Academic literature on the topic 'Scalar dependent diffusion'
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Journal articles on the topic "Scalar dependent diffusion"
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Winters, Kraig B., and Eric A. D'Asaro. "Diascalar flux and the rate of fluid mixing." Journal of Fluid Mechanics 317 (June 25, 1996): 179–93. http://dx.doi.org/10.1017/s0022112096000717.
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We define the rate at which a scalar θ mixes in a fluid flow in terms of the flux of θ across isoscalar surfaces. This flux θd is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state θ(t,z*.) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (∂/∂z*)θd.This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn–Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.
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GHOSH, S., A. LEONARD, and S. WIGGINS. "Diffusion of a passive scalar from a no-slip boundary into a two-dimensional chaotic advection field." Journal of Fluid Mechanics 372 (October 10, 1998): 119–63. http://dx.doi.org/10.1017/s0022112098002249.
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Using a time-periodic perturbation of a two-dimensional steady separation bubble on a plane no-slip boundary to generate chaotic particle trajectories in a localized region of an unbounded boundary layer flow, we study the impact of various geometrical structures that arise naturally in chaotic advection fields on the transport of a passive scalar from a local ‘hot spot’ on the no-slip boundary. We consider here the full advection-diffusion problem, though attention is restricted to the case of small scalar diffusion, or large Péclet number. In this regime, a certain one-dimensional unstable manifold is shown to be the dominant organizing structure in the distribution of the passive scalar. In general, it is found that the chaotic structures in the flow strongly influence the scalar distribution while, in contrast, the flux of passive scalar from the localized active no-slip surface is, to dominant order, independent of the overlying chaotic advection. Increasing the intensity of the chaotic advection by perturbing the velocity field further away from integrability results in more non-uniform scalar distributions, unlike the case in bounded flows where the chaotic advection leads to rapid homogenization of diffusive tracer. In the region of chaotic particle motion the scalar distribution attains an asymptotic state which is time-periodic, with the period the same as that of the time-dependent advection field. Some of these results are understood by using the shadowing property from dynamical systems theory. The shadowing property allows us to relate the advection-diffusion solution at large Péclet numbers to a fictitious zero-diffusivity or frozen-field solution, corresponding to infinitely large Péclet number. The zero-diffusivity solution is an unphysical quantity, but is found to be a powerful heuristic tool in understanding the role of small scalar diffusion. A novel feature in this problem is that the chaotic advection field is adjacent to a no-slip boundary. The interaction between the necessarily non-hyperbolic particle dynamics in a thin near-wall region and the strongly hyperbolic dynamics in the overlying chaotic advection field is found to have important consequences on the scalar distribution; that this is indeed the case is shown using shadowing. Comparisons are made throughout with the flux and the distributions of the passive scalar for the advection-diffusion problem corresponding to the steady, unperturbed, integrable advection field.
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WEICHMAN, PETER B., and ROMAN E. GLAZMAN. "Passive scalar transport by travelling wave fields." Journal of Fluid Mechanics 420 (October 10, 2000): 147–200. http://dx.doi.org/10.1017/s0022112000001452.
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We study turbulent transport of passive tracers by random wave fields of a rather general nature. A formalism allowing for spatial inhomogeneity and anisotropy of an underlying velocity field (such as that caused by a latitudinally varying Coriolis parameter) is developed, with the aim of treating problems of large-scale ocean transport by long internal waves. For the special case of surface gravity waves on deep water, our results agree with the earlier theory of Herterich & Hasselmann (1982), though even in that case we discover additional, off-diagonal elements of the diffusion tensor emerging in the presence of a mean drift. An advective diffusion equation including all components of the diffusion tensor D plus a mean, Stokes-type drift u is derived and applied to the case of baroclinic inertia–gravity (BIG) waves. This application is of particular interest for ocean circulation and climate modelling, as the mean drift, according to our estimates, is comparable to ocean interior currents. Furthermore, while on the largest (100 km and greater) scales, wave-induced diffusion is found to be generally small compared to classical eddy-induced diffusion, the two become comparable on scales below 10 km. These scales are near the present limit on the spatial resolution of eddy-resolving ocean numerical models. Since we find that uz and Dzz vanish identically, net vertical transport is absent in wave systems of this type. However, for anisotropic wave spectra the diffusion tensor can have non-zero off-diagonal vertical elements, Dxz and Dyz, and it is shown that their presence leads to non-positive definiteness of D, and a negative diffusion constant is found along a particular principal axis. However, the simultaneous presence of a depth-dependent mean horizontal drift u(z) eliminates any potential unphysical behaviour.
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Kay, Alison L., Jonathan A. Sherratt, and J. B. McLeod. "Comparison theorems and variable speed waves for a scalar reaction–diffusion equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 5 (October 2001): 1133–61. http://dx.doi.org/10.1017/s030821050000130x.
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This paper concerns the reaction-diffusion equation ut = uxx + u2(1 − u). Previous numerical solutions of this equation have demonstrated various different types of wave front solutions, generated by different initial conditions. In this paper, the authors use a phase-plane form of comparison theorems for partial differential equations (PDEs) to confirm analytically these numerical results. In particular, they show that initial conditions with an exponentially decaying tail evolve to the unique exponentially decaying travelling wave, while initial conditions with algebraically decaying tails evolve either to an algebraically decaying travelling wave, or to the exponentially decaying wave, or to a perpetually accelerating wave, dependent upon the exact form of the decay of the initial conditions. We then focus on the case of accelerating waves and investigate their form in more detail, by approximating the full equation in this case with a hyperbolic PDE, which we solve using the method of characteristics. We use this approximate solution to derive a leading-order approximation to the wave speed.
