Automated approach for optimizing dynamic systems

The optimal design of nonlinear dynamic systems can be formulated as a multicriteria optimization problem. On the basis of a multibody system model integral type objective functions are defined evaluating the dynamic behavior of the system under consideration. Multicriteria optimization methods reduce the problem to nonlinear programming problems which can be solved with standard algorithms like the SQP method. The gradients required for such an efficient optimization procedure are computed by solving, additional differential equations resulting from an adjoint variable approach. The whole design process can be highly automated by using computer algebra packages

Convergence of asymptotic systems of non-autonomous neural network models with infinite distributed delays

In this paper we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.The paper was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the Project PEstOE/MAT/UI0013/2014. The author thanks the referee for valuable comments.info:eu-repo/semantics/publishedVersio

Diurnal changes in seawater carbonate chemistry speciation at increasing atmospheric carbon dioxide

Natural variability in seawater pH and associated carbonate chemistry parameters is in part driven by biological activities such as photosynthesis and respiration. The amplitude of these variations is expected to increase with increasing seawater carbon dioxide (CO2) concentrations in the future, because of simultaneously decreasing buffer capacity. Here, we address this experimentally during a diurnal cycle in a mesocosm CO2 perturbation study. We show that for about the same amount of dissolved inorganic carbon (DIC) utilized in net community production diel variability in proton (H+) and CO2 concentrations was almost three times higher at CO2 levels of about 675 ± 65 in comparison with levels of 310 ± 30 μatm. With a simple model, adequately simulating our measurements, we visualize carbonate chemistry variability expected for different oceanic regions with relatively low or high net community production. Since enhanced diurnal variability in CO2 and proton concentration may require stronger cellular regulation in phytoplankton to maintain respective gradients, the ability to adjust may differ between communities adapted to low in comparison with high natural variability

Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly distributed source strength

The solution of the mixed boundary value problem of potential theory involves the computation of the potential field generated by monolayer and double layer source distributions on surfaces at which boundary conditions are known. Closed-form analytical expressions have been described in the literature for the potential field generated by double layers having a linearly distributed strength over triangular source elements. This contribution presents the corresponding expression for the linearly distributed monolayer strength. The solution is shown to be valid for all observation points in space, including those on the interior, edges and vertices of the source triangle

Kinematics and dynamics for computer animation

This tutorial will focus on the physical principles of kinematics and dynamics. After explaining the basic equations for point masses and rigid bodies a new approach for the dynamic simulation of multi-linked models with wobbling mass is presented, which has led to new insight in the field of biomechanics, but which has not been used in computer animation so far

Modelling the Influence of Foot-and-Mouth Disease Vaccine Antigen Stability and Dose on the Bovine Immune Response

Foot and mouth disease virus causes a livestock disease of significant global socio-economic importance. Advances in its control and eradication depend critically on improvements in vaccine efficacy, which can be best achieved by better understanding the complex within-host immunodynamic response to inoculation. We present a detailed and empirically parametrised dynamical mathematical model of the hypothesised immune response in cattle, and explore its behaviour with reference to a variety of experimental observations relating to foot and mouth immunology. The model system is able to qualitatively account for the observed responses during in-vivo experiments, and we use it to gain insight into the incompletely understood effect of single and repeat inoculations of differing dosage using vaccine formulations of different structural stability

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model