On the heat flux vector for flowing granular materials—Part I: effective thermal conductivity and background

Heat transfer plays a major role in the processing of many particulate materials. The heat flux vector is commonly modelled by the Fourier's law of heat conduction and for complex materials such as non‐linear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematical parameters such as temperature, shear rate, porosity or concentration, etc. In Part I, we will give a brief review of the basic equations of thermodynamics and heat transfer to indicate the importance of the modelling of the heat flux vector. We will also discuss the concept of effective thermal conductivity (ETC) in granular and porous media. In Part II, we propose and subsequently derive a properly frame‐invariant constitutive relationship for the heat flux vector for a (single phase) flowing granular medium. Standard methods in continuum mechanics such as representation theorems and homogenization techniques are used. It is shown that the heat flux vector in addition to being proportional to the temperature gradient (the Fourier's law), could also depend on the gradient of density (or volume fraction), and D (the symmetric part of the velocity gradient) in an appropriate manner. The emphasis in this paper is on the idea that for complex non‐linear materials it is the heat flux vector which should be studied; obtaining or proposing generalized form of the thermal conductivity is not always appropriate or sufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Resource allocation in the North Sea demersal fisheries: A goal programming approach

The management of a fishery is a complex task generally involving multiple, often conflicting, objectives. These objectives typically include economic, biological and social goals such as improving the income of fishers, reducing the catch of depleted species and maintaining employment.Multicriteria decision making (MCDM) techniques appear wellsuited to such a management problem, allowing compromises between conflicting objectives to be analysed in a structured framework. In comparison to other fields, such as water resource planning, forestry and agriculture, there have been few applications of MCDM to fisheries.In this paper, a goal programming model of the North Sea demersal fishery is presented. The model is used to demonstrate the potential applicability of this type of approach to the analysis and development of fisheries management plans with multiple objectives. Alternative scenarios are considered for the problem, and tradeoffs between given objectives are also highlighted and discussed.     

Soliton-antisoliton scattering and capture in λφ4 theory

In this work we have investigated the result of collisions of a soliton-antisoliton pair for various incident velocities in λφ⁴ theory through a series of numerical experiments. It is observed for incident velocities less than a critical velocity V_crit that we have two narrow regions in the velocity spectrum where the result of collision is a scattering of particles along with the emission of some radiation. Outside these two narrow windows the incident particles are captured and form resonances. For velocities greater than V_crit scattering is always obtained and it is found that the square of the outcoming velocity is a linear function of the square of the incoming velocity. From the approximate solution found, an effective potential for widely separated solitons is derived.     

Generalized framework for auxiliary extra dimensions

The theory of gravity with an auxiliary extra dimension is known to give the ghost-free cubic completion of the Fierz-Pauli mass term in the decoupling limit. Our work generalizes the boundary condition in the auxiliary dimension that avoids ghosts order-by-order, and to all orders, in the decoupling limit. Furthermore, we extend the formalism to the case of many auxiliary dimensions, and we show that the multi-dimensional extension with the rotationally invariant boundaries of the bulk, is equivalent to the model with a single auxiliary dimension. The above constructions require the appropriate adjustment of the boundary condition, which we discuss in detail. The other possible extension of the original model by the Gauss-Bonnet term is studied as well.     

Numerical study of electroosmotic micromixing of non-Newtonian fluids

Biofluids which exhibit non-Newtonian behavior are widely used in microfluidic devices which involve fluid mixing in microscales. In order to study the effects of shear depending viscosity of non-Newtonian fluids on characteristics of electroosmotic micromixing, a numerical investigation of flow of power-law fluid in a two-dimensional microchannel with nonuniform zeta potential distributions along the channel walls was carried out via finite volume scheme. The simulation results confirmed that the shear depending viscosity has a significant effect on the degree of mixing efficiency. It was shown as the fluid behavior index of power-law fluid, n, decreases, more homogeneous solution can be achieved at the microchannel outlet. Hence, electroosmotic micromixing was found more practical and efficient in microscale mixing of pseudoplastic fluids rather than those Newtonian and dilatant ones. Furthermore, it was found that increase in Reynolds number results in lower mixing efficiency while electroosmotic forces are kept constant.     

Horizon problem remediation via deformed phase space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans–Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.     

Monomial ideals with tiny squares and Freiman ideals

Czechoslovak Mathematical Journal - We provide a construction of monomial ideals in R = K[x, y] such that μ(I2) < μ(I), where μ denotes the least number of generators. This...