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We state solvability conditions for a multipoint boundary-value problem for linear second-order functional-differential equation.
In this paper, we obtain solvability conditions for the periodic boundary-value problem for a certain first-order differential equation unsolved with respect to the derivative. These condition were obtained by using the theorem on implicit operators.
We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.
We consider the initial-boundary value problem governing unsteady polytropic motions of viscous compressible multifluids. We prove the existence and uniqueness of a strong solution to the problem. Bibliography: 11 titles.
For nonstandard boundary-value problems for systems of equations of elliptic and parabolic types with vector boundary conditions, the well-posedness is proved. Typical examples are provided.
We consider boundary-value problems for differential-difference operators with perturbations in translations of the independent variable. We prove that the family of differential-difference operators is positive definite uniformly with respect to translations of the independent variable. Solutions of such problems depend continuously on these translations. We consider the coercivity problem for differential-difference operators with incommensurable translations of the independent variable and study the approximation of such operators by rational operators.
We study boundary properties of polyharmonic functions. In particular, a criterion is obtained (in terms of the radial growth of the derivative) for the existence a.e. of angular boundary values for a polyharmonic function bounded in the unit ball.
We consider a simplest elliptic pseudodifferential equation in a multi-dimensional cone (multi-dimensional angle) and describe all possible structures of its solutions related to the wave factorization of the elliptic symbol. Depending on the index of wave factorization, we consider various statements of well-posed boundary-value problems. The existence of solutions is studied in Sobolev–Slobodetskii spaces.
We consider the initial-boundary value problem for the nonstationary radiative transfer equation in a system of semitransparent bodies with the conditions of diffuse reflection and refraction of radiation. We establish the unique solvability of the problem with boundary and initial data in the complete scale of Lebesgue spaces. We obtain estimates for solutions.
We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.
The global geothermal power market has shown significant growth since the last decade and is expected to reach a total installed capacity of 18.4 gigawatts electric (GWe) by the end of 2021 (GEA, 2016). The global geothermal power plant turbine market is dominated by a small number of manufacturers. Between 2005 and 2015, 82% of the geothermal steam turbines were manufactured in Japan, and 74% of the geothermal binary cycle turboexpanders were manufactured in Israel. During this period, the United States played an important role in the global trade flow of fully assembled turbine units and turbine parts, with a high volume of imports and exports. Another significant growth area was in Italian turbine/turboexpander manufacturers, who have increased their market share in the last couple of years. One other important change in the manufacturing market was in Turkey, where the bonus on feed-in-tariff (FIT) for domestic hardware components boosted the national manufacturing sector between 2010 and 2020. When planning geothermal power projects, developers customize their power plant size to fit the available geothermal resource capacity. The turbine is designed and sized to optimize the efficiency and utilization of resource and revenue production. The rest of the power plant components such as heat exchangers (HX), water-cooled cooling towers (WCCT), or air-cooled condensers (ACC) are then chosen to complement the turbine size and design. These one-off manufacturing custom design turbines have relatively higher manufacturing set-up costs, longer lead times, and higher capital costs than the standard design turbines manufactured in larger volumes. However, turbines produced in standard increments and in larger manufacturing volumes could result in lower costs per turbine, but potentially lower efficiency. Based on pipeline projects and resource assessments, there is significant potential value in creating standard turbine sizes that could offer an economic advantage, as is done for modular microturbines.
Monte Carlo (MC) shielding calculations often use weight windows (WWs) and biased sources formed from a deterministic estimate of the adjoint flux to improve the convergence rate of tallies. This requires a significant amount of computer memory, which can limit the memory available for high-resolution tally output. A new method is proposed for reducing these memory requirements by using singular value decomposition (SVD) in linear or logarithmic space to approximate the adjoint flux. This method’s performance is evaluated using the Shift and Denovo codes for streaming and diffusion base case problems, followed by problems using the Westinghouse AP1000 and the Joint European Torus. The log SVD reduced WW memory requirements by an order of magnitude in all cases without a significant performance penalty. Additionally, the linear SVD reduced biased source memory requirements by an order of magnitude, but further investigation is needed to account for observed limitations.
