Parameter In Boundary Condition Research Articles

Optimal boundary conditions for ORCA-2 model

A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of the boundary conditions on the solution is analyzed as in the assimilation window and beyond the window. It is shown that optimal conditions for vertical operators allows to get stronger and finer jet streams (Gulf Stream, Kuroshio) in the solution. Analyzing the reasons of the jets reinforcement, we see that the major impact of the data assimilation is made on the parametrization of the bottom boundary conditions for lateral velocities u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.

Roles of Viscosity, Polarity, and Hydrogen-Bonding Ability of a Pyrrolidinium Ionic Liquid and Its Binary Mixtures in the Photophysics and Rotational Dynamics of the Potent Excited-State Intramolecular Proton-Transfer Probe 2,2′-Bipyridine-3,3′-diol

The room-temperature ionic liquid [C3mpyr][Tf2N] and its binary mixtures with methanol and acetonitrile provide microenvironments of varying viscosity, polarity, and hydrogen-bonding ability. The present work highlights their effects on the photophysics and rotational dynamics of a potent excited-state intramolecular double-proton-transfer (ESIDPT) probe, 2,2'-bipyridine-3,3'-diol [BP(OH)2]. The rotational diffusion of the proton-transferred diketo (DK) tautomer in [C3mpyr][Tf2N] ionic liquid was analyzed for the first time from the experimentally obtained temperature-dependent fluorescence anisotropy data using Stokes-Einstein-Debye (SED) hydrodynamic theory and Gierer-Wirtz quasihydrodynamic theory (GW-QHT). It was found that the rotation of the DK tautomer in neat ionic liquid is governed solely by the viscosity of the medium, as the experimentally observed boundary-condition parameter, Cobs, was very close to the GW boundary-condition parameter (CGW). On the basis of photophysical studies of BP(OH)2 in IL-cosolvent binary mixtures, we suggest that methanol molecules form hydrogen bonds with the cationic counterpart of the DK tautomers, as evidenced by the greater extent of the decrease in the fluorescence lifetime of BP(OH)2 upon addition of methanol compared to acetonitrile. It is also possible for the methanol molecules to form hydrogen bonds with the constituents of the RTIL, which is supported by the lesser extent of the decrease in the viscosity of the medium upon addition of methanol, leading to a less effective decrease in the rotational relaxation time compared to that observed upon acetonitrile addition.

Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance

We consider the fractional differential equation D 0 + q u(t)=f ( t , u ( t ) ) ,0<t<1, satisfying the boundary conditions D 0 + p u(t) | t = 0 = D 0 + p − 1 u(t) | t = 0 =⋯= D 0 + p − n + 1 u(t) | t = 0 =0,u(1)= ∑ i = 1 m − 2 α i u( ξ i ), where D 0 + q is the Riemann-Liouville fractional order derivative. The parameters in the multi-point boundary conditions are such that the corresponding differential operator is a Fredholm map of index zero. As a result, the minimal and maximal nonnegative solutions for the problem are obtained by using a fixed point theorem of increasing operators.MSC:26A33, 34A08.

Inverse problems for the Sturm–Liouville operator with discontinuity

In the previous works of the author (Applied Mathematics Letters. 2009;22:1315–1319, and Integral Equations and Operator Theory. 2009;65:593–604), provided that discontinuity parameters and boundary condition parameters are known a priori the inverse problems for the Sturm–Liouville operator with discontinuity inside a finite interval was studied. In fact, it is unnecessary to fix above mentioned parameters. In this work, we prove that the potential function and all parameters in discontinuity conditions and boundary conditions can be uniquely determined by a set of values of eigenfunctions in some interior point and one spectrum. We also establish Gesztesy–Simon type theorem and Ambarzumyan type theorem of inverse spectral aspects for discontinuous boundary value problem. The proofs in this work rely on the properties of analytic functions and Phragmén-Lindelöf theorem.

Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.

Hybrid modelling of 7449-T7 aluminium alloy friction stir welded joints

Many finite element models use adjustable parameters that control the heat loss to the backing bar, as well as the heat input to the weld. In this paper, we describe a method for determining these parameters with a hybrid artificial neural network (ANN) coupled thermal flow process model of the friction stir welding process. The method successfully determined temperature dependent boundary condition parameters for a series of friction stir welds in 3·2 mm thick 7449 aluminium alloy. The success of the technique depended on the method used to input thermal data into the ANN and the ANN topology. Using this technique to obtain the adjustable parameters of a model is more efficient than the conventional trial and error approach, especially where complex boundary conditions are implemented.

