Some generalizations of the Caginalp phase-field system

Our aim in this article is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi. In particular, we obtain well-posedness results and study the asymptotic and spatial behaviours of the solutions.     

The high frequency behaviour of continuous wavelet transforms

The high frequency behaviour of continuous wavelet transforms is characterized by the number of vanishing moments of the corresponding basic wavelets. As a consequence we give satisfying answers to the following questions of theoretical as well as practical interest:

What are the differences or similarities between transforms to different wavelets?

Why do wavelet transforms react so sensitively to abrupt signal changes ?     

Shape memory behaviour of annealed Ti48.5Ni(51.5− x )Cu x (x = 6.2–33.5) thin films

The shape memory behaviour of (Ni,Cu)-rich Ti–Ni–Cu thin films (Ti_48.9Ni_44.9Cu_6.2, Ti_48.5Ni₄₀Cu_11.5, Ti_48.6Ni_35.9Cu_15.5, Ti_48.3Ni_28.4Cu_23.3, Ti_48.3Ni_23.9Cu_27.8 and Ti_48.5Ni₁₈Cu_33.5) annealed at 773, 873 and 973 K for 1 h was investigated. The films with 6.2, 11.5–15.5 and 23.3–33.5 at% Cu showed a single-stage deformation due to a B2 ? B19′ transformation, a two-stage deformation due to the B2 ? B19 ? B19′ transformation and a single-stage deformation due to the B2 ? B19′ transformation, respectively. The martensitic transformation start temperature (M _s) increased with increasing Cu content and then levelled off for more than 15 at% Cu, indicating a high Ms temperature of 345 K. Temperature hystereses were almost 15 K for all films with more than 10 at% Cu. The critical stress for slip increased with increasing Cu content and increased significantly for the Ti_48.5Ni₁₈Cu_33.5 film, whereas the maximum recoverable strain significantly decreased for the Ti_48.5Ni₁₈Cu_33.5 film. With decreasing annealing temperature, the critical stress for slip increased, but the M _s temperature decreased. It was found that films with 11.5 at% Cu or more, annealed at 873 K, showed a high martensitic transformation temperature and a high critical stress for slip.     

Critical behavior and magnetic relaxation dynamics of Nd0.4Sr0.6MnO3 nanoparticles

Detailed DC and AC magnetic properties of chemically synthesized Nd_0.4Sr_0.6MnO₃ with different particle size (down to 27?nm) have been studied in details. We have found ferromagnetic state in the nanoparticles, whereas the bulk Nd_0.4Sr_0.6MnO₃ is known to be an A-type antiferromagnet. A Griffiths-like phase has also been identified in the nanoparticles. Further, critical behaviour of the nanoparticles has been studied around the second-order ferromagnetic-paramagnetic transition region (|(T?T _C)/T _C|???0.04) in terms of modified Arrott plot, Kouvel–Fisher plot and critical isotherm analysis. The estimated critical exponents (β, γ, δ) are quite different from those predicted according to three-dimensional mean-field, Heisenberg and Ising models. This signifies a quite unusual nature of the size-induced ferromagnetic state in Nd_0.4Sr_0.6MnO₃. The nanoparticles are found to be interacting and do not behave like ideal superparamagnet. Interestingly, we find spin glass like slow relaxation of magnetization, aging and memory effect in the nanometric samples. These phenomena have been attributed to very broad distribution of relaxation time as well as to inter-particle interaction. Experimentally, we have found out that the dynamics of the nanoparticle systems can be best described by hierarchical model of spin glasses.     

On solutions of a Boussinesq-type equation with displacement-dependent nonlinearities: the case of biomembranes

Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with displacement-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson for describing longitudinal waves in biomembranes and later improved by Engelbrecht, Tamm and Peets taking into account the microinertia of a biomembrane. The steady solution in the form of a solitary wave is derived and the influence of nonlinear and dispersive terms over a large range of possible sets of coefficients demonstrated. The solutions emerging from arbitrary initial inputs are found using the numerical simulation. The properties of emerging trains of solitary waves are analysed. Finally, the interaction of solitary waves which satisfy the governing equation is studied. The interaction process is not fully elastic and after several interactions radiation effects may be significant. This means that for the present case the solitary waves are not solitons in the strict mathematical sense. However, like in other cases known in solid mechanics, such solutions may be conditionally called solitons.     

Broad-band dielectric spectroscopy of tetragonal PLZT x /40/60

The dielectric behaviour of tetragonal PLZT x/40/60 ceramics doped with lanthanum (x?=?5,?12 and 15%) has been investigated at 100–10¹⁴?Hz. Dielectric, THz and infrared spectra were measured from 500 to 20?K. For x?≥?12 relaxor ferroelectric behaviour was observed. All three samples showed an additional relaxational mode below phonons. Analysis of the phonon modes for ferroelectric PLZT 5/40/60 is presented together with the complete dielectric behaviour.     

A class of blowup and global analytical solutions of the viscoelastic Burgersʼ equations

In this Letter, by employing the perturbational method, we obtain a class of analytical self-similar solutions of the viscoelastic Burgers? equations. These solutions are of polynomial-type whose forms, remarkably, coincide with that given by Yuen for the other physical models, such as the compressible Euler or Navier–Stokes equations and two-component Camassa–Holm equations. Furthermore, we classify the initial conditions into several groups and then discuss the properties on blowup and global existence of the corresponding solutions, which may be readily seen from the phase diagram.     

Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow

Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L^∞( L ²) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L^∞( L ²) as well as in L^∞( H )‐norms and the pressure in L^∞(L²)‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

DEA-based predictors for estimating fleet size changes when modelling the introduction of rights-based management

The introduction of individual transferable quotas (ITQs) into a fishery is going to change not only the amount of catch a fleet can take, but often also changes the fleet structure, particularly if total allowable catches are decreased. This can have an impact on the economic, social and environmental outcomes of fisheries management. Management Strategy Evaluation (MSE) modelling approaches are recognised as the most appropriate method for assessing impacts of management, but these require information as to how fleets may change under different management systems. In this study, we test the applicability of data envelopment analysis (DEA) based performance measures as predictors of how a fishing fleet might change under the introduction of ITQs and also at different levels of quota. In particular, we test the assumption that technical efficiency and capacity utilisation are suitable predictors of which boats are likely to exit the fishery. We also consider scale efficiency as an alternative predictor. We apply the analysis to the Torres Strait tropical rock lobster fishery that is transitioning to an ITQ-based management system for one sector of the fishery. The results indicate that capacity utilisation, technical efficiency and scale efficiency are reasonable indicators of who may remain in the fishery post ITQs. We find that the use of these measures to estimate the impacts of lower quota levels provides consistent fleet size estimates at the aggregate level, but which individual vessels are predicted to exit is dependent on the measure used.