Demand response (DR) is regarded as an effective tool to mitigate the operational uncertainties and enhance the reliability of power supply in smart grids. However, with the time-varying attribute, to what extent DR could be committed is a major concern for utilities. This paper proposes a new approach to assess the capacity value (CV) of DR with a methodological framework developed for the uncertainty modeling of DR. The novelty of this framework is its inclusion of both physical and human-related analyses in DR programs, which allows the characterization of DR variability to be accurate for the CV estimation. To achieve this, the demand-side activities in DR are disaggregated into several modules as load usage, contract selection and actual performance. Based on their intrinsic properties, different parametric models are proposed to represent the impact of each technical/social factor on the availability of DR. The parameters of these models are determined using learning based algorithms to adapt to various behavior patterns of consumers. The outputs of the framework will serve as the quantifiers of DR capability and are integrated into reliability-based CV evaluation. The results of case studies verify the effectiveness of the proposed methodology.
Representations are developed and illustrated for the distribution of link property values at the time of link failure in the presence of aleatory uncertainty in link properties. The following topics are covered: (i) defining properties for weak links and strong links, (ii) cumulative distribution functions (CDFs) for link failure time, (iii) integral-based derivation of CDFs for link property at time of link failure, (iv) sampling-based approximation of CDFs for link property at time of link failure, (v) verification of integral-based and sampling-based determinations of CDFs for link property at time of link failure, (vi) distributions of link properties conditional on time of link failure, and (vii) equivalence of two different integral-based derivations of CDFs for link property at time of link failure.
This paper presents an extension to generalized blockmodeling where there are more than two types of objects to be clustered based on valued network data. We use the ideas in homogeneity block modeling to develop an optimization model to perform the clustering of the objects and the resulting partitioning of the ties so as to minimize the inconsistency of an empirical block with an ideal block. The ideal block types used in this modeling are null, complete and a new type that is related to that developed in Ziberna (2007). Three case studies are presented, two based on the Southern Women dataset (Davis et al. 1941) and a third based on passenger air travel in the Continental United States.
Concentrating solar power (CSP) plants depend on thousands of heliostats whose reflectance declines as dust accumulates. Operators routinely measure reflectance to estimate soiling and, in turn, inform cleaning schedules, but the value of collecting more frequent or more accurate data has not been formally quantified. This study introduces a Monte Carlo discrete event simulation framework that integrates stochastic models of soiling, weather, and measurement error with a dynamic cleaning dispatch policy to estimate annual energy production and operations costs. Applied to two representative central-receiver field configurations, the results show that both the frequency and accuracy of reflectance measurements can meaningfully impact plant performance. In both case studies, reducing measurement intervals yields significant returns, with the energy gains greatly exceeding the cost of more frequent data collection. The simulation framework serves as a decision-support tool for CSP operators, allowing them to input site-specific soiling conditions, measurement accuracy, and survey frequency to evaluate the tradeoffs between data collection cost and energy recovery, and to identify measurement strategies that maximize plant profit.
Extreme Value theory seems to be a promising tool for analysing experimental continuum gamma decay spectra in order to obtain physical parameters at high excitation energy.
Nanocrystalline lithium fluoride (LiF) phosphors have been prepared by the chemical co-precipitation method at different pH values (7.0, 8.0, 9.0). The formation of nanocrystalline structure has been confirmed by X-ray diffraction and transmission electron microscope. The thermolumniscence (TL) properties of LiF phosphors irradiated with gamma rays at different doses have been studied. The analysis of TL glow curve has revealed the existence of two well resolved glow peaks, one low temperature peak at around 145 deg. C and other one at higher temperature around 375 deg. C. The LiF nano-crystallites synthesized at 8.00 pH have been found to show maximum TL intensity at studied gamma doses (0.1 Gy-15 Gy).