Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t > 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy

Spin and orbital ordering in double-layered manganites

We study theoretically the phase diagram of the double-layered perovskite manganites taking into account the orbital degeneracy, the strong Coulombic repulsion, and the coupling with the lattice deformation. Observed spin structural changes as the increased doping are explained in terms of the orbital ordering and the bond-length dependence of the hopping integral along $c$-axis. Temperature dependence of the neutron diffraction peak corresponding to the canting structure is also explained. Comparison with the 3D cubic system is made.Comment: 7 figure

Characterisation of serum IgG(T) responses to potential diagnostic antigens for equine cyathostominosis

Cyathostomins are ubiquitous parasitic nematodes of horses. These worms spend substantial periods as intestinal wall stage encysted larvae, which can comprise up to 90% of the total burden. Several million larvae have been reported in individuals. Emergence of these larvae from the gut wall can lead to life-threatening colitis. Faecal egg count tests, increasingly used by horse owners to inform anthelmintic treatments, do not correlate with the intra-host burden of cyathostomins; this represents a key gap in the diagnostic toolbox. Previously, a cyathostomin Gut Associated Larval Antigen was identified as a promising marker for the intra-host stages of infection. Here, cyathostomin Gut Associated Larval Antigen and an additional protein, Cyathostomin Immuno-diagnostic antigen, were investigated to examine their value in providing information on cyathostomin burden. ELISA analyses examined serum IgG(T) responses to recombinant proteins derived from individual cyathostomin species. Receiver Operator Characteristic curve analysis was performed on the ELISA data; proteins with the highest Area Under the Curve values were selected to test protein combinations to investigate which were the most informative in identifying the infection status of individuals. Three cocktail combinations were tested, comprising: (a) Cy-GALA proteins from two species and a Cy-CID protein from a third species (CT3), (b) Cy-GALA proteins from five species (CT5), and (c) all CT5 components, plus a Cy-CID protein from an additional species (CT6). The best predictive values for infection were obtained using CT3 and CT6, with similar values achieved for both. Proteins in CT3 are derived from the most commonly reported species, Cyathostomum catinatum, Cylicocyclus nassatus and Cylicostephanus longibursatus. This combination was selected for future development since it represents a more commercially viable format for a diagnostic test

Small-polaron hopping conductivity in bilayer manganite La1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7}

We report anisotropic resistivity measurements on a La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ single crystal over a temperature $T$ range from 2 to 400 K and in magnetic fields $H$ up to 14 T. For $T\geq 218$ K, the temperature dependence of the zero-field in-plane $\rho_{ab}(T)$ resistivity obeys the adiabatic small polaron hopping mechanism, while the out-of-plane $\rho_{c}(T)$ resistivity can be ascribed by an Arrhenius law with the same activation energy. Considering the magnetic character of the polarons and the close correlation between the resistivity and magnetization, we developed a model which allows the determination of $\rho_{ab,c}(H,T)$. The excellent agreement of the calculations with the measurements indicates that small polarons play an essential role in the electrical transport properties in the paramagnetic phase of bilayer manganites.Comment: 4 pages, 3 figures, to appear in Physical Review

Low-temperature electrical transport in bilayer manganite La1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7}

The temperature $T$ and magnetic field $H$ dependence of anisotropic in-plane $\rho_{ab}$ and out-of-plane $\rho_{c}$ resistivities have been investigated in single crystals of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$. Below the Curie transition temperature $T_c=$ 125 K, $\rho_{ab}$ and $\rho_{c}$ display almost the same temperature dependence with an up-turn around 50 K. In the metallic regime (50 K $\leq T \leq$ 110 K), both $\rho_{ab}(T)$ and $\rho_{c}(T)$ follow a $T^{9/2}$ dependence, consistent with the two-magnon scattering. We found that the value of the proportionality coefficient $B_{ab}^{fit}$ and the ratio of the exchange interaction $J_{ab}/J_c$ obtained by fitting the data are in excellent agreement with the calculated $B_{ab}$ based on the two-magnon model and $J_{ab}/J_c$ deduced from neutron scattering, respectively. This provides further support for this scattering mechanism. At even lower $T$, in the non-metallic regime ($T<$ 50 K), {\it both} the in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ conductivities obey a $T^{1/2}$ dependence, consistent with weak localization effects. Hence, this demonstrates the three-dimensional metallic nature of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ at $T<T_c$.Comment: 7 pages and 5 figures, accepted for publication in Phys. Rev.

Work function changes in the double layered manganite La1.2Sr1.8Mn2O7

We have investigated the behaviour of the work function of La1.2Sr1.8Mn2O7 as a function of temperature by means of photoemission. We found a decrease of 55 +/- 10 meV in going from 60 K to just above the Curie temperature (125 K) of the sample. Above T_C the work function appears to be roughly constant. Our results are exactly opposite to the work function changes calculated from the double-exchange model by Furukawa, but are consistent with other measurements. The disagreement with double-exchange can be explained using a general thermodynamic relation valid for second order transitions and including the extra processes involved in the manganites besides double-exchange interaction.Comment: 6 pages, 4 figures included in tex

Measurement of Pion Enhancement at Low Transverse Momentum and of the Delta-Resonance Abundance in Si-Nucleus Collisions at AGS Energy

We present measurements of the pion transverse momentum (p_t) spectra in central Si-nucleus collisions in the rapidity range 2.0<y<5.0 for p_t down to and including p_t=0. The data exhibit an enhanced pion yield at low p_t compared to what is expected for a purely thermal spectral shape. This enhancement is used to determine the Delta-resonance abundance at freeze-out. The results are consistent with a direct measurement of the Delta-resonance yield by reconstruction of proton-pion pairs and imply a temperature of the system at freeze-out close to 140 MeV.Comment: 12 pages + 4 figures (uuencoded at end-of-file