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APPLEBY, JOHN A. D. "DECAY AND GROWTH RATES OF SOLUTIONS OF SCALAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY AND STATE DEPENDENT NOISE." Stochastics and Dynamics 05, no. 02 (June 2005): 133–47. http://dx.doi.org/10.1142/s0219493705001353.
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This paper studies the growth and decay rates of solutions of scalar stochastic delay differential equations of Itô type. The equations studied have a linear drift which contains an unbounded delay term, and a nonlinear diffusion term, which depends on the current state only. We show that when the nonlinearity at zero or infinity is sufficiently weak, the same non-exponential decay and growth rates found in the corresponding underlying linear deterministic equation are recovered, in an almost sure sense.
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Michioka, Takenobu, and Fotini Katopodes Chow. "High-Resolution Large-Eddy Simulations of Scalar Transport in Atmospheric Boundary Layer Flow over Complex Terrain." Journal of Applied Meteorology and Climatology 47, no. 12 (December 1, 2008): 3150–69. http://dx.doi.org/10.1175/2008jamc1941.1.
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Abstract This paper presents high-resolution numerical simulations of the atmospheric flow and concentration fields accompanying scalar transport and diffusion from a point source in complex terrain. Scalar dispersion is affected not only by mean flow, but also by turbulent fluxes that affect scalar mixing, meaning that predictions of scalar transport require greater attention to the choice of numerical simulation parameters than is typically needed for mean wind field predictions. Large-eddy simulation is used in a mesoscale setting, providing modeling advantages through the use of robust turbulence models combined with the influence of synoptic flow forcing and heterogeneous land surface forcing. An Eulerian model for scalar transport and diffusion is implemented in the Advanced Regional Prediction System mesoscale code to compare scalar concentrations with data collected during field experiments conducted at Mount Tsukuba, Japan, in 1989. The simulations use horizontal grid resolution as fine as 25 m with up to eight grid nesting levels to incorporate time-dependent meteorological forcing. The results show that simulated ground concentration values contain significant errors relative to measured values because the mesoscale wind typically contains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observations of arc maximum concentrations, however, lie within acceptable error bounds. In addition, this paper investigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, which have received little attention in the literature—in particular, for high-resolution applications. The choice of lateral boundary condition update interval is found not to affect time-averaged quantities but to affect the scalar transport strongly. More frequent updates improve the simulated ground concentration values. In addition, results show that the computational mixing coefficient must be set to as small a value as possible to improve scalar dispersion predictions. The predicted concentration fields are compared as the horizontal grid resolution is increased from 190 m to as fine as 25 m. The difference observed in the results at these levels of grid refinement is found to be small relative to the effects of computational mixing and lateral boundary updates.
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Lastdrager, Boris, Barry Koren, and Jan Verwer. "Solution of Time-dependent Advection-Diffusion Problems with the Sparse-grid Combination Technique and a Rosenbrock Solver." Computational Methods in Applied Mathematics 1, no. 1 (2001): 86–98. http://dx.doi.org/10.2478/cmam-2001-0006.
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Abstract In the current paper the efficiency of the sparse-grid combination tech- nique applied to time-dependent advection-diffusion problems is investigated. For the time-integration we employ a third-order Rosenbrock scheme implemented with adap- tive step-size control and approximate matrix factorization. Two model problems are considered, a scalar 2D linear, constant-coe±cient problem and a system of 2D non- linear Burgers' equations. In short, the combination technique proved more efficient than a single grid approach for the simpler linear problem. For the Burgers' equations this gain in efficiency was only observed if one of the two solution components was set to zero, which makes the problem more grid-aligned.
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CHEREMNYKH, O. K., J. W. EDENSTRASSER, and V. V. GORIN. "Relaxation of a non-ideal incompressible plasma with mass flow." Journal of Plasma Physics 62, no. 2 (August 1999): 195–202. http://dx.doi.org/10.1017/s0022377899007849.
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The time evolution of an incompressible non-ideal magnetohydrodynamic (MHD), current-carrying plasma with mass flow is investigated. An approach for the reduction of the nonlinear vector MHD equations to a set of scalar partial differential equations is supposed. Analytical time-dependent solutions of this system are presented. They describe kinetic plasma equilibria both with well-defined nested-in magnetic and velocity surfaces and in the form of vortices. The obtained solutions may be called ‘diffusion-like’, since their temporal structure is very similar to the solutions of the diffusion problem. It is shown that the magnetic field and the velocity have different dumping rates. In the asymptotic limit t→∞, the plasma slowly relaxes towards the hydrostatic equilibrium of gravitating systems.
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Aiyer, Aditya K., Kandaswamy Subramanian, and Pallavi Bhat. "Passive scalar mixing and decay at finite correlation times in the Batchelor regime." Journal of Fluid Mechanics 824 (July 11, 2017): 785–817. http://dx.doi.org/10.1017/jfm.2017.364.
