Process control represents an important tool for meeting product quality, process safety and environmental regulation. Different control strategies have been recently proposed in the literature; however, internal model control (IMC) has received great attention. Fractional calculus represents a fast growing field involving non-integer order derivatives. The aim of this work is the application of fractional calculus to develop generalized internal model control loops transfer functions, which is presented in two different approaches: firstly, the process model is considered perfect, i.e., equal to the internal model; secondly, the internal model is described by fractional transfer function. Simulation results showed that the proposed generalization could successfully control an industrial oven and a biochemical reactor described by fractional models, allowing better results when compared to integer order IMC.

High production meeting product quality, process safety and environmental regulation provide to control systems a key role in biochemical plants operation. As a suitable mathematical model is essential for process control, this work reports an alternative tool, based on the use of fractional order differential equations, for biochemical reactor identification using previously reported experimental data. Three different approaches were considered: i) solving the nonlinear set of algebraic equations obtained from the derivatives of the objective function with respect to the parameters; ii) solving a multivariable nonlinear deterministic optimization problem; iii) solving a multivariable nonlinear heuristic optimization problem. All identified models were submitted to statistical fitting tests and the second approach (ii) proved to be the most efficient for process identification, satisfying all statistical tests. Common integer order models were identified, leading to poorer data fit when compared to the fractional model, proving the usefulness and success identification tool proposed.

We investigate solutions, by using the Green function approach, for a system governed by a non-Markovian Fokker-Planck equation and subjected to a Comb structure. This structure consists of the axis of structure as the backbone and fingers which are attached perpendicular to the axis. For this system, we consider an arbitrary initial condition, in the presence of time dependent diffusion coefficients and spatial fractional derivative, and analyze the connection to the anomalous diffusion.

We argue that nonlocal effects represented by fractionary terms in the kinetic energy can be relevant to achieve a satisfactory phenomenological description of the thermal behavior of the specific heat of non-crystalline solids at very low temperature. We propose a simple model formed by the direct sum of two Hamiltonians, one of which is obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, and the other one accounts for the presence of phonons in the system. Some experimental data are used to support the proposed description.

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated l times, with the probability distribution p(l) ∝ 1/l µ. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, for a suitable choice of q, a linear behavior. We also study the chain as a random walk-like process and observe a nonusual diffusive behavior depending on the values of the parameter µ.

Com vistas em avaliar a dinâmica do cádmio no sistema solo-planta, instalou-se um experimento em colunas de PVC (0,10 m de diâmetro e 0,80 m de altura), preenchidas com amostras de Latossolo Vermelho distrófico típico com 320 g kg-1 de argila (elevou-se V % a 70) onde se aplicou biossólido (pH 6) contaminado com Cd, incorporado na camada de 0-0,2 m da coluna. Os tratamentos com biossólido contaminado com cádmio foram (mg kg-1): 0 (testemunha), 2.500 e 5.000 de Cd e dois adicionais (2.500 Cd + 2.500 Pb e 5.000 Cd + 5.000 Pb). Cultivou-se milho nas colunas por um período de 80 dias. As concentrações de Cd nas amostras de solo e na parte aérea do milho foram determinadas em extrato nitro-perclórico. A alta concentração do Cd no solo restringiu-se apenas à camada de incorporação, não havendo lixiviação do elemento na coluna do solo. A concentração de 12 mg kg-1 de Cd não foi suficiente para provocar sintomas visuais de fitotoxidez de Cd em milho. O Pb adicionado juntamente com o Cd não apresentou interferência no sistema solo-planta.

Cadmium dynamics in the soil-plant system were evaluated in an experiment with a Typic Hapludox (320 g kg-1 of clay) PVC columns (diameter 0.10 m, height 0.80 m) were filled with soil samples (V % elevated to 70), and the surface layer (0-0.2 m) supplemented with Cd-contaminated biosolid (sewage sludge, pH 6). The biosolid treatments were contaminated as follows (in mg kg-1): 0 (control) 2,500 of Cd, 5,000 of Cd, 2,500 of Cd + 2,500 of Pb, and 5,000 of Cd + 5,000 of Pb. The soil columns were cultivated with maize for a period of 80 days. The total Cd concentrations in the soil samples and maize shoots were determined using nitro-perchloric extraction solution. There was no percolation of Cd into the soil column, so the high amounts of cadmium remained in the surface layer. The concentration of 12 mg kg-1 of Cd in the maize shoots was not enough to cause visible toxicity symptoms in the plants. Pb, applied together with Cd, did not affect the soil-plant system.

The generalized Bose-Einstein distribution, within the dilute gas assumption, in the nonextensive Tsallis statistics is worked without approximation for the Bose-Einstein condensation (BEC). The results obtained are compared with the recent results presented in Int. J. Mod. Phys. B 14, 405 (2000) by L. Salasnich. Furthermore, in order to promote a complete analysis for the BEC in the nonextensive scenario we also find exact expression within the normalized constraints in a harmonic trap.