Wide Range Of Initial Values Research Articles

A Modified JFNK for Solving the HTR Steady State Secondary Circuit Problem

A nuclear power plant is a complex coupling system, which features multi-physics coupling between reactor physics and thermal-hydraulics in the reactor core, as well as the multi-circuit coupling between the primary circuit and the secondary circuit by the shared steam generator (SG). Especially in the pebble-bed modular HTR nuclear power plant, different nuclear steam supply modules are further coupled together through the shared main steam pipes and the related equipment in the secondary circuit, since the special configuration of multiple reactor modules connects to a steam turbine. The JFNK (Jacobian-Free Newton–Krylov) method provides a promising coupling framework to solve the whole HTR nuclear power plant problem, due to its excellent convergence rate and strong robustness. In this work, the JFNK method was modified and applied to the steady-state calculation of the HTR secondary circuit, which plays an important role in simultaneous solutions for the whole HTR nuclear power plant. The main components in the secondary circuit included SG, steam turbine, condenser, feed pump, high/low-pressure heat exchanger, deaerator, as well as the extraction steam from the steam turbine. The results showed that the JFNK method can effectively solve the steady state issue of the HTR secondary circuit. Moreover, the JFNK method could converge well within a wide range of initial values, indicating its strong robustness.

Calculation of thermal conductivity coefficient of a binary mixture

A correct consideration of the thermal factors during the design phase of civil engineering structures in the permafrost area determines their reliable and safe exploitation. Among the important indicators in selection of design solutions is the thermal conductivity coefficient of the construction materials used. The thermal conductivity coefficient is usually chosen from reference tables, but when using mixtures, the thermal conductivity coefficient is determined through a calculation. The aim of the present research was to compare the calculated values of thermal conductivity coefficient of binary mixtures (a mixture of a binding material and a filler) obtained using Lichtenecker and Schwerdtfeger formulas. The comparison was conducted in the range of properties of materials used for thermal accumulation and thermal insulation mixtures. It was determined that for thermal accumilation binary mixtures the calculation results are quite similar within a wide range of initial values. For thermal insulation binary mixtures, the calculation results are significantly different. The divergencies are by hundreds of percents. At the current stage of research it is impossible to make a conclusion about suitability of either calculation method to determine the thermal conductivity of a thermal insulation binary mixture.

A modified JFNK with line search method for solving k-eigenvalue neutronics problems with thermal-hydraulics feedback

The k-eigenvalue neutronics/thermal-hydraulics coupling calculation is a key issue for reactor design and analysis. Jacobian-free Newton-Krylov (JFNK) method, featured with super-linear convergence rate and high efficiency, has been attracting more and more attention to solve the multi-physics coupling problem. However, it may converge to the high-order eigenmode because of the multiple solutions nature of the k-eigenvalue form of multi-physics coupling issue. Based on our previous work, a modified JFNK with a line search method is proposed in this work, which can find the fundamental eigenmode together with thermal-hydraulics feedback in a wide range of initial values. In detail, the existing modified JFNK method is combined with the line search strategy, so that the intermediate iterative solution can avoid a sudden divergence and be adjusted into a convergence basin smoothly. Two simplified 2-D homogeneous reactor models, a PWR model, and an HTR model, are utilized to evaluate the performance of the newly proposed JFNK method. The results show that the performance of this proposed JFNK is more robust than the existing JFNK-based methods.

A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

JFNK method has been used to solve the k-eigenvalue fundamental eigenmode problem recently, due to excellent local convergence rate and its promising application in multi-physics coupling problems. However, JFNK method is usually sensitive to the choice of initial values and may converge to high-order eigenmode. To enable JFNK method converge to fundamental eigenmode within a wide range of initial values, a modified JFNK method is proposed in this work. Based on physical-based information, two simple but practical modifications are utilized on eigenvector and k-eigenvalue respectively, which could adjust intermediate iterative solution into convergence basin of fundamental eigenmode. Four well-known k-eigenvalue benchmarks, as well as a k-eigenvalue problem with temperature feedback, are utilized to evaluate the performance of this modified JFNK method. The results show that the performance of modified JFNK method is significantly prior to that of traditional JFNK method, which can converge to the fundamental eigenmode globally.