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An elegant model for passive scalar mixing and decay was given by Kraichnan (Phys. Fluids, vol. 11, 1968, pp. 945–953) assuming the velocity to be delta correlated in time. For realistic random flows this assumption becomes invalid. We generalize the Kraichnan model to include the effects of a finite correlation time, $\unicode[STIX]{x1D70F}$, using renewing flows. The generalized evolution equation for the three-dimensional (3-D) passive scalar spectrum $\hat{M}(k,t)$ or its correlation function $M(r,t)$, gives the Kraichnan equation when $\unicode[STIX]{x1D70F}\rightarrow 0$, and extends it to the next order in $\unicode[STIX]{x1D70F}$. It involves third- and fourth-order derivatives of $M$ or $\hat{M}$ (in the high $k$ limit). For small-$\unicode[STIX]{x1D70F}$ (or small Kubo number), it can be recast using the Landau–Lifshitz approach to one with at most second derivatives of $\hat{M}$. We present both a scaling solution to this equation neglecting diffusion and a more exact solution including diffusive effects. To leading order in $\unicode[STIX]{x1D70F}$, we first show that the steady state 1-D passive scalar spectrum, preserves the Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) form, $E_{\unicode[STIX]{x1D703}}(k)\propto k^{-1}$, in the viscous–convective limit, independent of $\unicode[STIX]{x1D70F}$. This result can also be obtained in a general manner using Lagrangian methods. Interestingly, in the absence of sources, when passive scalar fluctuations decay, we show that the spectrum in the Batchelor regime at late times is of the form $E_{\unicode[STIX]{x1D703}}(k)\propto k^{1/2}$ and also independent of $\unicode[STIX]{x1D70F}$. More generally, finite $\unicode[STIX]{x1D70F}$ does not qualitatively change the shape of the spectrum during decay. The decay rate is however reduced for finite $\unicode[STIX]{x1D70F}$. We also present results from high resolution ($1024^{3}$) direct numerical simulations of passive scalar mixing and decay. We find reasonable agreement with predictions of the Batchelor spectrum during steady state. The scalar spectrum during decay is however dependent on initial conditions. It agrees qualitatively with analytic predictions when power is dominantly in wavenumbers corresponding to the Batchelor regime, but is shallower when box-scale fluctuations dominate during decay.
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Panna, Neelufar. "An Exact Solution of the Reaction-Diffusion Equation for the Speed of the Interface Propagation in Superconductors." Chittagong University Journal of Science 41, no. 1 (February 8, 2021): 85–95. http://dx.doi.org/10.3329/cujs.v41i1.51916.
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The speed of interface propagation in superconductors for the scalar reaction-diffusion equation ut = ∇2u+ F(u) is studied in detail. Here the non linear reaction term F (u) is the time-dependent Ginzburg-Landau or TDGL equation F(u)=u-u3 which describes the dynamics of the order-disorder transition. In contrast to what has been done in previous work [1] here an improved exact solution has derived by using TDGL equation to determine the speed of the front propagation. The analytical treatment of this study has been found in good agreement with the numerical simulation of V. Mendez et al. [2] and Di Bartolo and Dorsey [3].
The Chittagong Univ. J. Sci. 40(1) : 85-95, 2019
Dissertations / Theses on the topic "Scalar dependent diffusion"
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Larsson, Karl. "Scale-Space Methods as a Means of Fingerprint Image Enhancement." Thesis, Linköping University, Department of Science and Technology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2282.
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The usage of automatic fingerprint identification systems as a means of identification and/or verification have increased substantially during the last couple of years. It is well known that small deviations may occur within a fingerprint over time, a problem referred to as template ageing. This problem, and other reasons for deviations between two images of the same fingerprint, complicates the identification/verification process, since distinct features may appear somewhat different in the two images that are matched. Commonly used to try and minimise this type of problem are different kinds of fingerprint image enhancement algorithms. This thesis tests different methods within the scale-space framework and evaluate their performance as fingerprint image enhancement methods.
The methods tested within this thesis ranges from linear scale-space filtering, where no prior information about the images is known, to scalar and tensor driven diffusion where analysis of the images precedes and controls the diffusion process.
The linear scale-space approach is shown to improve correlation values, which was anticipated since the image structure is flattened at coarser scales. There is however no increase in the number of accurate matches, since inaccurate features also tends to get higher correlation value at large scales.
The nonlinear isotropic scale-space (scalar dependent diffusion), or the edge- preservation, approach is proven to be an ill fit method for fingerprint image enhancement. This is due to the fact that the analysis of edges may be unreliable, since edge structure is often distorted in fingerprints affected by the template ageing problem.
The nonlinear anisotropic scale-space (tensor dependent diffusion), or coherence-enhancing, method does not give any overall improvements of the number of accurate matches. It is however shown that for a certain type of template ageing problem, where the deviating structure does not significantly affect the ridge orientation, the nonlinear anisotropic diffusion is able to accurately match correlation pairs that resulted in a false match before they were enhanced.
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Men, Han (Han Abby). "Efficient reduced-basis approximation of scalar nonlinear time-dependent convection-diffusion problems, and extension to compressible flow problems." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39214.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.Includes bibliographical references (p. 61-65).
In this thesis, the reduced-basis method is applied to nonlinear time-dependent convection-diffusion parameterized partial differential equations (PDEs). A proper orthogonal decomposition (POD) procedure is used for the construction of reduced-basis approximation for the field variables. In the presence of highly nonlinear terms, conventional reduced-basis would be inefficient and no longer superior to classical numerical approaches using advanced iterative techniques. To recover the computational advantage of the reduced-basis approach, an empirical interpolation approximation method is employed to define the coefficient-function approximation of the nonlinear terms. Next, the coefficient-function approximation is incorporated into the reduced-basis method to obtain a reduced-order model of nonlinear time-dependent parameterized convection-diffusion PDEs. Two formulations for the reduced-order models are proposed, which construct the reduced-basis space for the nonlinear functions and residual vector respectively. Finally, an offline-online procedure for rapid and inexpensive evaluation of the reduced-order model solutions and outputs, as well as associated asymptotic a posterior error estimators are developed.
(cont.) The operation count for the online stage depends only on the dimension of our reduced-basis approximation space and the dimension of our coefficient-function approximation space. The extension of the reduced-order model to a system of equations is also explored.
by Han Men.
S.M.
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Allu, Pareekshith. "A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769.
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Srivastava, Shweta. "Stabilization Schemes for Convection Dominated Scalar Problems with Different Time Discretizations in Time dependent Domains." Thesis, 2017. http://etd.iisc.ernet.in/2005/3574.
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Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted meshes. The arbitrary Lagrangian- Eulerian (ALE) approach is a way to overcome this difficulty. Numerical simulations of convection-dominated problems have for long been the subject to many researchers. Galerkin formulations, which yield the best approximations for differential equations with high diffusivity, tend to induce spurious oscillations in the numerical solution of convection dominated equations. Though such spurious oscillations can be avoided by adaptive meshing, which is computationally very expensive on ne grids. Alternatively, stabilization methods can be used to suppress the spurious oscillations.
