Optimization of Li-ion solid electrolytes

The synthesis and optimization of two Li-ion solid electrolytes were studied in this work. Different combinations of precursors were used to prepare La0.5Li0.5TiO3 via mechanosynthesis. Despite the ability to form a perovskite phase by the mechanochemical reaction it was not possible to obtain a pure La0.5Li0.5TiO3 phase by this process. Of all the seven combinations of precursors and conditions tested, the one where La2O3, Li2CO3 and TiO2 were milled for 480min (LaOLiCO-480) showed the best results, with trace impurity phases still being observed. The main impurity phase was that of La2O3 after mechanosynthesis (22.84%) and Li2TiO3 after calcination (4.20%). Two different sol-gel methods were used to substitute boron on the Zr-site of Li1+xZr2-xBx(PO4)3 or the P-site of Li1+6xZr2(P1-xBxO4)3, with the doping being achieved on the Zr-site using a method adapted from Alamo et al (1989). The results show that the Zr-site is the preferential mechanism for B doping of LiZr2(PO4)3 and not the P-site. Rietveld refinement of the unit-cell parameters was performed and it was verified by consideration of Vegard’s law that it is possible to obtain phase purity up to x = 0.05. This corresponds with the phases present in the XRD data, that showed the additional presence of the low temperature (monoclinic) phase for the powder sintered at 1200ºC for 12h of compositions with x ≥ 0.075. The compositions inside the solid solution undergo the phase transition from triclinic (PDF#01-074-2562) to rhombohedral (PDF#01-070-6734) when heating from 25 to 100ºC, as reported in the literature for the base composition. Despite several efforts, it was not possible to obtain dense pellets and with physical integrity after sintering, requiring further work in order to obtain dense pellets for the electrochemical characterisation of Li Zr2(PO4)3 and Li1.05Zr1.95B0.05(PO4)3.

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

Electrolytes for ceramic oxide fuel cells

The main objective of this dissertation is the development and processing of novel ionic conducting ceramic materials for use as electrolytes in proton or oxide-ion conducting solid oxide fuel cells. The research aims to develop new processing routes and/or materials offering superior electrochemical behavior, based on nanometric ceramic oxide powders prepared by mechanochemical processes. Protonic ceramic fuel cells (PCFCs) require electrolyte materials with high proton conductivity at intermediate temperatures, 500-700ºC, such as reported for perovskite zirconate oxides containing alkaline earth metal cations. In the current work, BaZrO3 containing 15 mol% of Y (BZY) was chosen as the base material for further study. Despite offering high bulk proton conductivity the widespread application of this material is limited by its poor sinterability and grain growth. Thus, minor additions of oxides of zinc, phosphorous and boron were studied as possible sintering additives. The introduction of ZnO can produce substantially enhanced densification, compared to the un-doped material, lowering the sintering temperature from 1600ºC to 1300ºC. Thus, the current work discusses the best solid solution mechanism to accommodate this sintering additive. Maximum proton conductivity was shown to be obtained in materials where the Zn additive is intentionally adopted into the base perovskite composition. P2O5 additions were shown to be less effective as a sintering additive. The presence of P2O5 was shown to impair grain growth, despite improving densification of BZY for intermediate concentrations in the range 4 – 8 mol%. Interreaction of BZY with P was also shown to have a highly detrimental effect on its electrical transport properties, decreasing both bulk and grain boundary conductivities. The densification behavior of H3BO3 added BaZrO3 (BZO) shows boron to be a very effective sintering aid. Nonetheless, in the yttrium containing analogue, BaZr0.85Y0.15O3- (BZY) the densification behavior with boron additives was shown to be less successful, yielding impaired levels of densification compared to the plain BZY. This phenomenon was shown to be related to the undesirable formation of barium borate compositions of high melting temperatures. In the last section of the work, the emerging oxide-ion conducting materials, (Ba,Sr)GeO3 doped with K, were studied. Work assessed if these materials could be formed by mechanochemical process and the role of the ionic radius of the alkaline earth metal cation on the crystallographic structure, compositional homogeneity and ionic transport. An abrupt jump in oxide-ion conductivity was shown on increasing operation temperature in both the Sr and Ba analogues.