Loading and structural response models of circular plates subjected to near field explosions

Loading and structural response models were developed to estimate the elastic deformation of a circular plate due to near field explosions. The loading model generates the nonuniform loading characteristic of a near field explosion on a circular plate. This loading model is unique as it uses the TNT equivalence factors for pressure and impulse separately when deriving the pressure profile. Most loading models either average the two factors together or use only one of them.An analytical model and two finite element models were developed to capture the response of the circular plate due to this nonuniform loading. The analytical model utilizes the von Kármán thin plate equations with a new assumed deformation profile. The typical deformation profile for a circular plate uses two constants to satisfy the boundary conditions. By adding torsional springs to the boundary of the plate and equating the springs' moment to the plate's internal moment, as well as carrying through with the von Kármán model, a new assumed profile is derived which has one parameter representing the boundary. This allows for a sensitivity analysis to be performed on the boundary condition parameter. In addition, this parameter has physical meaning, as it represents the stiffness of the torsional springs.The plate center deflections for the three structural models were found to be in good agreement with the experimental data provided by the U.S. Department of Homeland Security. The results show that the loading becomes less accurate at very small scaled distances because the loading model is more phenomenological than physics-based.The sensitivity of the maximum plate center deflection to parameter changes was estimated. The maximum deflection was found to be most sensitive to plate thickness.

Pulsed Focused Nonlinear Acoustic Fields from Clinically Relevant Therapeutic Sources in Layered Media: Experimental Data and Numerical Prediction Results

Abstract In many therapeutic applications of a pulsed focused ultrasound with various intensities the finite- amplitude acoustic waves propagate in water before penetrating into tissues and their local heating. Water is used as the matching, cooling and harmonics generating medium. In order to design ultrasonic probes for various therapeutic applications based on the local tissue heating induced in selected organs as well as to plan ultrasonic regimes of treatment a knowledge of pressure variations in pulsed focused nonlinear acoustic beams produced in layered media is necessary. The main objective of this work was to verify experimentally the applicability of the recently developed numerical model based on the Time- Averaged Wave Envelope (TAWE) approach (Wójcik et al., 2006) as an effective research tool for predicting the pulsed focused nonlinear fields produced in two-layer media comprising of water and tested materials (with attenuation arbitrarily dependent on frequency) by clinically relevant axially-symmetric therapeutic sources. First, the model was verified in water as a reference medium with known linear and nonlinear acoustic properties. The measurements in water were carried out at a 25◦C temperature using a 2.25 MHz circular focused (f/3.0) transducer with an effective diameter of 29 mm. The measurement results obtained for 8-cycle tone bursts with three different initial pressure amplitudes varied between 37 kPa and 113 kPa were compared with the numerical predictions obtained for the source boundary condition parameters determined experimentally. The comparison of the experimental results with those simulated numerically has shown that the model based on the TAWE approach predicts well both the spatial-peak and spatial-spectral pressure variations in the pulsed focused nonlinear beams produced by the transducer used in water for all excitation levels complying with the condition corresponding to weak or moderate source-pressure levels. Quantitative analysis of the simulated nonlinear beams from circular transducers with ka ≫ 1 allowed to show that the axial distance at which sudden accretion of the 2nd or higher harmonics amplitude appears is specific for this transducer regardless of the excitation level providing weak to moderate nonlinear fields. For the transducer used, the axial distance at which the 2nd harmonics amplitude suddenly begins to grow was found to be equal to 60 mm. Then, the model was verified experimentally for two-layer parallel media comprising of a 60-mm water layer and a 60-mm layer of 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany). This medium was selected because of its tissue-mimicking acoustic properties and known nonlinearity parameter B/A. The measurements of both, the peak- and harmonic-pressure variations in the pulsed nonlinear acoustic beams produced in two-layer media (water/1.3-butanediol) were performed for the same source boundary conditions as in water. The measurement results were compared with those simulated numerically. The good agreement between the measured data and numerical calculations has shown that the model based on the TAWE approach is well suited to predict both the peak and harmonic pressure variations in the pulsed focused nonlinear sound beams produced in layered media by clinically relevant therapeutic sources. Finally, the pulsed focused nonlinear fields from the transducer used in two-layer media: water/castor oil, water/silicone oil (Dow Corning Ltd., Coventry, UK), water/human brain and water/pig liver were predicted for various values of the nonlinearity parameter of tested media.

Heat transfer to micropolar fluid flowing through an irregular arterial constriction

A mathematical model of unsteady non–Newtonian blood flow together with heat transfer through constricted arteries has been developed. The flowing blood is represented as the suspension of all erythrocytes assumed to be Eringen’s micropolar fluid and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the initial and the boundary conditions are solved numerically by Marker and Cell (MAC) method and the results are checked for numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and the temperature distribution over the entire arterial segment as well. The key factors like the wall shear stress, the stream lines, the separation-reattachment points, the pressure drop and the heat contours are also examined for further qualitative insight into the heat flow phenomena. Results show that the initiation of nonzero microspin velocity on the arterial wall prompts early flow separation and the occurrence of multiple separation zones may also be attributed due to the introduction of nonzero microspin boundary condition parameter S together with the rough valleys and ridges presented on the outline of the diverging part of the irregular stenosis. The present results also predict the excess pressure drop across the cosine stenoses than the irregular ones and show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.