In this work, the considered equation is designed within the framework of ALE formulation. In the first part, Streamline Upwind Petrov-Galerkin (SUPG) finite element method with conservative ALE formulation is proposed. Further, the first order backward Euler and the second order Crank-Nicolson methods are used for the temporal discretization. It is shown that the stability of the semi-discrete (continuous in time) ALE-SUPG equation is independent of the mesh velocity, whereas the stability of the fully discrete problem is unconditionally stable for implicit Euler method and is only conditionally stable for Crank-Nicolson time discretization. Numerical results are presented to support the stability estimates and to show the influence of the SUPG stabilization parameter in a time-dependent domain.
In the second part of this work, SUPG stabilization method with non-conservative ALE formulation is proposed. The implicit Euler, Crank-Nicolson and backward difference methods are used for the temporal discretization. At the discrete level in time, the ALE map influences the stability of the corresponding discrete scheme with different time discretizations, and it leads to schemes where conservative and non-conservative formulations are no longer equivalent. The stability of the fully discrete scheme, irrespective of the temporal discretization, is only conditionally stable. It is observed from numerical results that the Crank-Nicolson scheme induces high oscillations in the numerical solution compare to the implicit Euler and the backward difference time discretiza-tions. Moreover, the backward difference scheme is more sensitive to the stabilization parameter k than the other time discretizations. Further, the difference between the solutions obtained with the conservative and non-conservative ALE forms is significant when the deformation of domain is large, whereas it is negligible in domains with small deformation.
Finally, the local projection stabilization (LPS) and the higher order dG time stepping scheme are studied for convection dominated problems. The analysis is based on the quadrature formula for approximating the integrals in time. We considered the exact integration in time, which is impractical to implement and the Radau quadrature in time, which can be used in practice. The stability and error estimates are shown for the mathematical basis of considered numerical scheme with both time integration methods. The numerical analysis reveals that the proposed stabilized scheme with exact integration in time is unconditionally stable, whereas Radau quadrature in time is conditionally stable with time-step restriction depending on the ALE map. The theoretical estimates are illustrated with appropriate numerical examples with distinct features. The second order dG(1) time discretization is unconditionally stable while Crank-Nicolson gives the conditional stable estimates only. The convergence order for dG(1) is two which supports the error estimate.
Book chapters on the topic "Scalar dependent diffusion"
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Bayly, Brian. "Deformation and Diffusion Compared." In Chemical Change in Deforming Materials. Oxford University Press, 1993. http://dx.doi.org/10.1093/oso/9780195067644.003.0017.
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The suggestion in view is that when volume is lost by diffusive mass transfer, the consequent shortening rate along some direction n is controlled by ∇2σnn regardless of the spatial variations in other stress components. The nature of the argument advanced is comparable with the one on which the theory of relativity is based: “At two separate points in a universe, it is not reasonable to suppose that the fundamental laws of behavior will be different at one point from the other.” If it is only in respect to some reference frame set up by an observer that point P differs from point Q, one should not expect behavior at P to differ from behavior at Q. It is convenient to use anthropomorphic phrasing: “If there is nothing intrinsic about point P to tell the material there to behave differently, the material at P will behave in the same way as the material at Q.” The theme of this chapter is that the material process for diffusive mass transfer is almost indistinguishable from the process for volume-conserving viscous change of shape at a point. In fact it will be argued that the two processes are so similar that it is not reasonable to suppose that behavior will be governed by different laws in the two modes: only an observer can distinguish one process from the other. Again anthropomorphically, “The moving material itself has no means of knowing which process it is involved in. Hence, if it is direction-dependent quantities such as σnn that control behavior in change of shape at a point, it must also be direction-dependent quantities such as σnn that control diffusive mass transfer.” In presenting the argument, it is convenient to imagine an atomic material for purposes of example, and for the sake of concreteness; but it is emphasized at the outset that the atoms are of minimal significance—the objective is a theory for a continuum. We wish to treat a continuum in which diffusion occurs, and even a continuum with only one component in which self-diffusion occurs, and most people find that this requires imagining division of the continuum into particles on some scale: but we need this division only in the most abstract sense, just enough to permit the idea that the continuum is self-diffusive.
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Queiros-Condé, Diogo, and Michel Feidt. "A Scale-Dependent Fractal and Intermittent Structure to Describe Chemical Potential and Matter Diffusion." In Fractal and Trans-scale Nature of Entropy, 181–217. Elsevier, 2018. http://dx.doi.org/10.1016/b978-1-78548-193-2.50006-x.
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Koch, Christof. "Unconventional Computing." In Biophysics of Computation. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195104912.003.0026.
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As discussed in the introduction to this book, any (bio)physical mechanism that transforms some physical variable, such as the electrical potential across the membrane, in such a way that it can be mapped onto a meaningful formal mathematical operation, such as delayand- correlate or convolution, can be treated as a computation. Traditionally only Vm, spike trains, and the firing rate f(t) have been thought to play this role in the computations performed by the nervous system. Due to the recent and widespread usage of high-resolution calcium-dependent fluorescent dyes, the concentration of free intracellular calcium [Ca2+]i in presynaptic terminals, dendrites, and cell bodies has been promoted into the exalted rank of a variable that can act as a short-term memory and that can be manipulated using buffers, calcium-dependent enzymes, and diffusion in ways that can be said to instantiate specific computations. But why stop here? Why not consider the vast number of signaling molecules that are localized to specific intra- or extracellular compartments to instantiate specific computations that can act over particular spatial and temporal time scales? And what about the peptides and hormones that are released into large areas of the brain or that circulate in the bloodstream? In this penultimate chapter, we will acquaint the reader with several examples of computations that use such unconventional means. The computation in question constitutes a molecular switch that stores a few bits of information at each of the thousands of synapses on a typical cortical cell. In order to describe its principle of operation, it will be necessary to introduce the reader to some basic concepts in biochemistry. The ability of individual synapses to potentially store analog variables is important enough that this modest intellectual investment will pay off. (For an introduction to biochemistry, consult Stryer, 1995).
