Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.     

Conduction of heat in a semi-infinite solid with an exponential-type initial temperature profile: temperature and heat flux solutions due to an instantaneous laser source

A closed-form model for the computation of temperature and heat-flux distribution in a semi-infinite solid with an exponentially-decaying, initial-temperature profile is investigated. The solutions are presented for the case of an instantaneous laser source which is absorbed partially in the surface layers followed by an exponential decay with position in the material itself. The appropriate dimensionless parameters are identified and the reduced temperature and heat flux solutions are presented in the graphic form as a function of these parameters. Some limiting cases of practical interest are also discussed. It is demonstrated that the present analysis covers the classical case of no heat generation in the solid as well as some new solutions.     

On vector variational-like inequalities and vector optimization problems with (<Emphasis Type="Italic">G</Emphasis>, <Emphasis Type="Italic">α</Emphasis>)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.     

Characterizations of the Suzuki tower near polygons

In recent work, we constructed a new near octagon \(\mathcal {G}\) from certain involutions of the finite simple group \(G_2(4)\) and showed a correspondence between the Suzuki tower of finite simple groups, \(L_3(2)< U_3(3)< J_2< G_2(4) < Suz\), and the tower of near polygons, \(\mathrm {H}(2,1) \subset \mathrm {H}(2)^D \subset \mathsf {HJ} \subset \mathcal {G}\). Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall–Janko near octagon \(\mathsf {HJ}\) is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, \(\mathrm {H}(2)^D\). We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for \(\mathrm {H}(2)^D\).     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

Scalar variational analysis of single mode,graded-core,W-type fibres

A scalar variational analysis for the fundamental mode of a graded-core, W-type fibre based on single and two parameter trial fields has been presented. Comparison with the exact numerical results shows that the two parameter trial field estimates the propagation characteristics accurately.On study leave from Physics Department, G.M. College, Sambalpur-768004, India.     

Stationary lower probabilities and unstable averages

Summary This paper explores the possibilities for probability-like models of stationary nondeterministic phenomena that possess divergent but bounded time averages. A random sequence described by a stationary probability measure must have almost surely convergent time averages whenever it has almost surely bounded time averages. Hence, no measure can provide the mathematical model we desire. In turning to lower probability based models we first explore the relationships between divergence, stationarity, and monotone continuity and those between monotone continuity and unicity of extensions. We then construct several examples of stationary lower probabilities for sequences of uniformly bounded random variables such that divergence of time averages occurs with lower probability one. We conclude with some remarks on the problem of estimating lower probability models on the basis of cylinder set observations.     

The hyperfine interaction of gadolinium and holmium in cubic Ho: (Gd,Ce)Fe2 compounds

The low-temperature hyperfine parameters of the ferrimagnetic C15 intermetallic system Ho_0.03Ce_xGd_0.97-xFe₂ have been measured at Gd using the 87 keV γ-ray of ¹⁵⁵Gd and at Ho using spin echo nmr of ¹⁶⁵Ho. A linear decrease of the hyperfine field B_t with increasing x is observed, the slope being almost the same for both nuclei. The observed slope (dB_t/dx ? -37T) is nearly three times greater than that found for ¹⁵⁵Gd in the analogous H₀:(Y, Gd)Fe₂ system; this is attributed to the influence of the increased conduction electron density when trivalent lanthanide ions are replaced by Ce⁴⁺.