Investigation of Error Distribution in the Back-Calculation of Breakage Function Model Parameters via Nonlinear Programming

Despite its effectiveness in determining breakage function parameters (BFPs) for quantifying breakage characteristics in mineral grinding processes, the back-calculation method has limitations owing to the uncertainty regarding the distribution of the error function. In this work, using Korean uranium and molybdenum ores, we show that the limitation can be overcome by searching over a wide range of initial values based on the conjugate gradient method. We also visualized the distribution of the sum of squares of the error in the two-dimensional parameter space. The results showed that the error function was strictly convex, and the main problem in the back-calculation of the breakage functions was the flat surface of the objective function rather than the occurrence of local minima. Based on our results, we inferred that the flat surface problem could be significantly mitigated by searching over a wide range of initial values. Back-calculation using a wide range of initial values yields BFPs similar to those obtained from single-sized-feed breakage tests (SSFBTs) up to four-dimensional parameter spaces. Therefore, by searching over a wide range of initial values, the feasibility of the back-calculation approach can be significantly improved with a minimum number of SSFBTs.

Preinflationary Dynamics of Power-Law Potential in Loop Quantum Cosmology †

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential V ( ϕ ) ∝ ϕ n with n = 5 / 3 in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-singular quantum bounce. In the case of the kinetic energy-dominated initial conditions of the scalar field at the bounce, the numerical evolution of the Universe can be split up into three regimes: bouncing, transition, and slow-roll inflation. In the bouncing regime, the numerical evolution of the scale factor does not depend on a wide range of initial values, or on the inflationary potentials. I calculate the number of e-folds in the slow-roll regime, by which observationally identified initial conditions are obtained. Additionally, I display the phase portrait for the model under consideration.

New Approach to Resources Monitoring for Transport and Infrastructure Construction

Resources monitoring in the market economy is carried out to determine current market prices. Market pricing depends on a huge list of factors and in each case is carried out in a wide range of initial values with high probability assumptions. This approach is based on a set of organizational and economic mechanisms allowing tracking not potential, but real purchase and sale of construction resources. Systematization the received information allows planning and implementation of state construction contracts in the field of transport and other dispersed construction.

Development of Organizing and Economic Measures for Monitoring the Cost of Construction Resources

Resources monitoring in the market economy is carried out to determine current market prices. Market pricing depends on a huge list of factors and in each case is carried out in a wide range of initial values with high probability assumptions. This approach is based on a set of organizational and economic mechanisms allowing tracking not potential, but real purchase and sale of construction resources. Systematization the received information allows planning and implementation of state construction contracts in the field of transport and other dispersed construction.

Upper ocean oxygenation dynamics from I/Ca ratios during the Cenomanian‐Turonian OAE 2

AbstractGlobal warming lowers the solubility of gases in the ocean and drives an enhanced hydrological cycle with increased nutrient loads delivered to the oceans, leading to increases in organic production, the degradation of which causes a further decrease in dissolved oxygen. In extreme cases in the geological past, this trajectory has led to catastrophic marine oxygen depletion during the so‐called oceanic anoxic events (OAEs). How the water column oscillated between generally oxic conditions and local/global anoxia remains a challenging question, exacerbated by a lack of sensitive redox proxies, especially for the suboxic window. To address this problem, we use bulk carbonate I/Ca to reconstruct subtle redox changes in the upper ocean water column at seven sites recording the Cretaceous OAE 2. In general, I/Ca ratios were relatively low preceding and during the OAE interval, indicating deep suboxic or anoxic waters exchanging directly with near‐surface waters. However, individual sites display a wide range of initial values and excursions in I/Ca through the OAE interval, reflecting the importance of local controls and suggesting a high spatial variability in redox state. Both I/Ca and an Earth System Model suggest that the northeast proto‐Atlantic had notably higher oxygen levels in the upper water column than the rest of the North Atlantic, indicating that anoxia was not global during OAE 2 and that important regional differences in redox conditions existed. A lack of correlation with calcium, lithium, and carbon isotope records suggests that neither enhanced global weathering nor carbon burial was a dominant control on the I/Ca proxy during OAE 2.