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Epstein, Irving R., and John A. Pojman. "Polymer Systems." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0017.
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In the classic 1967 film “The Graduate” the protagonist, Benjamin (Dustin Hoffman), is attempting to plan his postcollege path. His neighbor provides one word of advice, “Plastics.” This counsel has become part of American culture and is often parodied. But, it is good advice, because not since the transformations from stone to bronze and then to iron have new materials so completely transformed a society. Plastics made from synthetic polymers are ubiquitous, from Tupperware to artificial hearts. About half the world’s chemists work in polymer-related industries. In this chapter, we will survey some of the work that has been done in applying nonlinear dynamics to polymerization processes. These systems differ from those we have considered so far because they do not involve redox reactions. We will consider polymerization reactions in a CSTR that exhibit oscillations through the coupling of temperature-dependent viscosity and viscosity-dependent rate constants. Emulsion polymerization, which produces small polymer particles dispersed in water, can also oscillate in a CSTR. Both types of systems are important industrially, and their stabilities have been studied by engineers with the goal of eliminating their time-dependent behavior. Our favorite oscillating system, the Belousov-Zhabotinsky reaction, can be used to create an isothermal periodic polymerization reaction in either a batch or continuous system. This, however, is not a practical system because of the cost of the reagents. In most industrial processes, nonlinear behavior is seen not as an advantage but as something to be avoided. However, we will look at several reaction-diffusion systems that have desirable properties precisely because of their nonlinear behavior. Replication of RNA is autocatalytic and can occur as a traveling front. Since not all RNA molecules replicate equally well, faster mutants gradually take over. At each mutation, the front propagates faster. Evolution can be directly observed in a test tube. Propagating polymerization fronts of synthetic polymers may be useful for making new materials, and they are interesting because of the rich array of nonlinear phenomena they show, with pulsations, convection, and spinning fronts. Finally, we will consider photopolymerization systems that exhibit spatial pattern formation on the micron scale, which can be used to control the macroscopic properties.
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Livesey, James. "Introduction." In Provincializing Global History, 1–16. Yale University Press, 2020. http://dx.doi.org/10.12987/yale/9780300237160.003.0001.
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This chapter talks about the elements of a new “thin” culture that was created in the European provinces in the eighteenth century. The capacity to manage change depended on the capacity for innovation, for reorientation to new values and ideas. It focuses on innovation particularly on the way new ideas created new kinds of cultural capacity. Global transformation at the beginning of the late eighteenth century was breath-taking in its scope. Growth rates in countries around the Atlantic began to rise and compound themselves annually as prices of a set of basic commodities became integrated across and between continents. Growth in trade networks was paralleled by the extension of public credit networks that stretched out to old empires and newly independent ex-colonies alike, imposing new disciplines and transforming politics. As new technologies lowered transport costs, they made possible exchanges on a new scale and intensity. The chapter also provides evidence that the diffusion of a profusion of manufactured objects and new experiences altered psychological character and the relationship of the species to the rest of nature. Commercial society promised, or threatened, to alter everything, even the foundations of human personality.
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Lee, Cheon-Pyo. "Mobile Business Applications." In Mobile Computing, 2163–68. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-054-7.ch174.
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As an increasing number of organizations and individuals are dependent on mobile technologies to perform their tasks, various mobile applications have been rapidly introduced and used in a number of areas such as communications, financial management, information retrieval, and entertainment. Mobile applications were initially very basic and simple, but the introduction of higher bandwidth capability and the rapid diffusion of Internet-compatible phones, along with the innovations in the mobile technologies, allow for richer and more efficient applications. Over the years, mobile applications have primarily been developed in consumer-oriented areas where products such as e-mail, games, and music have led the market (Gebauer & Shaw, 2004). According to the ARC group, mobile entertainment service will generate $27 billion globally by 2008 with 2.5 billion users (Smith, 2004). Even though mobile business (m-business) applications have been slow to catch on mobile applications for consumers and are still waiting for larger-scale usage, m-business application areas have received enormous attention and have rapidly grown. As entertainment has been a significant driver of consumer-oriented mobile applications, applications such as delivery, construction, maintenance, and sales of mobile business have been drivers of m-business applications (Funk, 2003). By fall of 2003, Microsoft mobile solutions partners had registered more than 11,000 applications including e-mail, calendars and contacts, sales force automation, customer relationship management, and filed force automation (Smith, 2004). However, in spite of their huge potential and benefits, the adoption of m-business applications appears much slower than anticipated due to numerous technical and managerial problems.
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Sharma, Sushil K. "Gender Inequalities for Use and Access of ICTs in Developing Countries." In Information Communication Technologies, 488–95. IGI Global, 2008. http://dx.doi.org/10.4018/978-1-59904-949-6.ch033.
