Dimensional Diffusion Research Articles

Neutronic studies for the second Egyptian research reactor ET-RR-2

Abstract The start up physics studies SPS of the Second Egyptian Research Reactor is presented in this work. The SPS consists of the approach to criticality, the power and flux distribution of the first critical core, criticality, power and flux distribution of the working core. The working core is the beryllium-reflected core with cobalt loaded for irradiation. Some of the neutronic parameters are determined, these parameters are the power peaking factor, power distribution, the excess reactivity for both the water and beryllium reflector cores, the core excess reactivity with the cobalt loaded, the reactivity worth of the cobalt irradiation box. Flux distribution for one fast, three eipthermal and one thermal energy group are also determined. All the above neutronic parameters are calculated by using the lattice cell code WIMSD4 and the two dimensional diffusion code DIXY2.

Part I: Hydrological properties within the eastern Indonesian throughflow region during the INDOMIX experiment

The Indonesian Mixing (INDOMIX) cruise of July 2010, resolves the Pacific Ocean water masses spreading from the Halmahera Sea through the Seram Sea, Manipa Strait, Banda Sea, to the Ombai Strait, and along the southern margin of Lesser Sunda Arc across the northern Savu Sea, Sumba Strait, and south of Lombok Strait. This paper focuses on the characteristics and stratification of the water masses, along this path and Part II of this study discusses the biogeochemical aspects. Two companion papers on quantification of turbulent mixing have been published elsewhere. We find: a) A marked transformation of South Pacific (SP) thermocline water within a sharp salinity front between the Halmahera Seram Seas. Tidally induced vertical mixing is the main process weakening the SP stratification, as suggested by a simple 1-dimensional diffusion model forced by vertical diffusivity of INDOMIX vertical microstructure profiler dataset. The transformation of SP water by vertical mixing can occur after 3 days, which is in good agreement with previously reported water mass residence times. Lateral advection plays a minor role; b) Interleaving salinity structure within the thermocline of the central Halmahera Sea and two deeper inflow channels. The interleaving salinity features within the central Halmahera Sea thermocline occurs where vertical diffusivity is relatively weak, compared to the vertical mixing at entry/exit portal that removes the interleaving salinity features. Two deeper inflow channels (about 950 m and 740 m depth) in the entry portal of the Halmahera Sea are mapped from the multi-beam echo sounder measurement, where both channels allow the renewal of SP thermocline water and salinity interleaving processes; c) Northward flow of thermocline water (100–200 m depth) in the Manipa Strait that injects Banda homogeneous salinity water into Seram Sea that erode Halmahera salty water via strong diapycnal mixing; d) Cyclonic upper layer circulation in Banda where eastward (westward) flow occurs in the northern (southern) Banda, confirmed by recent modeling study; and e) Relative salty Indian Ocean intermediate water flowing along southern margin of the Lesser Sunda Arc, within the South Java Undercurrent. Two distinct upper thermocline water, due to different source of Indonesian Throughflow (ITF) water, are found in the Banda Sea: fresher and colder water contrasting to saltier and warmer water that converge in this confluence region. Beneath it, Banda intermediate homogeneous salinity water and low dissolved oxygen water is dominant.

On the effects of CO2 atmosphere in the pyrolysis of Salicornia bigelovii

This study focuses on understanding the effects of a CO2 atmosphere on the pyrolysis of Salicornia bigelovii by performing a detailed kinetic analysis and investigating the pyrolysis products. In comparison to N2 pyrolysis, CO2 pyrolysis increased the amounts of acids, phenols, amines/amides and N-aromatics in the bio-oil. Biochar showed a 6.5% increase in carbon and a 5.8% decrease in oxygen due to the presence of CO2 in the pyrolysis atmosphere. CO2 also inhibited the volatilization of certain functional groups, such as phenols, tertiary alcohols and aromatics from the biochar, and the surface area of the biochar was 12 times larger than pyrolysis in N2 atmosphere. Pyrolysis in CO2 led to an increase in the average apparent activation energy from 146.5 kJ mol−1 in N2 to 163.4 kJ mol−1. The kinetic equation was found to conform to a three dimensional diffusion mechanism. Finally, the pre-exponential factor was determined for each reaction.

