Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Multi-zone TAP-reactors theory and application - IV. Ideal and non-ideal boundary conditions

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

Solving the problem of diffraction of an optical-band electromagnetic wave by metal nanostructured aperture arrays with the use of the method of impedance boundary conditions

The problem of diffraction of an optical wave by a 2D periodic metal aperture array with square, circular, and ring apertures is solved with allowance for the finite permittivity of a metal in the optical band. The correctness of the obtained results is verified through comparison with experimental data. It is shown that the transmission coefficient can be substantially greater than the corresponding value reached in the case of diffraction by a grating in a perfectly conducting screen.

Automotive waste heat recovery: Working fluid selection and related boundary conditions

This paper presents the rational for the selection of fluids for use in a model based study of sub and supercritical Waste Heat Recovery (WHR) Organic Rankine Cycle (ORC). The study focuses on multiple vehicle heat sources and the potential of WHR ORC’s for its conversion into useful work. The work presented on fluid selection is generally applicable to any waste heat recovery system, either stationary or mobile and, with careful consideration, is also applicable to single heat sources. The fluid selection process presented reduces the number of potential fluids from over one hundred to a group of under twenty fluids for further refinement in a model based WHR ORC performance study. The selection process uses engineering judgement, legislation and, where applicable, health and safety as fluid selection or de-selection criteria. This paper also investigates and discusses the properties of specific ORC fluids with regard to their impact on the theoretical potential for delivering efficient WHR ORC work output. The paper concludes by looking at potential temperature and pressure WHR ORC limits with regard to fluid properties thereby assisting with the generation of WHR ORC simulation boundary conditions.

Influence of Boundary Conditions on the Low Velocity Impact Damage Carbon Fibre Reinforced Plastic Plates (ICTWS2014-0501)

No abstract available

Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Quantum electronic transport in a configuration interaction basis

An overview of a many-body approach to calculation of electronic transport in molecular systems is given. The physics required to describe electronic transport through a molecule at the many-body level, without relying on commonly made assumptions such as the Landauer formalism or linear response theory, is discussed. Physically, our method relies on the incorporation of scattering boundary conditions into a many-body wavefunction and application of the maximum entropy principle to the transport region. Mathematically, this simple physical model translates into a constrained nonlinear optimization problem. A strategy for solving the constrained optimization problem is given. (C) 2004 Wiley Periodicals, Inc.

Hybridization of a class of "second order" models of traffic flow

Despite the simultaneous progress of traffic modelling both on the macroscopic and microscopic front, recent works [E. Bourrel, J.B. Lessort, Mixing micro and macro representation of traffic flow: a hybrid model based on the LWR theory, Transport. Res. Rec. 1852 (2003) 193–200; D. Helbing, M. Treiber, Critical discussion of “synchronized flow”, Coop. Transport. Dyn. 1 (2002) 2.1–2.24; A. Hennecke, M. Treiber, D. Helbing, Macroscopic simulations of open systems and micro–macro link, in: D. Helbing, H.J. Herrmann, M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’99, Springer, Berlin, 2000, pp. 383–388] highlighted that one of the most promising way to simulate efficiently traffic flow on large road networks is a clever combination of both traffic representations: the hybrid modelling. Our focus in this paper is to propose two hybrid models for which the macroscopic (resp. mesoscopic) part is based on a class of second order model [A. Aw, M. Rascle, Resurection of second order models of traffic flow?, SIAM J. Appl. Math. 60 (2000) 916–938] whereas the microscopic part is a Follow-the Leader type model [D.C. Gazis, R. Herman, R.W. Rothery, Nonlinear follow-the-leader models of traffic flow, Oper. Res. 9 (1961) 545–567; R. Herman, I. Prigogine, Kinetic Theory of Vehicular Traffic, American Elsevier, New York, 1971]. For the first hybrid model, we define precisely the translation of boundary conditions at interfaces and for the second one we explain the synchronization processes. Furthermore, through some numerical simulations we show that the waves propagation is not disturbed and the mass is accurately conserved when passing from one traffic representation to another.

