Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Understanding the origin of photoluminescence in disordered Ca0.60Sr0.40WO4: An experimental and first-principles study

Visible photoluminescence (PL) was observed for the first time at room temperature in structurally disordered calcium strontium tungstate powder, Ca0.60Sr0.40WO4 (CSW), obtained by the polymeric precursor method. The PL behavior of CSW powders has been analyzed as a function of the disorder rate, based on experimental and theoretical studies. Quantum mechanical theory based on density functional theory at the B3LYP level has been employed to study the electronic structure of two periodic models representing both crystalline and disordered powders. Their electronic structures have been analyzed in terms of density of states, band dispersion and charge densities. The calculations indicate a break in symmetry when passing from crystalline to disordered models, creating localized electronic levels above the valence band. Moreover, a negative charge transfer process takes place from the [WO3] cluster to the [WO4] cluster. The polarization induced by the break in symmetry and the existence of localized levels favors the creation of trapped holes and electrons, originating the PL phenomenon. (c) 2007 Elsevier B.V. All rights reserved.

Photoluminescence of barium titanate and barium zirconate in multilayer disordered thin films at room temperature

The emission of wide band photoluminescence showed a synergic effect on barium zirconate and barium titanate thin films in alternate multilayer system at room temperature by 488 nm exiting wavelength. The thin films obtained by spin-coating were annealed at 350, 450, and 550 degrees C for 2 h. The X-ray patterns revealed the complete separation among the BaTiO3 and BaZrO3 phases in the adjacent films. Visible and intense photoluminescence was governed by BaZrO3 thin films in the multilayer system. Quantum mechanics calculations were used in order to simulate ordered and disordered thin films structures. The disordered models, which were built by using the displacement of formers and modifier networks, showed a different symmetry in each system, which is in accordance with experimental photoluminescence emission, thus allowing to establish a correlation among the structural and optical properties of these multilayered systems.

Photoluminescence in disordered sm-doped PbTiO3: Experimental and theoretical approach

Sm-doped PbTiO3 powder was synthesized by the polymeric precursor method, and was heat treated at different temperatures. The x-ray diffraction, photoluminescence, and UV-visible were used as a probe for the structural order degree short-, intermediate-, and long-range orders. Sm-3+ ions were used as markers of these order-disorder transformations in the PbTiO3 system. From the Rietveld refinement of the Sm-doped PbTiO3 x-ray diffraction data, structural models were obtained and analyzed by periodic ab initio quantum mechanical calculations using the CRYSTAL 98 package within the framework of density functional theory at the B3LYP level. This program can yield important information regarding the structural and electronic properties of crystalline and disordered structures. The experimental and theoretical results indicate the presence of the localized states in the band gap, due to the symmetry break, which is responsible for visible photoluminescence at room temperature in the disordered structure. (c) 2006 American Institute of Physics.

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

Photoluminescence of crystalline and disordered BTO : Mn powder: Experimental and theoretical modeling

Disordered and crystalline Mn-doped BaTiO3 (BTO:Mn) powders were synthesized by the polymeric precursor method. After heat treatment, the nature of visible photoluminescence (PL) at room temperature in amorphous BTO:Mn was discussed, considering results of experimental and theoretical studies. X-ray diffraction (XRD), PL, and UV-vis were used to characterize this material. Rietveld refinement of the BTO:Mn from XRD data was used to built two models, which represent the crystalline BTO:Mn (BTO:Mn,) and disordered BTO:Mn (BTO:Mn-d) structures. Theses models were analyzed by the periodic ab initio quantum mechanical calculations using the CRYSTAL98 package within the framework of density functional theory at the B3LYP level. The experimental and theoretical results indicated that PL is related with the degree of disorder in the BTO:Mn powders and also suggests the presence of localized states in the disordered structure. (c) 2006 Elsevier B.V. All rights reserved.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

Towards an insight on the photoluminescence of disordered CaWO4 from a joint experimental and theoretical analysis

A joint experimental and theoretical study has been carried out to rationalize for the first time the photoluminescence (PL) properties of disordered CaWO4 (CWO) thin films. From the experimental side, thin films of CWO have been synthesized following a soft chemical processing, their structure has been confirmed by X-ray diffraction data and corresponding PL properties have been measured using the 488 nm line of an argon ion laser. Although we observe PL at room temperature for the crystalline thin films, the structurally disordered samples present much more intense emission. From the theoretical side, first principles quantum mechanical calculations, based on density functional theory at B3LYP level, have been employed to study the electronic structure of a crystalline (CWO-c) and asymmetric (CWO-a) periodic model. Electronic properties are analyzed in the light of the experimental results and their relevance in relation to the PL behavior of CWO is discussed. The symmetry breaking process on going from CWO-c to CWO-a creates localized electronic levels above the valence band and a negative charge transfer process takes place from threefold, WO3, to fourfold, WO4,. tungsten coordinations. The correlation of both effects seems to be responsible for the PL of amorphous CWO. (c) 2005 Elsevier B.V. All rights reserved.

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

A cooperative game theory analysis for transmission loss allocation

This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system. (c) 2007 Elsevier B.V. All rights reserved.

Intense and broad photoluminescence at room temperature in structurally disordered Ba[Zr0.25Ti0.75]O-3 powders: An experimental/theoretical correlation

Intense and broad photoluminescence (PL) emission at room temperature was observed on structurally disordered Ba[Zr0.25Ti0.75]O-3 (BZT) powders synthesized by the polymeric precursor method. BZT powders were annealed at 573 K for different times and at 973 K for 2 h in oxygen atmosphere. The single-phase cubic perovskite structure of the powder annealed at 973 K for 2 It was identified by X-ray diffraction and Fourier transform Raman techniques. PL emission increased with the increase of annealing time, which reached its maximum value in the powder annealed at 573 K for 192 h. First principles quantum mechanical calculations based on density functional theory (B3LYP level) were employed to study the electronic structure of ordered and disordered models. The theoretical calculations and experimental measurements of Ultraviolet-visible absorption spectroscopy indicate that the presence of intermediary energy levels in the band gap is favorable for the intense and broad PL emission at room temperature in disordered BZT powders. The PL behavior is probably due the existence of a charge gradient on the disordered structure, denoted by means of a charge transfer process from [TiO5]-[ZrO6] or [TiO6]-[ZrO5] clusters to [TiO6]-[ZrO6] clusters. (C) 2008 Elsevier Ltd. All rights reserved.