Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

Control and dynamics of fractional order systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Control and Dynamics of Fractional Order Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

Dinámica Cuántica de Sistemas Complejos: Fundamentos y Aplicaciones. Quantum Dynamics in Complex Systems: Fundamentals and Aplications.

El procedimiento de revertir la dinámica colectiva (diablillo de Loschmidt apresurado) mediante un pulso de radio frecuencia, permite generar un Eco de Loschmidt, es decir la refocalización de una excitación localizada. Alternativamente, en acústica es posible implementar un Espejo de Reversión Temporal, que consiste en la progresiva inyección de una débil excitación ultrasónica en la periferia de un sistema, para construir una excitación que se propaga "hacia atrás". Así, podemos afirmar que es posible revertir y controlar la dinámica. Sin embargo, aún no se posee una comprensión detallada de los mecanismos que gobiernan estos procedimientos. Este proyecto busca responder las preguntas que posibilitan esta comprensión.

Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Nitrogen dynamics in soil management systems. I - flux of inorganic nitrogen (NH4+ and NO3-)

In agricultural systems the N-NH4+ and N-NO3- contents is significantly affected by soil management. This study investigated the dynamics of inorganic nitrogen (N; NH4+ and NO3-) in an experimental evaluation of soil management systems (SMSs) adopted in 1988 at the experimental station of the ABC Foundation in Ponta Grossa, in the Central South region of the State of Paraná. The objective of this study was to evaluate the changes in N-NH4+ and N-NO3- flux in the surface layer of a Red Latosol arising from SMSs over a 12-month period. The experiment was arranged in a completely randomized block design in split plots, in three replications. The plots consisted of the following SMSs: 1) conventional tillage (CT); 2) minimum tillage (MT); 3) no-tillage with chisel plow every three years (NT CH); and 4) continuous no-tillage (CNT). To evaluate the dynamics of inorganic N, the subplots represented samplings (11 sampling times, T1 - T11). The ammonium N (N-NH4+) and nitric N (N-NO3-) contents were higher in systems with reduced tillage (MT and NT CH) and without tillage (CNT) than in the CT system. In the period from October 2003 to February 2004, the N-NH4+ was higher than the N-NO3- soil content. Conversely, in the period from May 2004 to July 2004, the N-NO3- was higher than the N-NH4+ content. The greatest fluctuation in the N-NH4+ and N-NO3- contents occurred in the 0-2.5 cm layer, and the highest peak in the N-NH4+ and N-NO3- concentrations occurred after the surface application of N. Both N-NH4+ and N-NO3- were strongly correlated with the soil organic C content, which indicated that these properties vary together in the system.

Nitrogen dynamics in soil management systems: II - mineralization and nitrification rates

Nitrogen is the main limiting factor in crop productivity and thereby soil management systems may change the mineralization and nitrification rates. In an experiment on soil management systems implemented in 1988 at the experimental station Fundação ABC, Ponta Grossa, in the central South region of the State of Paraná, inorganic N dynamics were examined to find a soil management strategy with a view to a sustainable environment. The objective of this study was to calculate the net mineralization and nitrification rates of soil N and the correlation with soil pH under management systems. Randomized complete block design was used, in split plots, in three replications. The following soil management systems (SMSs) were adopted in the plots: 1) conventional tillage (CT); 2) minimum tillage (MT); 3) no-tillage with chisel plow every three years (NT CH); and 4) continuous no-tillage (CNT). To evaluate the dynamics of inorganic N, samples were collected from sub-plots at different times (11 sampling times - T1 to T11). In the CNT and NT CH, the net mineralization rates were higher in the MT and CT systems in the 0-2.5 cm soil layer, while the nitrification rate was higher in the 2.5-5 cm layer. Soon after implementing the white oat management, the mineralization and nitrification rates in all soil layers were higher in the MT and CT systems. In the period of soybean development, in the 0-2.5 and 2.5-5 cm soil layers, the mineralization and nitrification rates were higher in the CNT and NT CH than in the MT and CT systems.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

Effect of management systems and cover crops on organic matter dynamics of soil under vegetables

Vegetable production in conservation tillage has increased in Brazil, with positive effects on the soil quality. Since management systems alter the quantity and quality of organic matter, this study evaluated the influence of different management systems and cover crops on the organic matter dynamics of a dystrophic Red Latosol under vegetables. The treatments consisted of the combination of three soil tillage systems: no-tillage (NT), reduced tillage (RT) and conventional tillage (CT) and of two cover crops: maize monoculture and maize-mucuna intercrop. Vegetables were grown in the winter and the cover crops in the summer for straw production. The experiment was arranged in a randomized block design with four replications. Soil samples were collected between the crop rows in three layers (0.0-0.05, 0.05-0.10, and 0.10-0.30 m) twice: in October, before planting cover crops for straw, and in July, during vegetable cultivation. The total organic carbon (TOC), microbial biomass carbon (MBC), oxidizable fractions, and the carbon fractions fulvic acid (C FA), humic acid (C HA) and humin (C HUM) were determined. The main changes in these properties occurred in the upper layers (0.0-0.05 and 0.05-0.10 m) where, in general, TOC levels were highest in NT with maize straw. The MBC levels were lowest in CT systems, indicating sensitivity to soil disturbance. Under mucuna, the levels of C HA were lower in RT than NT systems, while the C FA levels were lower in RT than CT. For vegetable production, the C HUM values were lowest in the 0.05-0.10 m layer under CT. With regard to the oxidizable fractions, the tillage systems differed only in the most labile C fractions, with higher levels in NT than CT in the 0.0-0.05 m layer in both summer and winter, with no differences between these systems in the other layers. The cabbage yield was not influenced by the soil management system, but benefited from the mulch production of the preceding maize-mucuna intercrop as cover plant.