Frequency down-conversion using cascading arrays of coupled nonlinear oscillators

A novel coupling scheme using M≥2 arrays of coupled nonlinear elements arranged in a specific configuration can produce multifrequency patterns or a frequency down-converting effect on an external (input) signal. In such a configuration, each array contains N≥3 nonlinear elements with similar dynamics and each element is coupled unidirectionally within the array. The subsequent arrays in the cascade are coupled in a similar fashion except that the coupling direction is arranged in the opposite direction with respect to that of the preceding array. Previous theoretical work and numerical results have already been reported in [P. Longhini, A. Palacios, V. In, J. Neff, A. Kho, A. Bulsara, Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion, Phys. Rev. E 76 (2007) 026201]. This paper is focused on results of experiments implemented on two distinct systems: the first system is fabricated using discrete component circuits to approximate an overdamped bistable Duffing oscillator described by a quartic potential system, and the second system is built in a microcircuit, where the nonlinearity is described by a hyperbolic tangent function, with the option of applying an external signal to investigate resonant effects. In particular, the circuit implementations for each case use M=2 arrays, but their voltage oscillations already demonstrate that the frequency relations between each of the successive arrays decrease by a rational factor, conforming to earlier theoretical and numerical results for the general case containing M arrays. This behavior is important for efficient frequency down-converting applications which are essential in many communication systems where heterodyning is typically used and it involves multi-step processes with complicated circuitry.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

Complex surfaces polarized by an ample and spanned line bundle of genus three

Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K _X L))/2=3 are classified by means of the main techniques of adjunction theory.     

A nonlinear parabolic free boundary problem

Summary When two immiscible fluids in a porous medium are in contact with one another, an interface is formed and the movement of the fluids results in a free boundary problem for determining the location of the interface along with the pressure distribution throughout the medium. The pressure satisfies a nonlinear parabolic partial differential equation on each side of the interface while the pressure and the volumetric velocity are continuous across the interface. The movement of the interface is related to the pressure through Darcy’s law. Two kinds of boundary conditions are considered. In Part I the pressure is prescribed on the known boundary. A weak formulation of the classical problem is obtained and the existence of a weak solution is demonstrated as a limit of a sequence of classical solutions to certain parabolic boundary value problems. In Part II the same analysis is carried out when the flux is specified on the known boundary, employing special techniques to obtain the uniform parabolicity of the sequence of approximating problems. Entrata in Redazione il 29 novembre 1975. This research was supported in part by the National Science Foundation, the Senior Fellowship Program of the North Atlantic Treaty Organization, the Italian Consiglio Nazionale delle Ricerche, and the Texas Tech. University.     

Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2).     

Rates of desorption from solid surfaces: Coverage dependence

The recently developed Classical Stochastic Diffusion Theory is applied to obtain the coverage dependence of desorption rates for Xe on W(111). Using the attractive Xe-Xe potential from gas phase experiments, we find a strong coverage dependence in the desorption rates and calculate Temperature Programmed Desorption Spectra (for a potential with reduced attractiveness) that are in excellent qualitative agreement with experimental results. We also investigated the effect of purely repulsive adsorbate-adsorbate interactions where we find, for some coverage ranges, that two different adsorption configurations can be stable (at different temperatures) leading to a marked change in the corresponding desorption rates and to distinct non-Arrhenius behavior.     

Transition from rigid to flexible structures in micelles of Undecylammonium chloride in aqueous solutions of NaCl

Small angle neutron scattering (SANS) data for Undecylammonium chloride (UAC) in heavy water in the presence of NaCl 0.0428 and 0.3422 M are consistent with the presence of elongated micelles. This micellar shape has been adopted to analyze viscosity data of UAC in water in the presence of NaCl. The results obtained from this last technique are consistent with the increase of the micelle aggregation number with increasing the surfactant concentration. Micelles change from prolate ellipsoidal shape to cylindrical and wormlike shapes by increasing the added NaCl concentration and surfactant concentrations. The differences between results for the micelle aggregation number calculated from viscosity, SANS and light scattering data have been attributed to the solvent effect on micelle formation as well as changes in the size, shape and flexibility of the micelle. Viscosity data provide qualitative information on the effect of the added NaCl concentration and surfactant concentration on the size, shape, flexibility of the micelles in diluted solutions.     

Long range disorder and Anderson transition in systems with chiral symmetry

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law H_ij|i−j|⁻. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states (DoS) and the two-level correlation function (TLCF) by mapping the chRBM onto a nonlinear σ model. We also put forward, by exploiting the relation between the chRBM at =1 and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to quantum chromodynamics (QCD).     

Numerical calculation of cutoff frequencies of optical fibers by a variational technique

A numerical method for calculating cutoff frequencies of modes of weakly guiding optical fibers is described. Starting from a properly constructed field representation, the method follows a variational approach to obtain an eigenvalue problem for the cutoff frequencies which can be easily solved by a standard numerical routine. The field representation uses an expansion in terms of the Laguerre–Gauss functions in the fiber core and limiting form for small arguments of modified Bessel functions in the fiber cladding. Fibers with power-law refractive index profiles and fibers with a profile showing a dip on the axis are analyzed. Results obtained for modes of arbitrary order (both azimuthal and radial) show that our method is very efficient and accurate.