Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent −2.     

Nilmanifolds with a calibrated G2-structure

We introduce obstructions to the existence of a calibrated G₂-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G₂-structure.     

A phase field approach to solidification and solute separation in water solutions

We propose a phase field model for the solid–liquid phase transition in a water-salt (sodium chloride) solution in the absence of macroscopic motion, under possibly non-isothermal conditions. A thermodynamic approach based on a free energy functional is assumed. The model consists of three evolution equations: a time-dependent Ginzburg–Landau equation for the solid–liquid phase change, a diffusion equation of the Cahn–Hilliard kind for the solute dynamics and the heat equation for the temperature change. The proposed system is aimed to contribute to the modelling of the brine channels formation in the ice of the polar seas.     

Substituent effects on the photophysical properties of amino-aurone-derivatives

ABSTRACT

Aurones are potential candidates to be employed as fluorescent probes or as pharmacophores for biological applications. This work describes a density functional theory (DFT) and time-dependent -DFT study at the PBE0/6-31?+?G(d) level of theory to analyse the structural, electronic and photophysical properties of a series of new proposed 4′-amine-aurone derivatives in its E and Z isomeric conformations. The maximum absorption wavelength of the proposed aurones appears in the range 390???514?nm, while the most allowed emission pathways were computed in the range 493–530?nm. The bathochromic shift of these compounds with respect to the non-substituted aurone is modulated by the acceptor strength of the added 4-substituents, in addition to the ability of the substituents to localise the frontier molecular orbitals over the acceptor benzofuranone moiety without losing the tricyclic planarity, which favours the push–pull nature of these molecules. The influence of the 4-substituent is also evidenced in the Stokes shifts for the whole series; as the electron-withdrawing character of the 4-substituents enhances, higher is the polarisation of the structure resulting in higher Stokes shifts. As a result, -CF₃ and -NO₂ substituents were responsible of larger Stokes shifts, then compounds containing these substituents are proposed as potential fluorescence probes for useful applications in biological systems.     

Evaluating cost impacts on reverse logistics using an Economic Order Quantity (EOQ) model with environmental and social considerations

Central European Journal of Operations Research - Societal awareness and legislation changes concerning sustainability have affected how organizations generate value for stakeholders, as well as...     

Collimating Montel mirror as part of a multi‐crystal analyzer system for resonant inelastic X‐ray scattering

Advances in resonant inelastic X‐ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the Ir L₃‐edge stands at ～25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid‐angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the Ir L₃‐absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X‐ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27‐ID at the Advanced Photon Source. X‐rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X‐ray measurements, ray‐tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high‐resolution RIXS multi‐crystal analyzer system.     

Charge dynamics,Majorana condition and the topology of the interacting electromagnetic field

In previous works [1, 2], the 2-dimensional charge transport with parallel (in plane) magnetic field was considered from the theoretical point of view showing explicitly that the specific form of the emergent equation enforces the respective field solution to fulfil the Majorana condition. In this paper we review, explain and analyze these important results in the context of the generated physical effects, namely, the quantum ring as spin filter, the quantum Hall effect and a new one of pure topological origin (as the described by the Aharonov–Casher theorems). The link with supersymmetrical models is briefly discussed.     

Effect of methoxyl groups on the NMR spectra: configuration and conformation of natural and synthetic indanic and tetralinic structures

Here, we studied the influence of the methoxyl groups attached at C‐7 and C‐2′ of natural and synthetic 1‐arylindanes on the chemical shift of the signal of bibenzylic hydrogen and carbon atoms and J_1,2 coupling constants. This influence was also analysed in natural 1‐aryltetralins and related compounds that possess methoxyl and/or hydroxyl groups bound at C‐8 and C‐2′. The methoxyl groups attached at C‐7 in indanes or at C‐8 in tetralins produce a deshielding signal at H‐1 and shield at C‐1 and a strong decrease in the value of J_1,2 due to the pseudoequatorial location adopted by the aryl group bound at C‐1, avoiding an ‘A^1,3 strain’. Furthermore, compounds with hydroxyl or methoxyl groups in C‐2′, in the absence of substituents of C‐7 or C‐8, present a strong deshielding signal at H‐1, strong shield of the C‐1 signal and a decrease in the value of J_1,2. This is attributed to the stereoelectronic effects of the methoxyl or hydroxyl groups, which we have called ‘Asarone effect’. NOESY experiments were conducted to confirm the configuration and conformation of some of the compounds included in this work. This study shows that both effects, A^1,3 strain and Asarone effect, must be taken into account when the structure of natural indanes and tetralins is analysed by using ¹H‐NMR and ¹³C‐NMR spectra. Copyright © 2016 John Wiley & Sons, Ltd.