The Effect of Compressibility on Turbulent Shear Flow: Direct Numerical Simulation Study

The study of the phenomenon of compressibility for modeling to second order has been made by several authors, and they concluded that models of the pressure-strain are not able to predict the structural evolution of the Reynolds stress. In particular studies and Simone Sarkar et al., a wide range of initial values of the parameters of the problem are covered. The observation of Sarkar was confirmed by the study of Simone et al. (1997,“The Effect of Compressibility on Turbulent Shear Flow: A Rapid Distortion Theory and Direct Numerical Simulation Study,” J. Fluid Mech., 330, p. 307;“Etude Théorique et Simulation Numérique de la Turbulence Compressible en Présence de Cisaillement où de Variation de Volume à Grande Échelle” thése, École Centrale de Lyon, France). We will then use the data provided by the direct simulations of Simone to discuss the implications for modeling to second order. The performance of different variants of the modeling results will be compared with DNS results.

Bifurcation Analysis and Control of Leslie–Gower Predator–Prey Model with Michaelis–Menten Type Prey-Harvesting

In this paper, a bi-dimensional system of ordinary differential equation prey–predator model with nonlinear prey-harvesting is analyzed. The model is a modified version of the well known Leslie–Gower type prey–predator model. The original Leslie–Gower type model has the unique interior equilibrium point which is globally asymptotically stable. We show here that the nonlinear harvesting in prey significantly modifies the dynamics of the system in comparison to the proportionate harvesting of prey. It has been observed that the system goes to extinction for a wide range of initial values. Moreover, the model can have two, one or no interior equilibrium point in the first quadrant where two interior equilibria collapse to one interior equilibrium point and then disappear through saddle-node bifurcation considering the rate of harvesting as bifurcation parameter. The local existence of limit cycle appearing through local Hopf bifurcation and its stability have also been investigated by computing first Lyapunov number. The conditions for existence of bionomic equilibria are analyzed. Pontryagin’s Maximum Principle is used to characterize the optimal singular control. Numerical examples are provided to validate our findings.

Speed of Convergence and Permissible Range of Initial Slope Value of York's Line Fitting Iteration Formulae

In studies of radiometric dating such as Rb-Sr, Pb-Pb, Ar-Ar dating, drawing isochrones is an essential technique. In determining the best straight line fitting to n data points [(x1, y1) - (xn, yn) ] with errors [(σx1, σy1) - (σxn, σyn)], an iteration introduced by York (1969) has been widely used. In most cases, the iteration accepts a wide range of initial values of slope and shows remarkably fast convergence. York (1969) showed two iteration formulae. In the present study I first demonstrate that the problem can be solved graphically by using a spreadsheet software. Then I try to evaluate the speed and range of these iteration formulae in comparison with the other possible iteration formulae, including Newton-Raphson formula.

Effect of indenter shapes on inverse materials characterization based on the dual indenters method

Abstract The indentation method is a useful tool for studying the onset of plastic flow and work hardening in small volumes. Several approaches based on either single and dual indenters have been reported to characterise a wide range of materials. In this work, the single and dual indenters approaches, with different indenter types, have been comparatively studied using an inverse finite element modelling program developed based on the Kalman filter method. The effect of indenter shapes on the accuracy and uniqueness of the predicted results, as well as convergence time of the program are systematically analysed by automatically mapping the results with a wide range of initial values.

Convergence of the solution of a nonsymmetric matrix Riccati differential equation to its stable equilibrium solution

We consider the initial value problem for a nonsymmetric matrix Riccati differential equation, where the four coefficient matrices form an M-matrix. We show that for a wide range of initial values the Riccati differential equation has a global solution X ( t ) on [ 0 , ∞ ) and X ( t ) converges to the stable equilibrium solution as t goes to infinity.

