B-spline collocation simulation of non-linear transient magnetic nanobio-tribological squeeze-film flow

A mathematical model is presented for magnetized nanofluid bio-tribological squeeze film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nano-suspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nano-particle) conservation equations are normalized with appropriate transformations which renders the original coupled, nonlinear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in nonlinear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems

Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.Comment: 7 page

Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales

We discuss the phase transition in 3+1 dimensional lambda Phi^4 theory from a very physical perspective. The particles of the symmetric phase (`phions') interact via a hard-core repulsion and an induced, long-range -1/r^3 attraction. If the phion mass is sufficiently small, the lowest-energy state is not the `empty' state with no phions, but is a state with a non-zero density of phions Bose-Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with neq 0 and its excitations ("phonons" in atomic-physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m^2 passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M_h. This interesting physics coexists with `triviality;' all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio m/M_h, which goes to zero in the continuum limit, can be viewed as a measure of non-locality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.Comment: 27 pages plus 2 files of figure

Large magnetic dipole moments for neutrinos with arbitrary masses

We show that there is a general sort of models in which it is possible to have large magnetic dipole moments for neutrinos while keeping their masses arbitrarily small. Some examples of these models are considered.Comment: REVTEX, 8 pages, 2 .eps figure

Three-Body approach to the K^- d Scattering Length in Particle Basis

We report on the first calculation of the scattering length A_{K^-d} based on a relativistic three-body approach where the two-body input amplitudes coupled to the Kbar N channels have been obtained with the chiral SU(3) constraint, but with isospin symmetry breaking effects taken into account. Results are compared with a recent calculation applying a similar set of two-body amplitudes,based on the fixed center approximation, considered as a good approximation for a loosely bound target, and for which we find significant deviations from the exact three-body results. Effects of the hyperon-nucleon interaction, and deuteron $D$-wave component are also evaluated.Comment: 5 pages, Submitted to Phys. Rev.

Chiral Corrections to Lattice Calculations of Charge Radii

Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.Comment: PostScript file only. Ten pages. Figures included. U. of MD Preprint #92-19

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic (MHD), incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted

Comparison of Transfer-to-Continuum and Eikonal Models of Projectile Fragmentation Reactions

Spectroscopic properties of nuclei are accessible with projectile fragmentation reactions, but approximations made in the reaction theory can limit the accuracy of the determinations. We examine here two models that have rather different approximations for the nucleon wave function, the target interaction, and the treatment of the finite duration of the reaction. The nucleon-target interaction is treated differently in the eikonal and the transfer-to-continuum model, but the differences are more significant for light targets. We propose a new parameterization with that in mind. We also propose a new formula to calculate the amplitude that combines the better treatment of the wave function in the eikonal model with the better treatment of the target interaction in the transfer-to-continuum model.Comment: 21 pages, latex file including 3 tables. 5 figures. Submitted to Phys. Rev.

Improved Theory of the Muonium Hyperfine Structure

Terms contributing to the hyperfine structure of the muonium ground state at the level of few tenths of kHz have been evaluated. The $\alpha^2 (Z\alpha)$ radiative correction has been calculated numerically to the precision of 0.02 kHz. Leading $\ln (Z\alpha )$ terms of order $\alpha^{4-n} (Z\alpha)^n , n=1,2,3,$ and some relativistic corrections have been evaluated analytically. The theoretical uncertainty is now reduced to 0.17 kHz. At present, however, it is not possible to test QED to this precision because of the 1.34 kHz uncertainty due to the muon mass.Comment: 11 pages + 2 figures (included), RevTeX 3.0, CLNS 94/127

Momentum and Coordinate Space Three-nucleon Potentials

In this paper we give explicit formulae in momentum and coordinate space for the three-nucleon potentials due to $\rho$ and $\pi$ meson exchange, derived from off-mass-shell meson-nucleon scattering amplitudes which are constrained by the symmetries of QCD and by the experimental data. Those potentials have already been applied to nuclear matter calculations. Here we display additional terms which appear to be the most important for nuclear structure. The potentials are decomposed in a way that separates the contributions of different physical mechanisms involved in the meson-nucleon amplitudes. The same type of decomposition is presented for the $\pi - \pi$ TM force: the $\Delta$, the chiral symmetry breaking and the nucleon pair terms are isolated.Comment: LATEX, 33 pages, 3 figures (available as postscript files upon request