Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Conservation laws for invariant functionals containing compositions

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 200

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Investigating the effects of channel aspect ratio on fluid flow and heat transfer in absorber plates with minichannels

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.This study experimentally investigates the fluid flow and heat transfer in two solar thermal absorber plates for compact (thin and light-weight) solar thermal collectors. Two metal plates with 270 mm long, 0. 5 mm deep mini-channels having aspect ratios of 1 and 4 were studied. Constant heat flux, forced convection experiments were performed using Tyfocor® LS (a propylene glycol-based heat transfer fluid for thermal solar systems) at various flow rates and temperatures. Reynolds numbers were in the range 5-200. Measured Nusselt numbers were much lower than classical theory and were observed to be directly proportional to the product of the Reynolds number and Prandtl number (RePr). The plate with rectangular channels produced slightly higher Nusselt numbers and much lower pressure drops, making them a preferred option for this application

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Is catchment geodiversity a useful surrogate of aquatic plant species richness?

Aim Conserving freshwater biodiversity in a rapidly changing world requires updated planning schemes and research efforts. Geodiversity – the diversity of Earth surface forms, materials and processes – and biodiversity are interlinked at a fundamental level. This relationship is being considered in a growing number of studies, yet research from freshwater environments is scarce. We used geodiversity (rock-type, soil-type and geomorphological richness), local and climatic variables to explore whether geodiversity can be used as a surrogate for aquatic plant species richness in lakes and rivers. Location Finland. Taxon Aquatic plants. Methods We compared geodiversity variables (measured within 1-km2 grid cells) to well-studied local (e.g. area, alkalinity) and climate (e.g. growing degree-days) variables, and examined the patterns between habitat types (lakes and rivers) and among all taxa and major functional groups (helophytes and hydrophytes). We modelled lake (n = 145) and river (n = 146) plant species richness with generalized linear models, and further partitioned variation to measure the independent and shared contributions of the geodiversity, climate and local environmental variable groups. As a complementary analysis, and to identify single important variables explaining variation in aquatic plant species richness, we utilized boosted regression trees. Results We found a positive relationship between aquatic plant species richness and catchment geodiversity variation with recurring patterns across two different freshwater habitat types and two aquatic plant functional groups. Higher variation in geodiversity (measured at landscape scale) supported higher freshwater biodiversity (measured at the local scale) of lakes and rivers. Main conclusions Geodiversity can be a useful addition to biodiversity modelling, and it should be considered in conservation schemes and monitoring efforts, further supporting the principle of conserving nature's stage. Yet, differences between habitats and functional groups suggest that more habitat-specific approaches and multiple biodiversity measures should be considered. Our study is an important signpost guiding further studies on the biodiversity–geodiversity relationship in freshwater ecosystems

Congenital myopathies: characteristic and subtypes in Hong Kong

This journal suppl. entitled: 20th International Congress of The World Muscle SocietyCongenital myopathies are a group of childhood onset neuromuscular disorder with the diagnosis mainly based on genetic and pathological features. This is a unique group with phenotypic, genotypic and pathological heterogeneity, so the confirmation of an underlying diagnosis is often challenging. This is the first congenital myopathy case series in Hong Kong. A total of 15 patients have been diagnosed to have congenital myopathies with 11 patients had the genetic mutations being identified (4 patients had RYR1 mutations, 3 patients had ACTA1 mutations, 2 patients had KLHL40 mutations, 1 patient had MTM1 mutation and 1 patient had DNM2 mutation).postprin

INFLUENCE OF LINEAR ALKYLBENZENE SULFONATE (LAS) AS ORGANIC COSOLVENT ON LEACHING BEHAVIOR OF PCDD/FS FROM FLY-ASH AND SOIL

The leaching of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) was measured in soil and standard fly ash column eluted with pure water and linear alkylbenzene sulfonate (LAS)- water. The data obtained were used to evaluate the leachability of PCDD/Fs from waste dump like incineration residual slag and fly ash deposition. The leaching rate was shown to be increased significantly by using LAS water. The leachate contents of PCDD/Fs were above their known water solubility. Concentration of PCDD/Fs in the leachates as well as the relative leaching (calculated on the fly ash content) increased with increasing chlorinating degree and decreasing water solubility. LAS above the critical micelle concentration (CMC) probably enhances PCDD/Fs solubility