Engineering generalized synchronization in chaotic oscillators

We report a method of engineering generalized synchronization (GS) in chaotic oscillators using an open-plus-closed-loop coupling strategy. The coupling is defined in terms of a transformation matrix that maps a chaotic driver onto a response oscillator where the elements of the matrix can be arbitrarily chosen, and thereby allows a precise control of the GS state. We elaborate the scheme with several examples of transformation matrices. The elements of the transformation matrix are chosen as constants, time varying function, state variables of the driver, and state variables of another chaotic oscillator. Numerical results of GS in mismatched Ro?ssler oscillators as well as nonidentical oscillators such as Ro?ssler and Chen oscillators are presented.     

Large molecular aggregates: From atmospheric aerosols to drug nanoparticles

Large molecular aggregates with sizes ranging from subnanometers to microns are ubiquitous. As atmospheric aerosols they influence our climate, in interstellar space they are discussed as reactive sites, and in medicine small particles are considered as promising candidates to achieve a targeted drug delivery. The present contribution is focused on the characterization of the physical-chemical properties of these particles and on their targeted generation. One of the greatest challenges is to understand the properties of these aggregates on a molecular level. The latter point is discussed in detail focussing on the vibrational dynamics of these particles.     

The Full Study of Planar Quadratic Differential Systems Possessing a Line of Singularities at Infinity

In this article we make a full study of the class of non-degenerate real planar quadratic differential systems having all points at infinity (in the Poincaré compactification) as singularities. We prove that all such systems have invariant affine lines of total multiplicity 3, give all their configurations of invariant lines and show that all these systems are integrable via the method of Darboux having cubic polynomials as inverse integrating factors. After constructing the topologically distinct phase portraits in this class we give invariant necessary and sufficient conditions in terms of the 12 coefficients of the systems for the realization of each one of them and give representatives of the orbits under the action of the affine group and time rescaling. We construct the moduli space of this class for this action and give the corresponding bifurcation diagram. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

A color-coded backlighted defocusing digital particle image velocimetry system

Defocusing digital particle image velocimetry (DDPIV), as a true three-dimensional (3D) measurement technique, allows for the measurement of 3D velocities within a volume. Initially designed using a single CCD and 3-pinhole mask (Willert and Gharib in Exp Fluids 12:353–358, 1992), it has evolved into a multi-camera system in order to overcome the limitations of image saturation due to multiple exposures of each particle. In order to still use a single camera and overcome this limitation, we have modified the original single CCD implementation by placing different color filters over each pinhole, thus color-coding each pinhole exposure, and using a 3-CCD color camera for image acquisition. Due to the pinhole mask, there exists the problem of a significant lack of illumination in a conventional lighting setup, which we have solved by backlighting the field-of-view and seeding the flow with black particles. This produces images with a white background superimposed with colored triple exposures of each particle. A color space linear transformation is used to allow for accurate identification of each pinhole exposure when the color filters’ spectrum does not match those of the 3-CCD color camera. Because the imaging is performed with a multi-element lens instead of a single-element lens, an effective pinhole separation, d _e, is defined when using a pinhole mask within a multi-element lens. Calibration results of the system with and without fluid are performed and compared, and a correction of the effective pinhole separation, d _e, due to refraction through multiple surfaces is proposed. Uncertainty analyses are also performed, and the technique is successfully applied to a buoyancy-driven flow, where a 3D velocity field is extracted.     

The effects of forced boundary conditions on flow within a cubic cavity using digital particle image thermometry and velocimetry (DPITV)