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Internet, wireless, mobile, multi-media (voice, video, 3D), broadband, and other information and communication technologies (ICTs) are rapidly consolidating global communication networks and international trade with implications for people in developing countries. Extensive literature suggests that use of ICTs have a great impact on society for improving their economic means and life styles. However, various studies conducted in different regions of the world indicate that the advantages of ICTs have not reached all sections of society, particularly rural communities, and women. Women face many obstacles before they can harness the benefits of ICTs (Accascina, 2001; Alloo, 1998; The Commonwealth of Learning, 1998, 1999, 2000, 2001). Information and technology development, adoption, and access are far from adequate in developing countries. Large scale illiteracy and disabling environments, including uncompetitive markets, restrict opportunities to harness ICTs. For example; in India only 0.6% of the population uses the Internet and the penetration rate of the personal computer is only 1.2% (Hafkin & Taggart, 2001; Nath, 2001; World Bank Report, 2002). Information chasms follow socioeconomic divisions, particularly income and education disparities, separating well-connected elites from the less privileged who remain detached from information access and use. Most women within developing countries are on the lowest side of the divide, further removed from the information age as compared to the men whose poverty they share (Accascina, 2001; Nath, 2001; Tandon, 1998, The Commonwealth of Learning, 1998, 1999, 2000, 2001). If access and use of these technologies is directly linked to social and economic development, then it is imperative that women in developing countries be taken into consideration while developing ICT diffusion strategies. ICTs can be an important tool in meeting women’s basic needs and can provide the access to resources to involve women as equal partners in socio-economic development (Cole et al., 1994). Addressing gender issues in the ICTs sector has shown significant results where women have been made a part of ICT use and access. For example, women have benefited greatly from South Korea’s push to make higher education available online. In corporate South Korea, more than 35% of high-level IT positions are now held by women. In Africa, 70% of agricultural produce is handled by women (World Bank Report, 2002). By using farm radios, women farmers can obtain information in local languages on markets, agricultural inputs, food preservation, and storage without traveling far, or being dependent on a middleman. ICTs use and access by women can offer significant opportunities for them in developing countries, including poor women living in rural areas. However, their ability to take advantage of these opportunities is contingent upon conducive policies, an enabling environment to extend communications infrastructure to where women live, and increasing educational levels. It is now, particularly appropriate to ensure the inclusion of gender concerns in national IT policy, as most developing countries are either in the process of or about to start elaborating these policies (Accascina, 2001; Marcelle, 2000; Ponniah & Reardon, 1999; The Commonwealth of Learning, 1998, 1999, 2000, 2001). Women face considerably higher barriers in terms of literacy, access to education and information, productive and financial resources, and time. Many of the obstacles women face in accessing and using technology are entrenched in behavioral, cultural, and religious practices. Unless explicit measures are taken to address these divides, there is a risk that ICT will increase gender disparities and that the impact of ICTs will not be maximized. Integrating gender considerations into ICT strategies and policies will enable policy-makers and implementers to address these differences, which in turn will lead to remove gender inequalities for ICTs use and access (The Commonwealth of Learning, 1998, 1999, 2000, 2001).
Conference papers on the topic "Scalar dependent diffusion"
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El Afif, A., D. De Kee, R. Cortez, and D. P. Gaver. "Relationships Between Mass Transfer and Morphology in Deformable Complex Interfacial Systems." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32230.
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We propose a model for isothermal mass transport into immiscible complex fluids. The interface is described by two, space and time dependent, structural variables: a scalar Q(r,t) denoting the interfacial area density and a traceless symmetric second order tensor q(r,t) accounting for the shape anisotropy. The mass flux expression includes new contributions attributed to the dynamical changes of the interface. The diffusion-morphology coupling is found to influence both the mass transfer and the dynamics of the interface. The former exhibits non-Fickian behavior while the latter undergoes interfacial deformations that affect both its size and shape, creating internal stresses at the same time.
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Motie Shirazi, Mohsen, Omid Abouali, Homayoon Emdad, Mohammad Reza Nabavizade, Hossein Mirhadi, and Goodarz Ahmadi. "Numerical Investigation of Irrigant Penetration Into Dentinal Microtubules." In ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icnmm2014-21743.
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Root canal irrigation is an important procedure in endodontic treatment. After mechanical preparation of root canal, NaOCl, which is the most common antibacterial irrigant, is inserted by special needles. This work helps to remove bacteria and debris and dissolves the organic tissues in the root canal. In the vicinity of the main root canal, there are a large number of microchannels attached to its wall named “dentinal tubules”. The success of irragation depends on the penetration of irrigant in these tubules, which results in killing the bacteria and preventing complexities after root canal therapy. There is rather limited earlier research on modeling of dentinal tubules. Nevertheless, it has been shown that the flow rate, insertion depth and needle types affect the flow pattern in the root canal. The concentration difference between inserted irrigant and the liquid filling the tubules is the main driving force for penetration. Diffusion of irrigant, however, is a time dependent process and should be analyzed as an unsteady problem. In prior studies, the geometry was considered as cylinders with a constant diameter of 2.5μm and the effect of tapering was neglected. In reality the diameter varies from about 2.5μm near the pulp to about 1.5μm at the distance of 1 mm from the pulp. In the present study, a more detailed and exact model of dentinal tubules geometry was considered. The computational fluid dynamics (CFD) is used for the modeling of flow and diffusion of irrigant as a function of time. The unsteady and 3D continuity and Navier-Stokes equations as well as a scalar transport equation are solved and the flow field and the concentration of antibacterial irrigant were evaluated. The simulation results were compared to the earlier works. It was shown that the use of the correct detailed geometry of tubules led to noticeable differences compared to those found for the idealized model.
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Gonzalez, Andres, Zoya Heidari, and Olivier Lopez. "Electrical, Diffusional, and Hydraulic Tortuosity Anisotropy Quantification Using 3D CT-Scan Image Data." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/206109-ms.
