Discretization of complex-order algorithms for control applications

In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.

Emplacement of ultramafic rocks into the continental crust monitored by light and other trace elements: An example from the Geisspfad body (Swiss-Italian Alps)

In order to evaluate the influence of continental crustal rocks on trace element budgets of serpentinized peridotites incorporated into the continental crust, we have analyzed the chemical composition of whole rock samples and minerals of the Geisspfad ultramafic complex (Swiss-Italian Alps). This complex represents a relict oceanic succession composed of serpentinites, ophicarbonates and metabasic rocks, emplaced into crustal gneisses during Alpine collision. Following peak metamorphic amphibolite facies conditions, fluid flow modified some of the trace element contents of ophicarbonates and deformed serpentinites close to the contact with country rocks. The fluid originated from the surrounding continental crustal rocks as documented by the increase of Pb in the serpentinites, and by the strongly negative all) values (-112 parts per thousand) of some ultramafic rocks close to the contact with surrounding gneisses. Little or no modification of the fluid mobile elements Li, B or U was observed in the serpentinite. In-situ analysis of light elements of serpentinite minerals indicate redistribution of light elements coupled to changes of mineral modes towards the outer 100-150 m of the massif. In the centre of the massif, Li is preferentially concentrated in olivine, while Be and B are hosted by tremolite. In contrast, at the outer rim of the massif, Li and Be are preferentially incorporated into diopside, and B into antigorite. This redistribution of light elements among the different minerals is visible in the serpentinite, at a maximum distance of -100-150 m from the ophicarbonate-metabasite contact. Our results show that interaction of ultramafic rocks and crust-derived fluids can be easily detected by studies of Pb and partial derivative D in whole rocks. We argue that small ultramafic bodies potentially record an emplacement-related trace element signature, and that crustal light element values in ultramafic rocks are not necessarily derived from a subducting slab. (C) 2008 Elsevier B.V. All rights reserved.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Índices de seleção para um rebanho Caracu de duplo propósito

Neste trabalho, objetivou-se determinar índices de seleção para um rebanho da raça Caracu de duplo propósito, cujo objetivo de seleção (H) incluiu a venda de bezerros desmamados e a produção de leite. As características que compuseram H foram: produção total de leite, idade ao primeiro parto, período de serviço, peso à desmama e duração da vida produtiva. Foram propostos dois índices de seleção para H. Os critérios de seleção adotados no índice 1 foram: produção de leite na primeira lactação, primeiro período de serviço, peso à desmama (PD) e perímetro escrotal. No índice 2, foram consideradas as mesmas características, sendo, entretanto, o ganho médio diário do nascimento à desmama empregado como critério de seleção para PD. As análises estatísticas para a obtenção dos componentes de (co)variâncias e das estimativas dos parâmetros genéticos e fenotípicos foram realizadas pelo método da máxima verossimilhança restrita livre de derivada, por um modelo animal (uni e bi-característica). As informações zootécnicas e genealógicas, os preços e as quantidades dos insumos e dos produtos foram obtidos no escritório da empresa estudada. Os custos de produção e as receitas da atividade pecuária foram determinados para o período de 1994 a 2000. A equação de lucro foi tomada em base anual, usando-se valores médios para número de animais por categoria, características biológicas e preços..¹ O valor econômico para cada característica foi obtido pela derivada parcial da função de lucro em relação à característica em questão. Os dois índices econômicos de seleção trariam considerável resposta para o objetivo proposto. Entretanto, o índice 1, que incluiu PD, seria um pouco mais eficiente em termos de resposta à seleção total.

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

Static potential in QED(3) with nonminimal coupling

Here we study the effect of the nonminimal coupling j(mu)epsilon(munualpha)partial derivative(nu)A(alpha) on the static potential in multiflavor QED(3). Both cases of four and two components fermions are studied separately at leading order in the 1/N expansion. Although a nonlocal Chern-Simons term appears, in the four components case the photon is still massless leading to a confining logarithmic potential similar to the classical one. In the two components case, as expected, the parity breaking fermion mass term generates a traditional Chern-Simons term which makes the photon massive and we have a screening potential which vanishes at large intercharge distance. The extra nonminimal couplings have no important influence on the static potential at large intercharge distances. However, interesting effects show up at finite distances. In particular, for strong enough nonminimal coupling we may have a new massive pole in the photon propagator, while in the opposite limit there may be no poles at all in the irreducible case. We also found that, in general, the nonminimal couplings lead to a finite range repulsive force between charges of opposite signs.

A new spin-2 self-dual model in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Static potential in scalar QED(3) with non-minimal coupling

Here we compute the static potential in scalar QED(3) at leading order in 1/Nf. We show that the addition of a non-minimal coupling of Pauli-type (is an element of(mu nu alpha)j(mu)partial derivative(nu)A(alpha)), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic ( confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on Moller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behaviour of the potential turning it into a constant.

Cálculo fracionário aplicado em dinâmica tumoral: método da Transformada Diferencial generalizada

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.