Controllability for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper, we prove controllability results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.     

Discrete X-wave formation in nonlinear waveguide arrays

We present experimental evidence for the spontaneous formation of discrete X waves in AlGaAs waveguide arrays. This new family of optical waves has been excited, for the first time, by using the interplay between discrete diffraction and normal temporal dispersion, in the presence of Kerr nonlinearity. Our experimental results are in good agreement with theoretical predictions.     

Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions

In this paper, we establish sufficient conditions for the controllability ofsecond-order differential inclusions in Banach spaces with nonlocalconditions. We rely on a fixed-point theorem for condensing maps due toMartelli.     

Radiocolorings in periodic planar graphs: PSPACE-completeness and efficient approximations for the optimal range of frequencies

The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function such that |Λ(u)−Λ(v)|2, when u,v are neighbors in G, and |Λ(u)−Λ(v)|1 when the distance of u,v in G is two. The discrete number of frequencies used is called order and the range of frequencies used, span. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span (min span RCP) or the order (min order RCP).In this paper, we deal with an interesting, yet not examined until now, variation of the radiocoloring problem: that of satisfying frequency assignment requests which exhibit some periodic behavior. In this case, the interference graph (modelling interference between transmitters) is some (infinite) periodic graph. Infinite periodic graphs usually model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they can model very large networks produced by the repetition of a small graph.A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph G_i(V_i,E_i). The edge set of G is derived by connecting the vertices of each iteration G_i to some of the vertices of the next iteration G_i+1, the same for all G_i. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest.We give two basic results:

• We prove that the min span RCP is PSPACE-complete for periodic planar graphs.

• We provide an O(n(Δ(G_i)+σ)) time algorithm (where|V_i|=n, Δ(G_i) is the maximum degree of the graph G_i and σ is the number of edges connecting each G_i to G_i+1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to as Δ(G_i)+σ tends to infinity.

We remark that, any approximation algorithm for the min span RCP of a finite planar graph G, that achieves a span of at most αΔ(G)+constant, for any α and where Δ(G) is the maximum degree of G, can be used as a subroutine in our algorithm to produce an approximation for min span RCP of asymptotic ratio α for periodic planar graphs.

The bend angle of water in ice Ih and liquid water: The significance of implementing the nonlinear monomer dipole moment surface in classical interaction potentials

The implementation of the physically accurate nonlinear dipole moment surface of the water monomer in the context of the Thole-type, polarizable, flexible interaction potential results in the only classical potential, which, starting from the gas phase value for the bend angle (104.52 degrees), reproduces its experimentally observed increase in the ice Ih lattice and in liquid water. This is in contrast to all other classical potentials to date, which predict a decrease of the monomer bend angle in ice Ih and in liquid water with respect to the gas phase monomer value. Simulations under periodic boundary conditions of several supercells consisting of up to 288 molecules of water used to sample the proton disorder in the ice Ih lattice yield an average value of vartheta(HOH)(I(h))=108.4 degrees +/-0.2 degrees for the minimized structures (T=0 K) and 108.1 degrees +/-2.8 degrees at T=100 K. Analogous simulations for liquid water predict an average value of vartheta(HOH)(liquid)=106.3 degrees +/-4.9 degrees at T=300 K. The increase of the monomer bend angle of water in condensed environments is attributed to the use of geometry-dependent charges that are used to describe the nonlinear character of the monomer's dipole moment surface. Our results suggest a new paradigm in the development of classical interaction potential models of water that can be used to describe condensed aqueous environments.     

Existence Results for Semilinear Perturbed Functional Differential Equations of Neutral Type with Infinite Delay

In this paper, by using semigroup theory and a nonlinear alternative for the sum of a completely continuous and a contraction operator, we establish sufficient conditions for the existence of solutions for perturbed semilinear neutral functional differential equations with infinite delay.     

Electrical conductance study of theta-liquid bridges

This work investigates the behavior of small liquid bridges that are formed between two horizontal supporting surfaces, aligned at the vertical direction. The contact lines of the liquid bridges are not edge-pinned but free to move across the supporting surfaces with the contact angle as a parameter (theta-bridges). An a.c. electrical conductance technique coupled with high resolution optical images is used to characterize the geometrical details of constant volume liquid bridges when their length is increased gradually until rupture. A mathematical framework is developed for the identification of the geometrical characteristics of theta-liquid bridges explicitly from conductance data. Theoretical predictions show good agreement with measurements for most of the bridge lengths (separation distance between supports) except close to the rupture point where the bridge is highly stretched. It is further shown that for short and moderate separation distances the present model can be used with confidence to determine the bridge volume and neck radius from the electrical signal.     

Structural dependence of the efficiency of functionalization of silica-coated FeOx magnetic nanoparticles studied by ATR-IR

The efficiency of propylamino functionalization of magnetic silica-coated FeO_x nanoparticles prepared by different methods, including coprecipitation and flame aerosol synthesis, has been evaluated by attenuated total reflection infrared spectroscopy (ATR-IR) combined with a specific surface reaction, thus revealing the availability of the grafted functional groups. Large differences in the population of reactive groups were observed for the investigated materials, underlining the tight relation between the structure of nanoparticles and their suitability for organic functionalization. The materials possessed different core structure, surface area, and porosity, as evidenced by transmission electron microscopy and nitrogen adsorption-desorption isotherms. Grafting of aminopropyl groups using a standard procedure based on reaction with (3-aminopropyl)trimethoxysilane as source of the propylamino groups was performed, followed by classical dry analysis methods to determine the specific concentration of the organic functional groups (in mmol g⁻¹ of material). ATR-IR spectroscopy in a specially constructed reactor cell was applied as wet methodology to determine the chemically available amount of such functional groups, showing that the materials possess largely different loading capacity, with a variability of up to 70% in the chemical availability of the organic functional group. The amount of (3-aminopropyl)trimethoxysilane used for functionalization was optimized, thus reaching a saturation limit characteristic of the material.