$. We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing Nonlinear Schrodinger equation with non constant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.Comment: 5 pages, 5 figure

Classical r-matrix of the su(2|2) SYM spin-chain

In this note we straightforwardly derive and make use of the quantum R-matrix for the su(2|2) SYM spin-chain in the manifest su(1|2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r-matrix from the first order expansion in the ``deformation'' parameter 2 \pi / \sqrt{\lambda}, and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters and its pole structure. We notice that it still preserves an su(1|2) subalgebra, thereby admitting an expression in terms of a combination of projectors, which spans only a subspace of su(1|2) \otimes su(1|2). We study the residue at its simple pole at the origin, and comment on the applicability of the classical Belavin-Drinfeld type of analysis.Comment: 14 pages, LaTeX, no figures; corrections made, further analysis of the residue and references adde

Unitarity of noncommutative field theories from string theory

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.Comment: 8 pages, no figures. Work done in collaboration with A. Bassetto and R. Valandro (Padua Univ.). Submitted for the proceedings of the conference "Spacetime and Fundamental Interactions: Quantum Aspects. A conference to honour A.P.Balachandran's 65th birthday", Vietri, 26-31 May 200

On the Hopf algebra structure of the AdS/CFT S-matrix

We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1|2) subsector due to Janik to the full algebra by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by length-changing effects and results in an unusual central braiding. As an application we explicitly determine the antiparticle representation by means of the established antipode.Comment: 12 pages, no figures, minor changes, typos corrected, comments and references added, v3: three references adde

Capacity-building barriers to S3 implementation: an empirical framework for catch-up regions

In this paper, we investigate the implementation challenge of Smart Specialisation Strategies (S3) in catch-up regional environments, through the lens of capacity building. We analyse capacity building at two levels: micro-level (individual organisations) and meso-level (regional inter-organisational networks). We use empirical evidence from 50 interviews conducted in the period 2015–2017 from two Greek regions dramatically hit by the economic crisis (Crete and Central Macedonia). We argue that in the Cretan and Central Macedonian context, the difficulty of implementing S3 is directly linked with firms’ lack of adsorptive capability to exploit university-generated knowledge, university knowledge that is too abstract for firm’s to easily acquire, as well as to the capability of regional actors to build inter-organisational networking that fits their strategic needs

Stochastic Stability For A Model Representing The Intake Manifold Pressure Of An Automotive Engine

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)The paper presents conditions to assure stochastic stability for a nonlinear model. The proposed model is used to represent the input-output dynamics of the angle of aperture of the throttle valve (input) and the manifold absolute pressure (output) in an automotive spark-ignition engine. The automotive model is second moment stable, as stated by the theoretical result-data collected from real-time experiments supports this finding.31Spanish Ministry of Economy and Competitiveness [DPI2015-64170-R/MINECO/FEDER, DPI2011-25822]Government of Catalonia (Spain) [2014SGR859]FAPESP [03/06736-7]CNPq [304856/2007-0]CAPES Grant Programa PVE [88881.030423/2013-01]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

On the Integrable Structure of the Ising Model

Starting from the lattice $A_3$ realization of the Ising model defined on a strip with integrable boundary conditions, the exact spectrum (including excited states) of all the local integrals of motion is derived in the continuum limit by means of TBA techniques. It is also possible to follow the massive flow of this spectrum between the UV $c=1/2$ conformal fixed point and the massive IR theory. The UV expression of the eigenstates of such integrals of motion in terms of Virasoro modes is found to have only rational coefficients and their fermionic representation turns out to be simply related to the quantum numbers describing the spectrum.Comment: 18 pages, no figure

Innovative Micro- and Nanostructured Materials and Devices for Energy Applications

1 Dipartimento di Ingegneria Elettrica e dell'Informazione (DEI), Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy 2 Consiglio Nazionale delle Ricerche-Istituto di Fotonica e Nanotecnologie (CNRIFN), Via alla Cascata 56/C, 38123 Trento, Italy 3 Istituto Italiano di Tecnologia (IIT), Center for Biomolecular Nanotechnologies (CBN), Via Barsanti 1, 73010 Arnesano, Italy 4Department of Physics and Meteorology, Indian Institute of Technology Kharagpur, Kharagpur 721302, Indi