Static (hyper)polarizabilities and absorption spectra of single [2.2]<Emphasis Type="Italic">p</Emphasis>-cyclophane NO<Subscript>2</Subscript>/NH<Subscript>2</Subscript> substituted from DFT methods

We explore the behavior of the average of polarizability (< α >), total first hyperpolarizability (β_total) and average of second hyperpolarizability (< γ >) for single A/D (-NO₂/-NH₂) substituted [2.2]p-cyclophane. The geometric optimization was carried out at HF and DFT (SVWN, PBE, B3LYP, PBE0, BHHLYP and CAM-B3LYP) level, in gas phase, using the 6-31 + G(d,p) basis set. The static tensor components of < α > and β_total, in gas phase, were calculated using Field Finite (FF) methods with electric field intensities of E = ± 0.001 a.u. in each (x,y,z) axis direction. The substitution of A/D groups in positions 7–15 (structure 2 in Fig. 1) produced an increment in the < α > values. Regardless of the A/D positions, the < α > values showed not significant changes at all theory level. < α > DFT results are overestimated up to 20%, if HF values are taken into account, being SVWN and PBE functionals those that give the main deviation. There are monotonic and progressive behaviors of β_total for the 1–5 structure change as expected by orientation of the dipolar moment in both aromatic rings. With respect to the performance of DFT functionals, < γ > and β_total results are significantly overestimated if HF values are taken into account. In fact, the relative percentage error of β_total at DFT level with respect to HF ones is between 58 and 132%, being PBE functional those that give the main deviation. The close overlap of the orbitals between the rings facilitates chromophore delocalization to account for the observation of high β_total in these compounds. Therefore, we expected that the contribution by coupling of the transition moment between first and higher excited states should be lie much higher due to phane effect than that for ring units.

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Fig. 1 a Single [2.2]p-cyclophane core molecule. b Geometric parameters of interest c Highlights for the 4, 7, 12, and 15 positions, which are substituted by (-NO₂/-NH₂) acceptor/donor pair

     

Magnetic field effects in the Casimir force between two parallel anti-ferromagnetic slabs

We study the Casimir force F$F$ between two parallel anti-ferromagnetic slabs taking into account an external magnetic field in the Voigt configuration. Using a frequency and magnetic field dependent magnetic permeability tensor and a frequency independent dielectric permittivity, to describe the slabs, we calculate the Casimir force using non-normal incidence reflectivity of the electromagnetic waves in the free space between the slabs. We determine the Casimir force by performing two-dimensional calculations. F$F$ is investigated as a function of the layer thickness d$d$, the vacuum gap width L$L$ between slabs, and the external magnetic field strength H$H$. Features of F$F$ as function of the external field include the presence of sharp dips and peaks, which appear in the vicinity of the resonance frequency, and are consequences of the interaction of the external magnetic field with the electron spin. In addition, an external field may diminish F$F$, which is an important effect not found in any other system.     

BRS cohomology and topological anomalies

The occurrence of non-abelian anomalies in gauge theories and gravitation, first discovered via perturbative techniques, is now completely explained from the mathematical point of view by means of the family index theorem of Atiyah and Singer. Here we make contact between this approach and BRS cohomology, by showing that they yield the same non-abelian anomalies, provided a certain restriction to local functionals is not introduced from the very beginning. In particular, this solves the unicity problem for this kind of anomalies. Local BRS cohomology is still relevant for the abelian case.Work partially supported by Gruppo Nazionale di Fisica Matematica del CNR and Progetto Nazionale Geometria e Fisica del MPI     

Approximated algorithms for the minimum dilation triangulation problem

The complexity status of the minimum dilation triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the sequential parameter optimization toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.     

Bianchi Permutability for the Anti‐Self‐Dual Yang‐Mills Equations

The anti‐self‐dual Yang‐Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the anti‐self‐dual Yang‐Mills (ASDYM) equations generated by a Darboux matrix with an affine dependence on the spectral parameter is obtained, together with its Bianchi permutability equation. We give examples in which we obtain BTs of symmetry reductions of the ASDYM equations by reducing this ASDYM BT. Some discrete integrable systems are obtained directly from reductions of the ASDYM Bianchi system.     

A GRASP metaheuristic for humanitarian aid distribution

Large scale disasters, natural or human-made, have huge consequences on people and infrastructures. After a disaster strikes, the distribution of humanitarian aid to the population affected is one of the main operations to be carried out, and several crucial decisions must be made in a short time. This paper addresses a last-mile distribution problem in disaster relief operations, under insecure and uncertain conditions. A model is presented that takes into account the cost and time of operation, the security and reliability of the routes, and the equity of aid handed out. The output of the model consists of a detailed set of itineraries that can be used to build an implementable distribution plan. Given its high complexity, the resulting problem is solved using a multi-criteria metaheuristic approach. In particular, a constructive algorithm and a GRASP based metaheuristic are developed, which are tested in a case study based on the 2010 Haiti earthquake.     

A delayed biophysical system for the Earth's climate

Summary We consider further the Differential Daisyworld model of Watson and Lovelock that we have analyzed in a previous paper (De Gregorio et al., 1992). In this work we introduce a delay in the birthrate of the species. We consider three different models: the constant time lag model and the strong and the weak delay models. In the weak delay case no value of the delay changes the asymptotic stability of the stationary solutions. In the constant time lag and in the strong delay models, however, there exists a critical value of the delay, above which periodic solutions appear. These periodic solutions are numerically found to be globally attracting even for large delay when the linear approximation analysis is no longer valid. For both models, very regular behavior is obtained if the percentage coverage of the fertile ground of the Earth is much less than 1. As the percentage of the fertile ground increases, however, chaotic behavior is possible.     

Reactivity of hydroxo palladium and platinum complexes towards N-substituted salicylaldimines and β-ketoimines

The binuclear hydroxo complexes [{M(C6F5)2(OH)}2]2–(M=PdandPt)reactwithN-substituted salicylaldimines (HSal=NR) or -ketoimines (RN=CMeCH2COR) to give the corresponding N-substituted salicylaldiminato or -ketoiminato mononuclear complexes, [M(C6F5)2(Sal=NR)]– (M=Pd or Pt; R= Me, Et, Ph, o-MeC6H4, p-MeC6H4 or p-ClC6H4) or [(C6F5)2M{N(R)C(CH3)CHC(O)R}]– (M=Pd or Pt; R=o-MeC6H4 or p-MeC6H4; R=Me or Ph), respectively. The complexes have been characterized by partial elemental analyses, conductance measurements and spectroscopic (i.r. and 1H and 19F- n.m.r.) methods.     

Unfolding Tin–Cobalt Interactions in Oxide‐Based Composite Electrodes for Li‐Ion Batteries by Mössbauer Spectroscopy

With a view to the development of new composite electrodes for lithium-ion batteries with electroactive tin and cobalt, Co-doped tin dioxide samples are studied. The role played by oxygen and cobalt atoms in the electrochemical behavior of tin-based electrodes for Li-ion batteries is examined by the powerful and selective (119)Sn M?ssbauer spectroscopy. For the discharged electrodes, the oxygen atoms in the lithia matrix tend to destabilize the Sn(0) atoms. In contrast, the presence of cobalt atoms helps to form a matrix that stabilizes the reduced tin atoms. Cobalt-tin interactions in electrochemical reduced Co(x)Sn(1-x)O(2) electrodes are deduced from the electrochemical and M?ssbauer results.