Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Ontogenetic changes of swimming kinematics in a semi-aquatic reptile (Crocodylus porosus)

Semi-aquatic animals represent a transitional locomotor condition characterised by the possession of morphological features that allow locomotion both in water and on land. Most ecologically important behaviours of crocodilians occur in the water, raising the question of whether their 'terrestrial construction' constrains aquatic locomotion. Moreover, the demands for aquatic locomotion change with life-history stage. It was the aim of this research to determine the kinematic characteristics and efficiency of aquatic locomotion in different-sized crocodiles (Crocodylus porosus). Aquatic propulsion was achieved primarily by tail undulations, and the use of limbs during swimming was observed only in very small animals or at low swimming velocities in larger animals. Over the range of swimming speeds we examined, tail beat amplitude did not change with increasing velocity, but amplitude increased significantly with body length. However, amplitude expressed relative to body length decreased with increasing body length. Tail beat frequency increased with swimming velocity but there were no differences in frequency between different-sized animals. Mechanical power generated during swimming and thrust increased non-linearly with swimming velocity, but disproportionally so that kinematic efficiency decreased with increasing swimming velocity. The importance of unsteady forces, expressed as the reduced frequency, increased with increasing swimming velocity. Amplitude is the main determinant of body-size-related increases in swimming velocity but, compared with aquatic mammals and fish, crocodiles are slow swimmers probably because of constraints imposed by muscle performance and unsteady forces opposing forward movement. Nonetheless, the kinematic efficiency of aquatic locomotion in crocodiles is comparable to that of fully aquatic mammals, and it is considerably greater than that of semi-aquatic mammals.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Mechanical Behavior of the Lamellar Structure in Semi-Crystalline Polymers

We have employed molecular dynamics simulations to study the behavior of virtual polymeric materials under an applied uniaxial tensile load. Through computer simulations, one can obtain experimentally inaccessible information about phenomena taking place at the molecular and microscopic levels. Not only can the global material response be monitored and characterized along time, but the response of macromolecular chains can be followed independently if desired. The computer-generated materials were created by emulating the step-wise polymerization, resulting in self-avoiding chains in 3D with controlled degree of orientation along a certain axis. These materials represent a simplified model of the lamellar structure of semi-crystalline polymers,being comprised of an amorphous region surrounded by two crystalline lamellar regions. For the simulations, a series of materials were created, varying i) the lamella thickness, ii) the amorphous region thickness, iii) the preferential chain orientation, and iv) the degree of packing of the amorphous region. Simulation results indicate that the lamella thickness has the strongest influence on the mechanical properties of the lamella-amorphous structure, which is in agreement with experimental data. The other morphological parameters also affect the mechanical response, but to a smaller degree. This research follows previous simulation work on the crack formation and propagation phenomena, deformation mechanisms at the nanoscale, and the influence of the loading conditions on the material response. Computer simulations can improve the fundamental understanding about the phenomena responsible for the behavior of polymeric materials, and will eventually lead to the design of knowledge-based materials with improved properties.

Angular and linear accelerations of a rolling cylinder acted by an external force

The dynamics of a cylinder rolling on a horizontal plane acted on by an external force applied at an arbitrary angle is studied with emphasis on the directions of the acceleration of the centre-of-mass and the angular acceleration of the body. If rolling occurs without slipping, there is a relationship between the directions of these accelerations. If the linear acceleration points to the right, then the angular acceleration is clockwise. On the other hand, if it points to the left, then the angular acceleration is counterclockwise. In contrast, if rolling and slipping occurs, the direction of the linear acceleration does not determine the direction of the angular acceleration. For example, the linear acceleration may point to the right and the angular acceleration clockwise or counterclockwise depending on the external force orientation and point of application.

Species composition of arbuscular mycorrhizal fungi differ in semi-natural and intensively managed pastures in an isolated oceanic island (Terceira, Azores)

Copyright © Springer Science+Business Media Dordrecht 2014.

Assessment of data-driven modeling strategies for water delivery canals

The aim of this paper is to develop models for experimental open-channel water delivery systems and assess the use of three data-driven modeling tools toward that end. Water delivery canals are nonlinear dynamical systems and thus should be modeled to meet given operational requirements while capturing all relevant dynamics, including transport delays. Typically, the derivation of first principle models for open-channel systems is based on the use of Saint-Venant equations for shallow water, which is a time-consuming task and demands for specific expertise. The present paper proposes and assesses the use of three data-driven modeling tools: artificial neural networks, composite local linear models and fuzzy systems. The canal from Hydraulics and Canal Control Nucleus (A parts per thousand vora University, Portugal) will be used as a benchmark: The models are identified using data collected from the experimental facility, and then their performances are assessed based on suitable validation criterion. The performance of all models is compared among each other and against the experimental data to show the effectiveness of such tools to capture all significant dynamics within the canal system and, therefore, provide accurate nonlinear models that can be used for simulation or control. The models are available upon request to the authors.

Use of solvent extraction to remediate soils contaminated with hydrocarbons

The main objective of this research is to exploit the possibility of using an ex situ solvent extraction technique for the remediation of soils contaminated with semi-volatile petroleum hydrocarbons. The composition of the organic phase was chosen in order to form a single phase mixture with an aqueous phase and simultaneously not being disturbed (forming stable emulsions) by the soil particles hauling the contaminants. It should also permit a regeneration of the organic solvent phase. As first, we studied the miscibility domain of the chosen ternary systems constituted by ethyl acetate–acetone–water. This system proved to satisfy the previous requirements allowing for the formation of a single liquid phase mixture within a large spectrum of compositions, and also allowing for an intimate contact with the soil. Contaminants in the diesel range within different functional groups were selected: xylene, naphthalene and hexadecane. The analytical control was done by gas chromatography with FID detector. The kinetics of the extractions proved to be fast, leading to equilibrium after 10 min. The effect of the solid–liquid ratio on the extraction efficiency was studied. Lower S/L ratios (1:8, w/v) proved to be more efficient, reaching recoveries in the order of 95%. The option of extraction in multiple contacts did not improve the recovery in relation to a single contact. The solvent can be regenerated by distillation with a loss around 10%. The contaminants are not evaporated and they remain in the non-volatile phase. The global results show that the ex situ solvent extraction is technically a feasible option for the remediation of semi-volatile aromatic, polyaromatic and linear hydrocarbons.

Introduction to fractional linear systems. Part 1 : continuous-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.