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Impact of Routine Fractional Flow Reserve Evaluation During Coronary Angiography on Management Strategy and Clinical Outcome: One-Year Results of the POST-IT.

Penetration of fractional flow reserve (FFR) in clinical practice varies extensively, and the applicability of results from randomized trials is understudied. We describe the extent to which the information gained from routine FFR affects patient management strategy and clinical outcome. METHODS AND RESULTS: Nonselected patients undergoing coronary angiography, in which at least 1 lesion was interrogated by FFR, were prospectively enrolled in a multicenter registry. FFR-driven change in management strategy (medical therapy, revascularization, or additional stress imaging) was assessed per-lesion and per-patient, and the agreement between final and initial strategies was recorded. Cardiovascular death, myocardial infarction, or unplanned revascularization (MACE) at 1 year was recorded. A total of 1293 lesions were evaluated in 918 patients (mean FFR, 0.81±0.1). Management plan changed in 406 patients (44.2%) and 584 lesions (45.2%). One-year MACE was 6.9%; patients in whom all lesions were deferred had a lower MACE rate (5.3%) than those with at least 1 lesion revascularized (7.3%) or left untreated despite FFR≤0.80 (13.6%; log-rank P=0.014). At the lesion level, deferral of those with an FFR≤0.80 was associated with a 3.1-fold increase in the hazard of cardiovascular death/myocardial infarction/target lesion revascularization (P=0.012). Independent predictors of target lesion revascularization in the deferred lesions were proximal location of the lesion, B2/C type and FFR. CONCLUSIONS: Routine FFR assessment of coronary lesions safely changes management strategy in almost half of the cases. Also, it accurately identifies patients and lesions with a low likelihood of events, in which revascularization can be safely deferred, as opposed to those at high risk when ischemic lesions are left untreated, thus confirming results from randomized trials.

Fractional variational problems depending on indefinite integrals and with delay

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Effects of synthetic conditions on the structural, stability and ion conducting properties of Li0.30(La0.50Ln0.50)0.567TiO3 (Ln= La, Pr, Nd) solid electrolytes for rechargeable lithium batteries

The structure, thermal stability, morphology and ion conductivity of titanium perovskites with the general formula Li3xLn2/3−xTiO3 (Ln = rare earth element; 3x= 0.30) are studied in the context of their possible use as solid electrolyte materials for lithium ion batteries. Materials are prepared by a glycine-nitrate method using different sintering treatments, with a cation-disorder-induced structural transition from tetragonal to cubic symmetry, detected as quenching temperature increases. SEM images show that the average grain size increases with increasing sintering temperature and time. Slightly higher bulk conductivity values have been observed for quenched samples sintered at high temperature. Bulk conductivity decreases with the lanthanide ion size. A slight conductivity enhancement, always limited by grain boundaries, is observed for longer sintering times. TDX measurements of the electrolyte/cathode mixtures also show a good stability of the electrolytes in the temperature range of 30-1100ºC.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Modeling some real phenomena by fractional differential equations

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

Finite time extinction for nonlinear fractional evolution equations and related properties

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Finite time extinction for nonlinear fractional evolution equations and related properties.

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Part-time and fractional staff in the learning and skills sector

This Universities and College Union Launch Event presentation reported on the findings of Learning and Skills Research Network (LSRN) London and South East (LSE) Regional Research Project. The presentation reflected on research carried out during 2002-06 on the development and deployment of part-time staff in the Learning and Skills Sector. Although the lifelong learning sector is the largest UK education sector, little attention has as yet been paid to the role of LSC sector part-time staff. Worrying trends of an increasing casualisation of staffing have been reported. The role of part-timers as highly committed (philanthropic) but generally underpaid and exploited staff (ragged-trousered) emerged from the data collected by this investigation, which examined the role of part-timers in several colleges and adult education institutions in London and the South East. The metaphor of the 'ragged-trousered philanthropist' was consciously selected to investigate the interactivity between philantrophy, employment practices for PT staff, and education as social action, in addressing the need for good practice to achieve quality outcomes in learning and teaching. The results are to some extent transferable to other education and training sectors employing part-time staff, e.g. higher education institutions and work-based training organisations.