A New Method to Determine the Upper Boundary Condition for a Permafrost Thermal Model: An Example from the Qinghai‐Tibet Plateau

ABSTRACTAssessing possible permafrost degradation related to engineering projects, climate change and land use change is of critical importance for protecting the environment and in developing sustainable designs for vital infrastructure in cold regions. A major challenge in modelling the future degradation of permafrost is finding ways to constrain changes in the upper thermal boundary condition over time and space at appropriate scales. Here, we report on an approach designed to predict time series of air, ground surface and shallow ground temperatures at a spatial scale on the order of 102 m2 for engineering design of a railway or highway project. The approach uses a regional‐scale atmospheric model to downscale global climate model output, and then stepwise multiple regression to develop an equation that provides a best‐fit prediction of site‐specific observational data using bilinearly interpolated output from the atmospheric model. This approach bridges the scale difference between atmospheric climate models and permafrost thermal models, and allows for a wider range of factors to be used in predicting the thermal boundary condition. For a research site located in Beiluhe, China, close to the Qinghai‐Tibet Railway, a comparison of model predictions with observational data not used in the construction of the model shows that this method can be used with a high degree of accuracy to determine the upper boundary condition for a permafrost thermal model. Once a model is constructed, it can be used to predict future changes in boundary condition parameters under different greenhouse emission scenarios for climate change. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Bending Analysis of Thin Plates with Variable Thickness Resting on Elastic Foundation by Element Free Galerkin Method

AbstractElement Free Galerkin method was used to analyze bending of thin plates with variable thickness resting on one parameter elastic foundation. Thickness of plate is considered as linearly varying in one direction. Formulation could be applied to plates of any shape with general boundary conditions and loadings. Convergence of solution was examined for different number of nodes, thickness variation and foundation parameters. It was found that for deflection good results were achieved even with small number of nodes regardless of boundary condition, thickness variation and foundation parameters. Accuracy of method is checked against available results and good agreements were found. Applicability of method is demonstrated by solving numerical examples with different boundary conditions, thickness and foundation parameters, and loadings.

Numerical evaluation of turbulence models for dense to dilute gas–solid flows in vertical conveyor

A two-fluid model (TFM) of multiphase flows based on the kinetic theory and small frictional limit boundary condition of granular flow was used to study the behavior of dense to dilute gas–solid flows in vertical pneumatic conveyor. An axisymmetric 2-dimensional, vertical pipe with 5.6m length and 0.01m internal diameter was chosen as the computation domain, same to that used for experimentation in the literature. The chosen particles are spherical, of diameter 1.91mm and density 2500kg/m3. Turbulence interaction between the gas and particle phases was investigated by Simonin's and Ahmadi's models and their numerical results were validated for dilute to dense conveying of particles. Flow regimes transition and pressure drop were predicted. Voidage and velocity profiles of each phase were calculated in radial direction at different lengths of the conveying pipe. It was found that the voidage has a minimum, and gas and solid velocities have maximum values along the center line of the conveying pipe and pressure drop has a minimum value in transition from dense slugging to dilute stable flow regime. Slug length and pressure fluctuation reduction were predicted with increasing gas velocity, too. It is shown that solid phase turbulence plays a significant role in numerical prediction of hydrodynamics of conveyor and the capability of particles turbulence models depends on tuning parameters of slip-wall boundary condition.

Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality

In this article we investigate the relation between consequences of Dirichlet boundary conditions (momenta noncommutativity and parameters of the effective theory) and background fields of fermionic T-dual theory. We impose Dirichlet boundary conditions on the endpoints of the open string propagating in background of type IIB superstring theory with constant background fields. We showed that on the solution of the boundary conditions the momenta become noncommutative, while the coordinates commute. Fermionic T-duality is also introduced and its relation to noncommutativity is considered. We use compact notation so that type IIB superstring formally gets the form of the bosonic one with Grassman variables. Then momenta noncommutativity parameters are fermionic T-dual fields. The effective theory, the initial theory on the solution of boundary conditions, is bilinear in the effective coordinates, odd under world-sheet parity transformation. The effective metric is equal to the initial one and terms with the effective Kalb-Ramond field vanish.

