Persistence and breakdown of Airy beams driven by an initial nonlinearity

We study the behavior of Airy beams propagating from a nonlinear medium to a linear medium. We show that an Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. The unusual behavior of Airy beams is examined from their energy flow as well as the Brillouin zone spectrum of self-induced chirped photonic lattices.     

Uniformly recurrent subgroups of simple locally finite groups

It is shown that for the conjugation action of the symmetric group Sn, when n = 6 or n ≥ 8, all S _n -irreducibles appear as constituents of a single conjugacy class, namely, one indexed by a partition λ of n with at least two parts, whose parts are all distinct and taken from the set of odd primes and 1. A simple characterisation of conjugacy classes containing all irreducibles is proved.     

Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs

A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known Lévy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on periodic graphs, we present a construction of such a non-trivial drift and give an explicit formula for it. Several examples with explicit computations are included.     

Quasi-ordered rings - A uniform approach to orderings and valuations

A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [3 Fakhruddin, S. M. (1987). Quasi-ordered fields. J. Pure Appl. Algebra 45:207–210.[Crossref], [Web of Science ®] , [Google Scholar]], Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. The aim of the present paper is to prove that an analogous dichotomy holds for commutative rings with 1 as well.     

Funktionen mit Stammfunktion

The aim of this note is to analyze the class \(St[a,b]\) of all real functions on \([a,b]\) with primitive with respect to its size and its relations to other function classes. Apart from recalling previously known results and discussing new results we put a particular emphasis on examples and counterexamples.     

Complex Inorganic/Organic Core-Shell Particles by an Inverse Emulsion Technique

Two synthetic approaches to modify the surface of inorganic particles are presented. In the first approach the inorganic particles are prepared in-situ in a confined space in inverse emulsions. The used amphiphilic statistical copolymers act not only as emulsifiers, but they also hydrophobize the remaining inorganic particles after the precipitation. This approach represents a versatile method to obtain various inorganic nanoparticles as well as more complex inorganic materials like core-multiple shell and perovskite-based nanoparticles. The second procedure uses preformed inorganic particles, as an aqueous dispersion, to modify them with surface active amphiphilic copolymers in a multicomponent solvent system. This method turns out to be a simple but highly efficient method to modify preformed inorganic nanoparticles. The particles are characterized by SEM, TEM and dynamic light scattering. The modified inorganic nanoparticles are suitable to be homogenously incorporated into a polymer matrix to form transparent nanocomposite materials.     

NZ‐flows in strong products of graphs

We prove that the strong product G₁? G₂ of G₁ and G₂ is ?₃‐flow contractible if and only if G₁? G₂ is not T? K₂, where T is a tree (we call T? K₂ a K₄‐tree). It follows that G₁? G₂ admits an NZ 3 ‐flow unless G₁? G₂ is a K₄ ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G₁? G₂ is not a K₄ ‐tree, and an NZ 4‐flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010     

Corresponding-states laws for protein solutions

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.     

Molecular dynamics simulation of hydrogen fluoride mixtures with 1-ethyl-3-methylimidazolium fluoride: a simple model for the study of structural features

Mixtures of hydrogen fluoride with ionic liquids show unique physicochemical properties, including their ability to form polyfluoride species (pointed out for the first time in this media by von Rosenvinge et al. J. Chem. Phys. 1997, 107, 8012). Among those systems the acidic 1-ethyl-3-methylimidazolium fluoride (EMIF.2.3HF) has been widely studied experimentally since it is the more promising for electrochemical applications. Recent studies (Hagiwara et al. J. Electrochem. Soc. 2002, 149, D1), while yielding many results, raised some questions about structural features of the liquid: absence of hydrogen bonds between the EMI+ ring hydrogen atoms and the fluoride anions, persistence of stacks and layers of cations similar to those existing in the crystal, and interpretation of the X-ray diffraction spectra. To address these questions, we have developed a simple molecular dynamics model. Our simulations are very consistent with experimental results and complete them, providing an atomic scale interpretation.     

Controlling the energy transfer in dipole chains

Processing digital signals on the molecular scale is of great interest. In this paper, we discuss the control of pulselike energy propagation through one-dimensional arrays of dipoles. Three systems are explored. In the first system, a chain of coaxial dipoles is gated by two control dipoles. Changing the orientation of these control dipoles lets us control the transfer of energy in the chain. In the other two systems, the chain-branch system and the two-branch system, two chains are used as an input and the propagation of energy is controlled by sending one or two signals toward the junction. Both systems can operate as a logical AND port. Their geometrical configurations are key to a well-defined control and operation of the AND port.