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Abstract Depositional mechanisms of sediments and post-depositional process often cause spatial variation and heterogeneity in rock fabric, which can impact the directional dependency of petrophysical, electrical, and mechanical properties. Quantification of the directional dependency of the aforementioned properties is fundamental for the appropriate characterization of hydrocarbon-bearing reservoirs. Anisotropy quantification can be accomplished through numerical simulations of physical phenomena such as fluid flow, gas diffusion, and electric current conduction in porous media using multi-scale image data. Typically, the outcome of these simulations is a transport property (e.g., permeability). However, it is also possible to quantify the tortuosity of the media used as simulation domain, which is a fundamental descriptor of the microstructure of the rock. The objectives of this paper are (a) to quantify tortuosity anisotropy of porous media using multi-scale image data (i.e., whole-core CT-scan and micro-CT-scan image stacks) through simulation of electrical potential distribution, diffusion, and fluid flow, and (b) to compare electrical, diffusional, and hydraulic tortuosity. First, we pre-process the images (i.e., CT-scan images) to remove non-rock material visual elements (e.g., core barrel). Then, we perform image analysis to identify different phases in the raw images. Then, we proceed with the numerical simulations of electric potential distribution. The simulation results are utilized as inputs for a streamline algorithm and subsequent direction-dependent electrical tortuosity estimation. Next, we conduct numerical simulation of diffusion using a random walk algorithm. The distance covered by each walker in each cartesian direction is used to compute the direction-dependent diffusional tortuosity. Finally, we conduct fluid-flow simulations to obtain the velocity distribution and compute the direction-dependent hydraulic tortuosity. The simulations are conducted in the most continuous phase of the segmented whole-core CT-scan image stacks and in the segmented pore-space of the micro-CT-scan image stacks. Finally, the direction-dependent tortuosity values obtained with each technique are employed to assess the anisotropy of the evaluated samples. We tested the introduced workflow on dual energy whole-core CT-scan images and on smaller scale micro-CT-scan images. The whole-core CT-scan images were obtained from a siliciclastic depth interval, composed mainly by spiculites. Micro-CT-scan images we obtained from Berea Sandstone and Austin Chalk formations. We observed numerical differences in the estimates of direction-dependent electrical, diffusional, and hydraulic tortuosity for both types of image data employed. The highest numerical differences were observed when comparing electrical and hydraulic tortuosity with diffusional tortuosity. The observed differences were significant specially in anisotropic samples. The documented comparison provides useful insight in the selection process of techniques for estimation of tortuosity. The use of core-scale image data in the proposed workflow provides semi-continuous estimates of tortuosity and tortuosity anisotropy which is typically not attainable when using pore-scale images. Additionally, the semi-continuous nature of the tortuosity and tortuosity anisotropy estimates in whole-core CT-scan image data provides an excellent tool for the selection of core plugs coring locations.
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Groll, Rodion. "Mathematical Modeling of Binary Nano Scale Diffusion of Molecular Gas Suspensions in Liquid Media." In ASME 2007 5th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2007. http://dx.doi.org/10.1115/icnmm2007-30092.
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A model describing the suspension diffusion process of gas molecules in liquid media is presented in this paper. This process is not yet solved by a satisfactory model for micro-scale applications at this time. The new model allows the simulation of diffusion processes in continuous media considering the molecular mass flux in a suspension/carrier phase mixture. Modelling the diffusion of gas suspensions in liquid media the saturation mass ratio is reached near the liquid/gas surface very quickly. The increase of gas concentration in the liquid domain depends on the elapsed time and the physical properties of gas and liquid media. The molecular gas velocity is described by a Maxwell probability density function. Based on this spectral method macroscopic physical values are modelled to describe time-dependent global concentration changes. Modelling the gas species diffusion the molecular convection is considered. Modelling the mass flux of the molecular gas suspension characteristic time scales are developed describing the completion level of the saturation progress based on non-dimensional formulations of the molecular convection equation. The present model is implemented in a CFD code and validated by a family of parametric simulation results depending on the saturation mass ratio of the suspended gas phase. This simulation result array shows the dependency of saturation time and saturation mass ratio of the suspended gas molecules. Based on this relation macroscopic diffusion processes in micromixers and microchannels are described with this model and without an extra solution of molecule trajectories or spectral fields of molecule velocity.
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Pacheco, J. Rafael, KangPing Chen, and Arturo Pacheco-Vega. "Rate of Decay of a Passive Scalar in a Micro-Mixer and the Frequency of the Advecting Velocity Fields." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88626.
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In the current work, the mixing of a diffusive passive-scalar, e.g., thermal energy or species concentration, driven by electro-osmotic fluid motion being induced by an applied potential across a micro-channel is studied numerically. Secondary time-dependent periodic or random electric fields, orthogonal to the main stream, are applied to generate cross-sectional mixing. This investigation focuses on the mixing dynamics and its dependence on the frequency (period) of the driving mechanism. For periodic flows, the probability density function (PDF) of the scaled passive scalar (i.e., concentration), settles into a self-similar curve showing spatially repeating patterns. In contrast, for random flows there is a lack of self-similarity in the PDF for the interval of time considered in this investigation. The present study confirms an exponential decay of the variance of the concentration for the periodic and random flows.
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Shibahara, Masahiko, and Kiyoshi Takeuchi. "A Molecular Dynamics Study on the Effects of Nanostructural Clearances on Thermal Resistance at a Liquid-Solid Interface." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22152.
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The effects of the surface structures and the surface structural clearances at the nanometer scale on the thermal resistance at a liquid water-solid interface, as well as the self-diffusion behaviors of liquid molecules, were investigated directly by the non-equilibrium classical molecular dynamics simulations. When the potential parameter between liquid molecules and nanostructure atoms is equal to that between liquid molecules and solid wall atoms, the geometric surface area change depending on the nanostructures as well as their clearances and the self-diffusion coefficient change of the liquid molecules at the interface depending on the nanostructural clearances cause the thermal resistance change depending on the nanostructures at the liquid-solid interface. When the potential parameter between liquid molecules and nanostructure atoms is different from that between liquid molecules and solid wall atoms, the interfacial thermal resistance is dependent on the potential parameter between liquid molecules and nanostructure atoms itself rather than the geometric surface area in a molecular scale.