Convection in a horizontal layer of high porosity with an exothermic surface reaction on the lower boundary

The onset of instability in a porous medium of high porosity subject to a chemical surface reaction on the lower boundary and no slip conditions on both the upper and lower boundaries is studied. The equations are developed and then solved numerically to find the critical Rayleigh number. The influence that the boundary condition parameters and the Brinkman term have on the critical Rayleigh number is examined.

Rotational Diffusion of Neutral and Charged Solutes in 1-Butyl-3-Methylimidazolium-Based Ionic Liquids: Influence of the Nature of the Anion on Solute Rotation

Temperature-dependent fluorescence anisotropies of two organic solutes, 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and rhodamine 110 (R110), have been measured in 1-butyl-3-methylimidazolium ([bmim(+)])-based ionic liquids containing the anions hexafluorophosphate ([PF(6)(-)]), bis(trifluoromethylsulfonyl)imide ([Tf(2)N(-)]), tetrafluoroborate ([BF(4)(-)]), trifluoromethanesulfonate ([TfO(-)]), and nitrate ([NO(3)(-)]). This data has been used in conjunction with the recently published results (Dutt, G. B. J. Phys. Chem. B2010, 114, 8971) for the same solutes in [bmim(+)] tris(pentafluoroethyl)trifluorophosphate ([FAP(-)]) to understand the influence of various anions on solute rotation. The boundary condition parameter C(obs), which has been obtained from the analysis of the data using Stokes-Einstein-Debye hydrodynamic theory, for the neutral solute DMDPP is more or less the same in all the ionic liquids. Moreover, C(obs) values are close to the predictions of slip boundary condition, which indicates that solvent viscosity alone governs the rotation of DMDPP. In contrast, for R110, which experiences specific interactions with the anions of the ionic liquids, the C(obs) values are close to stick hydrodynamics. It has also been noticed that the C(obs) values vary with the nature of the anion and this variation correlates with the hydrogen bond basicities of the anions of the ionic liquids.

Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions

Let L denote the operator generated in ℓ2(ℕ, ℂ2) by , , n∈ℕ, and the boundary condition , where (an) , (bn), (pn), and (qn) , n∈ℕ are complex sequences, γi, βi∈ℂ , i = 0,1, and λ is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of L.

Parameter Analysis of Diesel Helical Intake Port Numerical Design

In order to research about the performance of diesel helical intake port, the method of steady flow test and CFD numerical simulation was combined to do structure study. By the steady flow test, the parameters of boundary condition for simulation calculation were provided, such as the flow coefficient and swirl ratio. Based on the experiment results, CFD simulation was calculated on the three-dimensional models of intake port with the modification of center distance, valve chamber height and the valve cone angle. And the results basically analyze that the flow characteristic of intake port was affected by above three parameters. This research shows the direction of detailed design of intake port and further experiment, which can shorten development time and costs of intake port.

Free Convection over a Permeable Horizontal Flat Plate Embedded in a Porous Medium with Radiation Effects and Mixed Thermal Boundary Conditions

Problem statement: In this study, the mathematical modelling of free convection boundary layer flow over a permeable horizontal flat plate e mbedded in a porous medium under mixed thermal boundary conditions and radiation effects is consid ered. Approach: The transformed boundary layer equations are solved numerically using the shooting method. Results: Numerical solutions are obtained for the wall temperature, the heat transfe r coefficient, as well as the velocity and temperat ure profiles. The features of the flow and heat transfe r characteristics for different values of the radia tion parameter NR, the mixed thermal boundary condition parameter e and the suction or injection parameter γ are analyzed and discussed. Conclusion: We can conclude that when the suction or injection parameter γ is fixed, an increase in the radiation parameter N R leads to the increase of - θ' (0) (for the case of constant surface temperature). How ever, when γ is fixed, an increase in N R leads to the decrease of θ (0) (for both cases of constant surface heat flux and mixed thermal boundary conditions).

Inverse Nodal Problem for Dirac System with Spectral Parameter in Boundary Conditions

An inverse nodal problem lies in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with an inverse nodal problem of reconstructing the Dirac system with the spectral parameter in the boundary conditions. We prove that a set of nodal points of one of the components of the eigenfunctions uniquely determines all the parameters of the boundary conditions and the coefficients of the Dirac equations. We also provide a constructive procedure for solving this inverse nodal problem.

On the uniform convergence of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter

We study the uniform convergence, on a closed interval, of spectral expansions of Holder functions in a given complete and minimal system of eigenfunctions corresponding to a spectral problem with spectral parameter in a boundary condition. We consider boundary conditions of the third kind and subject the function to be expanded to a condition of nonlocal type ensuring the uniform convergence. We prove a theorem stating that expansions in the entire system of eigenfunctions of the problem are possible without any additional conditions.