Epitaxial strain and electric boundary condition effects on the structural and ferroelectric properties of BiFeO3 films

The influence of both compressive and tensile epitaxial strain along with the electrical boundary conditions on the ferroelastic and ferroelectric domain patterns of bismuth ferrite films was studied. BiFeO3 films were grown on SrTiO3(001), DyScO3(110), GdScO3(110), and SmScO3(110) substrates to investigate the effect of room temperature in-plane strain ranging from -1.4% to +0.75%. Piezoresponse force microscopy, transmission electron microscopy, x-ray diffraction measurements, and ferroelectric polarization measurements were performed to study the properties of the films. We show that BiFeO3 films with and without SrRuO3 bottom electrode have different growth mechanisms and that in both cases reduction of the domain variants is possible. Without SrRuO3, stripe domains with reduced variants are formed on all rare earth scandate substrates because of their monoclinic symmetry. In addition, tensile strained films exhibit a rotation of the unit cell with increasing film thickness. On the other side, the presence of SrRuO3 promotes step flow growth of BiFeO3. In case of vicinal SrTiO3 and DyScO3 substrates with high quality SrRuO3 bottom electrode and a low miscut angle of approximate to 0.15 degrees we observed suppression of the formation of certain domain variants. The quite large in-plane misfit of SrRuO3 with GdScO3 and SmScO3 prevents the growth of high quality SrRuO3 films and subsequent domain variants reduction in BiFeO3 on these substrates, when SrRuO3 is used as a bottom electrode.

A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.

Substrate Clamping Effects on Irreversible Domain Wall Dynamics in Lead Zirconate Titanate Thin Films

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE NONRESONANT, COSMIC-RAY-DRIVEN INSTABILITY IN SUPERNOVA REMNANT SHOCKS

In supernova remnants, the nonlinear amplification of magnetic fields upstream of collisionless shocks is essential for the acceleration of cosmic rays to the energy of the "knee" at 10(15.5) eV. A nonresonant instability driven by the cosmic ray current is thought to be responsible for this effect. We perform two-dimensional, particle-in-cell simulations of this instability. We observe an initial growth of circularly polarized nonpropagating magnetic waves as predicted in linear theory. It is demonstrated that in some cases the magnetic energy density in the growing waves can grow to at least 10 times its initial value. We find no evidence of competing modes, nor of significant modification by thermal effects. At late times, we observe saturation of the instability in the simulation, but the mechanism responsible is an artifact of the periodic boundary conditions and has no counterpart in the supernova-shock scenario.

Validated Cfd Study of Indoor Environmental Conditions in a Highly Glazed , Cross-Ventilated Meeting Room

This paper investigates the environmental conditions inside a highly-glazed cross-ventilated meeting room. A 3D computational fluid dynamics (CFD) model of an indoor environment is developed with the support of the field measurements performed in a normally operating room. The work presented here follows the steps of the formal calibration methodology for the development of CFD models of naturally ventilated environments. This paper utilises the calibration methodology in order to predict environmental conditions within the highly-glazed cross-ventilated room occupied by people. The CFD model is verified and validated with field measurements performed in an operating building. Moreover, parametric analysis determines the most influential boundary conditions on indoor air temperatures and air speeds

Arching action in high strength concrete slabs

The corrosion of reinforcement in bridge deck slabs has been the cause of major deterioration and high costs in repair and maintenance.This problem could be overcome by reducing the amount of reinforcement and/or altering the location.This is possible because, in addition to the strength provided by the reinforcement, bridge deck slabs have an inherent strength due to the in-plane arching forces set up as a result of restraint provided by the slab boundary conditions. This is known as arching action or Compressive Membrane Action (CMA). It has been recognised for some time that laterally restrained slabs exhibit strengths far in excess of those predicted by most design codes but the phenomenon has not been recognised by the majority of bridge design engineers. This paper presents the results of laboratory tests on fifteen reinforced concrete slab strips typical of a bridge deck slab and compares them to predicted strengths using the current codes and CMA theory. The tests showed that the strength of laterally restrained slabs is sensitive to both the degree of external lateral restraint and the concrete compressive strength.The tests particularly highlighted the benefits in strength obtained from very high strength concrete slabs. The theory extends the existing knowledge of CMA in slabs with concrete compressive strengths up to 100 N/mm[2] and promotes more economical and durable bridge deck construction by utilising the benefits of high strength concrete.