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Qaddoura, Rabab, Mohammed Aldhuhoori, Hamda Alkuwaiti, and Hadi Belhaj. "Modeling Fluid Flow in Tight Unconventional Reservoirs: Micro/Nano Scale Approach." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18470.
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Abstract The need for a tool to predict transport phenomena in petroleum unconventional tight reservoirs is placing more stringent demand on establishing more realistic models beyond the currently used viscous and inertial dependent models. Since diffusion is the principal mechanism in tight unconventional reservoirs that take place in both Micro and Nano scales, a diffusive term was added to the diffusivity model that operates both viscous and inertial forces, introduced by (Belhaj, et al., 2003). This diffusive term is a modified Fick’s 1st Law. It counts for the flow velocity caused by the diffusion process. Using the three-term model as a rate equation, in addition to the continuity equation and the EOS, a new model (a form of PDE) has been developed. The new model works ideally in unconventional tight reservoirs where oil and/or gas flow. The model has been numerically solved and tested. A comprehensive parametric study has been conducted and revealed clear trends. It has been concluded that diffusion mechanism contribution to flow increases with low permeability of the medium and low viscosity of the flowing fluid. An index (a combination of permeability and viscosity) has been developed and used to verify the influence and impact of the diffusion forces.
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Jevremovic, Tatjana, Mathieu Hursin, Nader Satvat, John Hopkins, Shanjie Xiao, and Godfree Gert. "Performance, Accuracy and Efficiency Evaluation of a Three-Dimensional Whole-Core Neutron Transport Code AGENT." In 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/icone14-89561.
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The AGENT (Arbitrary GEometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) the theory of R-functions used to generate real three-dimensional whole-cores of square, hexagonal or triangular cross sections, (2) the planar method of characteristics used to solve isotropic neutron transport in non-homogenized 2D) reactor slices, and (3) the one-dimensional diffusion theory used to couple the planar and axial neutron tracks through the transverse leakage and angular mesh-wise flux values. The R-function-geometrical module allows a sequential building of the layers of geometry and automatic submeshing based on the network of domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through a set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: Coarse Mesh Rebalancing (CMR) and Coarse Mesh Finite Difference (CMFD). The stand-alone originally developed graphical user interface of the AGENT code design environment allows the user to view and verify input data by displaying the geometry and material distribution. The user can also view the output data such as three-dimensional maps of the energy-dependent mesh-wise scalar flux, reaction rate and power peaking factor. The AGENT code is in a process of an extensive and rigorous testing for various reactor types through the evaluation of its performance (ability to model any reactor geometry type), accuracy (in comparison with Monte Carlo results and other deterministic solutions or experimental data) and efficiency (computational speed that is directly determined by the mathematical and numerical solution to the iterative approach of the flux convergence). This paper outlines main aspects of the theories unified into the AGENT code formalism and demonstrates the code performance, accuracy and efficiency using few representative examples. The AGENT code is a main part of the so called virtual reactor system developed for numerical simulations of research reactors. Few illustrative examples of the web interface are briefly outlined.
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Volkov, Dmitry V., Alexandr A. Belokon, Dmitry A. Lyubimov, Vladimir M. Zakharov, and George Opdyke. "Flamelet Model of NOx in a Diffusion Flame Combustor." In ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0099.
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This paper describes a model used for the prediction of the formation of nitrogen oxides in modifications of an industrial diffusion flame, natural gas fueled can combustor. The flow field inside the modified combustors is calculated using a Navier-Stokes solver. A fast chemistry assumption is used for modeling the heat release. Calculated turbulence parameters are then used for the calculation of the NOx formation rate in the post-processing mode with the aid of a flamelet model. The flamelet model permits the use of detailed kinetics with only minimal computational expense. The dependence of the NOx formation rate on the mixture fraction and scalar dissipation is calculated separately for each given condition. The validation of the model predictions is based on field test data taken earlier on several low NOx modifications recently applied to an industrial, reverse flow can type combustor. The reduced level of NOx emissions was achieved in these modifications by changes in the air distribution within the combustor liner. A comparison of the predicted and measured NOx emission levels shows good potential of the flamelet model.
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Ji, Pengfei, Mengzhe He, Yiming Rong, Yuwen Zhang, and Yong Tang. "Multiscale Investigation of Thickness Dependent Melting Thresholds of Nickel Film Under Femtosecond Laser Heating." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86947.
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A multiscale modeling that integrates electronic scale ab initio quantum mechanical calculation, atomic scale molecular dynamics simulation, and continuum scale two-temperature model description of the femtosecond laser processing of nickel film at different thicknesses is carried out in this paper. The electron thermophysical parameters (heat capacity, thermal conductivity, and electron-phonon coupling factor) are calculated from first principles modeling, which are further substituted into molecular dynamics and two-temperature model coupled energy equations of electrons and phonons. The melting thresholds for nickel films of different thicknesses are determined from multiscale simulation. Excellent agreement between results from simulation and experiment is achieved, which demonstrates the validity of modeled multiscale framework and its promising potential to predict more complicate cases of femtosecond laser material processing. When it comes to process nickel film via femtosecond laser, the quantitatively calculated maximum thermal diffusion length provides helpful information on choosing the film thickness.
Reports on the topic "Scalar dependent diffusion"
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H. Liu, Q. Zhou, and Y. Zhang. POTENTIAL SCALE DEPENDENCE OF EFFECTIVE MATRIX DIFFUSION COEFFICIENT. Office of Scientific and Technical Information (OSTI), March 2006. http://dx.doi.org/10.2172/886038.
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H.H. Liu and Y. Zhang. Scale Dependence of Effective Matrix Diffusion Coefficient Evidence and Preliminary Interpertation. Office of Scientific and Technical Information (OSTI), June 2006. http://dx.doi.org/10.2172/893877.
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