Photosynthetic models with maximum entropy production in irreversible charge transfer steps

Steady-state bacterial photosynthesis is modelled as cyclic chemical reaction and is examined with respect to overall efficiency, power transfer efficiency, and entropy production. A nonlinear flux–force relationship is assumed. The simplest two-state kinetic model bears complete analogy with the performance of an ideal (zero ohmic resistance of the P–N junction) solar cell. In both cases power transfer to external load is much higher than the 50% allowed by the impedance matching theorem for the linear flux–force relationship. When maximum entropy production is required in the transition with a load, one obtains high optimal photochemical yield of 97% and power transfer efficiency of 91%. In more complex photosynthetic models, entropy production is maximized in all irreversible electron/proton (non-slip) transitions in an iterative procedure. The resulting steady-state is stable with respect to an extremely wide range of initial values for forward rate constants. Optimal proton current increases proportionally to light intensity and decreases with an increase in the proton-motive force (the backpressure effect). Optimal affinity transfer efficiency is very high and nearly perfectly constant for different light absorption rates and for different electrochemical proton gradients. Optimal overall efficiency (of solar into proton-motive power) ranges from 10% (bacteriorhodopsin) to 19% (chlorophyll-based bacterial photosynthesis). Optimal time constants in a photocycle span a wide range from nanoseconds to milliseconds, just as corresponding experimental constants do. We conclude that photosynthetic proton pumps operate close to the maximum entropy production mode, connecting biological to thermodynamic evolution in a coupled self-amplifying process.

Evolution of the mass function of the Galactic globular cluster system

In this work we investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two‐body relaxation, disc shocking and dynamical friction on the evolution of individual globular clusters. We have adopted a lognormal initial GCMF and considered a wide range of initial values for the dispersion, σ, and the mean value, 〈log M〉. We have studied in detail the dependence on the initial conditions of the final values of σ, 〈log M〉, the fraction of the initial number of clusters surviving after one Hubble time and the difference between the properties of the GCMF of clusters closer to the Galactic Centre and those of clusters located in the outer regions of the Galaxy. In most of the cases considered, evolutionary processes alter significantly the initial population of globular clusters and the disruption of a significant number of globular clusters leads to a flattening in the spatial distribution of clusters in the central regions of the Galaxy. The initial lognormal shape of the GCMF is preserved in most cases and if a power‐law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a lognormal GCMF. The difference between initial and final values of σ and 〈log M〉 as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions. A significant effect of evolutionary processes does not necessarily give rise to a strong trend of 〈log M〉 with the galactocentric distance. The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive, suggested by Vesperini, is confirmed.

Substrate Control of Biotechnical Fedbatch Processes Robustness and the Role of Adaptivity

Results from experiments on laboratory scale fedbatch processes are presented as well as analysis and design of the control system. The main reason for control is to track the drastic growth in feed demand during a cultivation. Variations in the amount and quality of the inocculum makes precalculated dosage schemes of limited value to obtain reproducible cultivation conditions. Two processes have been studied on a laboratory scale, production of bakers’ yeast, and production of the enzyme salicylate hydroxylase using a strain of bacteria. Direct measurement was used to monitor the feed demand. A regulator structure is proposed based on an observer for the exponentially growing feed demand. It can be viewed as a modified PID regulator around a dosage scheme, but it is less sensitive to errors in the dosage scheme than conventional PID control. The a priori knowledge of the feed profile is further relaxed by introduction of adaptation of the growth rate parameter. The obtained non-linear control system has a simple structure and stability is garanteed for a wide range of initial values using the technique of Liapunov function. The linearized system is analysed in the frequency domain and the adaptation is shown to have negligible influence on the loop phase margin. The adaptive regulator is tested in simulation against real feed profiles and shows good results.

Optimization of process and device characteristics for MOSFETs by using the BFGS method

This paper proposes an improved process/device optimization technique, which effectively determines the optimum process conditions for realizing the desired MOSFET performance. The BFGS method, which is the best quasi-Newton method now available, is introduced to save computational time. Furthermore, upper and lower boundaries are also implemented to facilitate the search for more realistic solutions. In order to demonstrate the practicality of the present simulator, channel doping conditions, such as implanted boron dose and annealing temperature, were optimized. Optimization within constraint boundaries was successfully carried out using the relationship between measured drain current and drain voltage characteristics. Consequently, it was verified that the optimization works well for a wide range of initial values and that CPU time is less dependent upon the initial values than that was obtained by using the previous method. Owing to optimization improvements, the computational time has been significantly reduced. Therefore, the present simulator is expected to become an important tool for device design.