Joint Online Parameter Estimation and Optimal Sensor Placement for the Partially Observed Stochastic Advection-Diffusion Equation

In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the form of a continuous-time, two-timescale stochastic gradient descent algorithm, which recursively seeks to maximise the log-likelihood with respect to the unknown model parameters, and to minimise the expected mean squared error of the hidden state estimate with respect to the sensor locations. We also provide extensive numerical results illustrating the performance of the proposed approach in the case that the hidden signal is governed by the two-dimensional stochastic advection-diffusion equation.

Sodium diffusion and dynamics in Na2Ti3O7: neutron scattering and ab initio simulations

Low dimensional sodium diffusion preferentially through interstitial sites.

Improved data efficiency for NMR diffusion-relaxation processing

Two dimensional diffusion and transverse (T2) NMR relaxation measurements are effective for a variety of research and industrial processes. Conversion of the measurements into a D-T2 map is performed using an inverse integral transformation. A difficulty with D-T2 estimation from data acquired without pulsed field gradients (using, for example, the inherent static field gradient of a single-sided magnet) is that the diffusion and relaxation kernels are coupled. One commonly used solution is to introduce a time offset to enable the kernels to be decoupled, but this has the undesirable results of causing some of the data, and a large proportion of the signal energy, to become unusable. This paper presents two methods of processing the data that do not require this wastage. Both methods are based on insights that arise from considering the linear operator that describes the forwards integral transformation. One method involves data compression, while the other method is an application (that we call FLINT) of the fast iterative soft thresholding algorithm. Both methods are able to use all of the available data. The paper demonstrates the improved accuracy that results from these methods on simulated data, as well as the improved discovery of important features on measured data.

A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients

In this paper, an efficient cell-centered extrapolation cascadic multigrid (CEXCMG) method is proposed for solving large linear system of equations resulting from finite volume (FV) discretizations of three dimensional (3D) anisotropic diffusion equations with discontinuous coefficients. For cell-centered FV schemes, the values at vertex need to be approximated often by a linear combination of neighboring cell-centered values. In the literature, the weighted coefficients are obtained by solving local linear system of equations which is costly in 3D. One of the novelties of this paper is a new approach for obtaining vertex values by interpolating the cell-centered ones, which avoids solving local linear system of equations even with arbitrary diffusion tensors. Another main novelty of this paper is a new cascadic multigrid solver based on a prolongation operator, the newly developed explicit gradient transfer method, and a splitting extrapolation operator for solving 3D anisotropic diffusion equations with discontinuous coefficients. Numerical experiments are presented to demonstrate the efficiency and robustness of the CEXCMG method in terms of the mesh size and the contrast in the coefficients of the anisotropic diffusion tensor.

The electro-chemical properties and intercalation mechanism of low strain Li2TiO3 as a high-performance anode material for lithium-ion batteries

In this article, the sol-gel synthesized β-Li2TiO3, referred to as sg-β-Li2TiO3, exhibits superior electro-chemical performance, compared with the theoretical specific capacities of frequently investigated Titanium based oxides, for example, LiTiO2 (143 mAh g-1), Li4Ti5O12 (175 mAh g-1) and Li2Ti3O7 (198 mAh g-1). It delivers a considerable specific capacity of more than 200 mAh g-1 within 100 cycles and close to 200 mAh g-1 after 200 cycles and preserves coulombic efficiency above 97% for all the cycles. After more than 500 cycles, the reversible specific capacity of sg-β-Li2TiO3 is more than 170 mAh g-1 and a less than 2% capacity degeneration is observed for the followed several hundreds of cycles. DFT calculations and MD simulations show 8 f void mediated diffusion comprise the two dimensional diffusion layer on a-b plane and the neighboring diffusion layers are interconnected by two 8 f voids via a Li2 atom. Low energy barriers and high Li+ activities are observed. Three intermediate phases, corresponding to intercalation level x = 0.5, 0.75 and 0.875 in β-Li2+xTiO3, are identified for the intercalation process with the maximal intercalation level 0.875. Both ex-situ XRD and theoretical calculations reveal low volume change or strain less than 5% in the intercalation process. Also, an insulator-metal transition upon lithiation is observed by the electronic structure analysis.

Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Hoegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

3D heat flow effects in the imaging of subsurface graphical features in semi-transparent media by pulsed thermography

Pulsed thermography has proven to be a useful tool to detect subsurface features in ancient bookbindings and, in particular, to provide the IR image of texts buried beneath the end-leaves of the books. In this paper the theory is presented to analyze the influence of the geometrical and physical parameters involved in the processes leading to the distortion in the IR image of the detected buried graphical features. The distortion is mainly due to the lateral diffusion of the heat generated at the ink feature after the absorption of an excitation light. A comprehensive analysis taking into account the three dimensional heat diffusion process, in an optically semi-transparent medium, is considered. Numerical results are reported showing the behavior of the contrast and of a distortion parameter of the buried inked feature detected by the IR imaging in the various considered cases.

Collocation method for one dimensional nonlocal diffusion equations

In this paper, the collocation method for solving one dimensional steady state and time dependent nonlocal diffusion equations is analyzed. The difficulty of applying collocation method to nonlocal diffusion equations comes from the singularity of the kernel. If the kernel is weakly singular, however, if the kernel is not integrable in Riemann sense. So that the Hadamard finite part integral is introduced to overcome this difficulty. For analysis and performance, a “balance” term is added to discretize the nonlocal operator. Numerical results validate the theorems.

Study of kinetic and thermal decomposition from municipal solid waste pellets using model-fitting methods

Reaction rate model could be determined from kinetic characteristics. Kinetic and thermal decomposition of municipal solid waste (MSW) pellets, consist of organic material, plastic, paper and leaves, with tapioca flour as binder (0%, 3% and 6%) were studied in thermogravimetric analyzer from temperature 50°C to 800°C at heating rate 10 0C/min in N2 atmospheres. The kinetic parameter were determined by Model Fitting or Coats Redfern Methods with different kinetic reaction model. Results of this study have shown that MSW pellets in various binder has activation energy values 64.64 kJ/mol and 22.06 kJ/mol for 0%, 68.83 kJ/mol and 21.99 kJ/mol for 3%, and 69.29 kJ/mol and 22.62 kJ/mol for 6% at temperature ranges between 200°C-400°C and 400°C-500°C respectively in typical three dimensional diffusion (D3) mechanism kinetic reaction model.

The law of large numbers for quantum stochastic filtering and control of many-particle systems

There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Scrodinger equations or Hartree equations, or Gross-Pitaevski equations. In this paper we extend some of these convergence results to a stochastic framework. Concretely we work with the Belavkin stochastic filtering of many particle quantum systems. The resulting limiting equation is an equation of a new type, which can be seen as a complex-valued infinite dimensional nonlinear diffusion of McKean-Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.

The law of large numbers for quantum stochastic filtering and control of many-particle systems

Существует обширная литература, где рассматривается динамический закон больших чисел для систем квантовых частиц, т. е. выводится уравнение, описывающее предельное поведение отдельных частиц внутри большого ансамбля одинаковых взаимодействующих частиц. Полученные уравнения обычно называют нелинейными уравнениями Шредингера, или уравнениями Хартри, или уравнениями Гросса-Питаевского. Дано стохастическое обобщение некоторых из этих результатов, касающихся сходимости. Рассмотрена стохастическая фильтрация Белавкина для многочастичных квантовых систем. Полученное предельное уравнение - это уравнение нового типа, которое можно трактовать как комплекснозначную бесконечномерную нелинейную диффузию типа Маккина-Власова. Этот результат является ключевым для теории квантовых игр среднего поля, разработанной автором в предыдущей работе.

