Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.     

Synthesis of novel O-alkylbenzochromeno-1,5-benzodiazepinones. Study of the N–H····N and CO····HN hydrogen bonding interactions with 2-aminopyridines

A series of novel 6-(O-alky)lbenzochromeno-1,5-benzodiazepin-2-ones 4a–c was prepared through the condensation between the [1]benzopyrano[4,3-c][1,5]benzodiazepin-7(8H)one 1 and a series of alkylalcohols. Scaffold 4 exhibited interesting hydrogen-bonding interaction with 2-aminopyridine derivatives. The so obtained self-assembled systems 5 were fully characterized by 1D/2D-NMR techniques and mass spectrometry. The hydrogen-bonding interaction was supported by IR and Raman spectroscopy and by ¹H NMR titration experiments, and was confirmed by an X-ray crystal structure analysis.     

Adatom Defect Induced Spin Polarization of Asymmetric Structures

The spin polarization of carbon nanomaterials is crucial to design spintronic devices. In this paper, the first-principles is used to study the electronic properties of two defect asymmetric structures, Cap-(9, 0)-Def [6, 6] and Cap-(9, 0)-Def [5, 6]. We found that the ground state of Cap-(9, 0)-Def [6, 6] is sextet and the ground state of Cap-(9, 0)-Def [5, 6] is quartet, and the former has a lower energy. In addition, compared with Cap-(9, 0) CNTs, the C adatom on C₃₀ causes spin polarization phenomenon and Cap-(9, 0)-Def [6, 6] has more spin electrons than Cap-(9, 0)-Def [5, 6] structure. Moreover, different adsorb defects reveal different electron accumulation. This finding shows that spin polarization of the asymmetric structure can be adjusted by introducing adatom defects.     

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Characterisation of colloidal drug delivery systems from the naked eye to Cryo-FESEM

Poly(ethylcyanoacrylate) nanoparticles prepared by interfacial polymerisation on the basis of microemulsions were prepared in this study and both colloidal systems, nanoparticles and microemulsions, were analysed by visual observation and several microscopic techniques. Phase boundaries for the microemulsions of the two pseudoternary systems ethyloleate, polyoxyethylene 20 sorbitan mono-oleate/sorbitan monolaurate and water with and without butanol as a cosurfactant were determined by visual observation of the samples. Microemulsions containing liquid crystals were determined by polarisation light microscopy. Using freeze-fracture transmission electron microscopy and Cryo-field emission scanning electron microscopy the type of microemulsion (w/o droplet, bicontinuous, solution) was characterised. Nanoparticles prepared from the different types of microemulsion were additionally observed by conventional scanning electron microscopy. The size of the nanoparticles obtained from electron microscopy was in good agreement with particle sizing techniques (photon correlation spectroscopy) from earlier studies and no morphological differences could be observed in particles prepared from the different types of microemulsions. Cryo-field emission scanning electron microscopy proved to be a most valuable technique in the visualisation of the colloidal systems as samples could be observed close to their natural state.     

Non-integrability vs. integrability in pentagram maps

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.     

Azobenzene‐Functionalized Metal–Organic Polyhedra for the Optically Responsive Capture and Release of Guest Molecules

Stimuli‐responsive metal–organic polyhedra (srMOPs) functionalized with azobenzene showed UV‐irradiation‐induced isomerization from the insoluble trans‐srMOP to the soluble cis‐srMOP, whereas irradiation with blue light reversed this process. Guest molecules were trapped and released upon cis‐to‐trans and trans‐to‐cis isomerization of the srMOPs, respectively. This study provides a new direction in the ever‐diversifying field of MOPs, while laying the groundwork for a new class of optically responsive materials.     

Systematic Tuning and Switching of Neutral and Ionic Phases in a Donor–Acceptor Chain Compound by Doping with Less‐Active Donors and by Pressure Application

The temperature‐induced stepwise neutral–ionic (N–I) phase transition in the covalently bonded donor–acceptor chain compound [Ru₂(2,3,5,6‐F₄PhCO₂)₄DMDCNQI] ? 2(p‐xylene) (2,3,5,6‐F₄PhCO₂^?=2,3,5,6‐tetrafluorobenzoate; DMDCNQI=2,5‐dimethyl‐N,N′‐dicyanoquinodiimine) was systematically tuned over a wide temperature range using two techniques: 1) A chemical technique based on doping with a less‐active donor unit [Ru₂^II,II(F₅PhCO₂)₄] (F₅PhCO₂^?=pentafluorobenzoate), thereby providing an isostructural doped series [{Ru₂^II,II(2,3,5,6‐F₄PhCO₂)₄}_1?x{Ru₂^II,II(F₅PhCO₂)₄}_xDMDCNQI] ? 2(p‐xylene), with x=0.06, 0.10, 0.21, and 0.24; and 2) a physical technique, which was the application of hydrostatic pressure to the doped compounds. The stepwise N–I transition observed in the original compound was systematically varied in terms of the viewpoints of both transition temperature and transition features (stepwise or monotonic) dependent on the amount of dopants x. Application of pressure efficiently tuned the N–I transitions, with the oxidation phases being dramatically modified by applying only weak pressure up to 4 kbar. Even in cases that led to N–I transitions in small domains of the chains at ambient pressure, the application of pressure caused an expansion of the domains that enabled N–I transitions, finally leading to a complete change in the oxidation state of the chains, from neutral to ionic, accompanied by a change from a paramagnetic state to a ferrimagnetically ordered state.