Buoyancy-driven convection within a cavity, whose sidewalls are heated and cooled, is a problem of great interest, because it has applications in heat transfer and mixing. Most studies to date have studied one of two cases: the steady-state case or the development of the transient flow as it approaches steady state. Our main concern was to study the response of the cavity to time-varying thermal boundary conditions. We therefore decided to observe the flow phenomena within a convection cavity under sinusoidal thermal forcing of the sidewalls. To map the flow properly, it is necessary to have simultaneous kinematic and thermal information. Therefore, the digital particle image thermometry and velocimetry (DPITV) is used to acquire data. Implementing this technique requires seeding the flow with encapsulated liquid crystal particles and illuminating a cross section of the flow with a sheet of white light. Extraction of the thermal and kinematic content is in two parts. For the first, the liquid crystals will reflect different colors of the visible spectrum, depending on the temperatures to which they are subjected. Therefore, calibrating their color reflection with temperature allows for the extraction of the thermal content. For the second part, the kinematic information is obtained through the use of a digital cross-correlation particle image velocimetry technique. With the use of DPITV, the flow within a convection cavity is mapped and studied under steady forcing and sinusoidally forced boundary conditions at the Brunt-Väisälä frequency. For the sinusoidally forced case, three cases are studied. In the first, the heating between the two walls is in phase. In the second, the heating between the two walls is 180° out of phase. In the third, the heating between the two walls is 90° out of phase. For steady forcing, the thermal plots show that the flow develops a linearly stratified profile within the center of the cell. At the sidewalls, however, owing to forcing, hot/cold thermal boundary layers develop at the left/right walls. These hot/cold thermal boundary layers then turn around the upper-left/lower-right corners and develop into intrusion layers that extend across the top and bottom walls. The vorticity and streamlines show that the bulk of the fluid motion is concentrated around the walls, whereas the fluid within the center of the cell remains stationary. For the sinusoidally forced cases, the thermal plots show the existence of many thermal “islands,” or pockets of fluid where the temperature is different with respect to its surroundings. The vorticity plots show that the center of the cell is mostly devoid of vorticity and that the vorticity is mainly confined to the sidewalls, with some vorticity at the top and bottom walls. For the 0° forcing, the streamlines show the development of two counterrotating rollers. For the 180° forcing, the streamlines show the development of only one roller. Finally, for the 90° forcing, the streamlines show the development of both a two-roller and a one-roller system, depending on the position within the forcing cycle.     

Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities

In this work we classify, with respect to the geometric equivalence relation, the global configurations of singularities, finite and infinite, of quadratic differential systems possessing exactly three distinct finite simple singularities. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddles) of different orders. Such distinctions are, however, important in the production of limit cycles close to the foci (or loops) in perturbations of the systems. The notion of geometric equivalence relation of configurations of singularities allows us to incorporate all these important geometric features which can be expressed in purely algebraic terms. The geometric classification of all configurations of singularities, finite and infinite, of quadratic systems was initiated in a work published in 2013 when the classification was done for systems with total multiplicity m _f of finite singularities less than or equal to one. That work was continued in an article which is due to appear in 2014 where the geometric classification of configurations of singularities was done for the case m _f = 2. In this article we go one step further and obtain the geometric classification of singularities, finite and infinite, for the subclass mentioned above. We obtain 147 geometrically distinct configurations of singularities for this family. We give here the global bifurcation diagram of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for this class of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants, a fact which gives us an algorithm for determining the geometric configuration of singularities for any quadratic system in this particular class.     

Structure of Pareto optima in an infinite-horizon economy where agents have recursive preferences

This article generalizes the one-agent growth theory with discounting to the case of several agents with recursive preferences. In a multi-consumption goods world, we show that, under some regularity conditions, any Pareto optimum can be viewed as a function of a trajectory of a dynamical system. The state space can be chosen to be the product of the space of capitals and the unit simplex. We define and study the properties of generalized value functions.     

Tris[2‐(morpholin‐4‐ylmethyl)phenyl‐κ2C1,N]antimony(III)

The title compound, [Sb(C₁₁H₁₄NO)₃], is monomeric with the Sb atom located on a threefold axis. The complex exhibits distorted trigonal–antiprismatic geometry around the Sb atom, owing to the presence of intramolecular N→Sb interactions. H...phenyl intermolecular interactions lead to the formation of dimers stacked along the c axis. The morpholine rings exhibit almost ideal chair conformations. No intermolecular interactions between the morpholine rings of neighbouring molecules were observed.     

Monadic <Emphasis Type=Italic>GMV</Emphasis>-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed. The first author was supported by the Council of Czech Government, MSM 6198959214.     

An equivariant Brauer semigroup and the symmetric imprimitivity theorem

Suppose that is a second countable locally compact transformation group. We let denote the set of Morita equivalence classes of separable dynamical systems where is a -algebra and is compatible with the given -action on . We prove that is a commutative semigroup with identity with respect to the binary operation for an appropriately defined balanced tensor product on -algebras. If and act freely and properly on the left and right of a space , then we prove that and are isomorphic as semigroups. If the isomorphism maps the class of to the class of , then is Morita equivalent to .