Molecular dynamics simulations of oxide ion migration in La2Ga3O7.5 with completely ordered interstitial oxide ions

Molecular dynamics simulations were performed on metastable La2Ga3O7.5 melilite ceramics, which were synthesized previously by direct crystallization of an under-cooled melt. La2Ga3O7.5 possesses the theoretically maximum content of interstitial oxide ions featuring complete ordering but ~3 orders of magnitude lower oxide ion conductivities compared with disordered La1·54Sr0.46Ga3O7.27 within 573–773 ​K. One dimensional diffusion paths of interstitial oxide ion was identified in La2Ga3O7.5 based on the molecular dynamics simulations, which shows that the interstitial oxide ions can migrate from the pentagonal ring containing GaO5 pyramid unit to its neighboring pentagonal ring free of interstitial oxide ion mainly along the a axis through a synergic mechanism involving continuous breaking and reformation of Ga2O8 units assisted by rotation and deformation of GaOn polyhedra and knock-on process between interstitial and framework oxygen atoms. Such constrained dimensionality on the diffusion paths arising from the confining effect for a large number of oxygen interstitials in the highly relaxed and ordered melilite superstructure accounts for the lower oxide ion conductivity in La2Ga3O7.5.

A new numerical scheme for solving the two dimensional fractional diffusion equation

A new numerical scheme for solving the two dimensional fractional diffusion equation

The Explicit Formula for Solution of Anomalous Diffusion Equation in the Multi-Dimensional Space

This paper intends on obtaining the explicit solution of $$n$$ -dimensional anomalous diffusion equation in the infinite domain with non-zero initial condition and vanishing condition at infinity. It is shown that this equation can be derived from the parabolic integro-differential equation with memory in which the kernel is $$t^{-\alpha}E_{1-\alpha,1-\alpha}(-t^{1-\alpha})$$ , $$\alpha\in(0,1),$$ where $$E_{\alpha,\beta}$$ is the Mittag-Liffler function. Based on Laplace and Fourier transforms the properties of the Fox H-function and convolution theorem, explicit solution for anomalous diffusion equation is obtained.

Monte Carlo Method to Solve Diffusion Equation and Error Analysis

Three different mathematical approaches for the evolution of diffusion equation are presented. The evolution process of the diffusion equation is explained by principle of conservation law, probability distribution procedure, and finally though stochastic differential equation (SDE) driven by Brownian motion. The Monte Carlo method is discussed to solve the diffusion equation by generating the normally distributed random numbers and the root mean square error is derived for the Monte Carlo method. The numerical solutions are computed for 1-dimensional diffusion equation and results are compared with exact solution. Finally, theoretical root mean square error is compared with the maximum error and the L2-error by increasing the number of simulated points.

Green's functions, linear second‐order differential equations, and one‐dimensional diffusion advection models

AbstractGreen's functions to linear second‐order ordinary differential equations with general separated boundary conditions (BCs) are derived, where the parameters used in the BCs are allowed to take negative values. Previous results only considered the nonnegative parameters and such separated BCs arise in the usual Thomas–Fermi BCs. Properties of the Green's functions with possibly negative parameters are obtained and are new. As applications, we study the steady‐state solutions of the one‐dimensional diffusion advection models arising in chemical reactor theory and mathematical biology. We exhibit that the BCs arising from the one‐ dimensional diffusion advection models contain negative parameters.

High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions

For the two dimensional anisotropic diffusion problems, we postprocess the k-th order finite element solution to satisfy the local conservation law on a certain dual mesh. The postprocessing technique is independently implemented by solving a 3-by-3 and 4-by-4 local linear algebraic system on each triangular and quadrilateral element, respectively. For any full anisotropic diffusion tensors, and arbitrary triangular and trapezoidal meshes, the existence and uniqueness of the postprocessed solutions are proved theoretically. Consequently, some existing results are improved, and the traditional h1+γ-parallelogram assumption is replaced with a more general one. The optimal H1 and L2 norm error estimates of the postprocessed solutions are also proved. Finally, some numerical experiments are presented to validate the theoretical findings.