174 research outputs found

    Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model

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    We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behaviour, and dissipative spin dynamics in the spin boson modelComment: 4 pages, 4 figures, revised version accepted for publication in PR

    Efficient Reduced Basis Methods for Saddle Point Problems with Applications in Groundwater Flow

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    К ВОПРОСУ СОВЕРШЕНСТВОВАНИЯ АВТОМАТИЗАЦИИ УПРАВЛЕНИЯ СТРОИТЕЛЬНЫМИ И ДОРОЖНЫМИ МАШИНАМИ С ГИДРАВЛИЧЕСКИМ ПРИВОДОМ

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    Competitiveness of modern building and road machinery is determined by a number of factors: ease of machine control, automation level of technological processes, construction machinery cost, operational expenditures, maintainability and productivity.In order to improve automation level of technological processes for drives of multi-functional mobile machines such as universal single-bucket excavator and loader it is proposed to apply multi-circuit hydraulics with closed flows of working fluid on the basis of multi-positional valve.Combination of a regulated reversible pump, elements of hydraulic automation with a new con-trol valve in a multistage hydraulic drive with closed flows makes it possible to control building and road machinery. Конкурентоспособность современной строительной и дорожной техники определяется рядом факторов: удобством управления машиной, уровнем автоматизации производства технологических процессов, стоимостью строительной техники, эксплуатационными затратами, ремонтопригодностью и производительностью.С целью повышения уровня автоматизации технологических процессов для приводов многофункциональных мобильных машин, таких как универсальные одноковшовые экскаваторы, погрузчики, предлагается многоконтурная гидросистема с замкнутыми потоками рабочей жидкости на базе многопозиционного крана управления.Сочетание регулируемого реверсивного насоса, элементов гидроавтоматики с новым краном управления в многоконтурном гидроприводе с замкнутыми потоками позволяет управлять строительными и дорожными машинами

    Tractability of multivariate problems for standard and linear information in the worst case setting: part II

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    We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well defined. We prove QPT for algorithms that use only function values under the three assumptions: 1) the minimal errors for the univariate case decay polynomially fast to zero, 2) the largest singular value for the univariate case is simple and 3) the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point. The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces

    H2, HD, and D2 in the small cage of structure II clathrate hydrate: vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates

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    We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H2, HD, and D2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H2O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H2 in the hydrate domain, based on an ab initio 6D H2–H2O pair potential for flexible H2 and rigid H2O. They extend to the first excited (v = 1) vibrational state of H2, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm−1 for H2). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H2, our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H2) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm−1 for H2 is only 14% away from the experimental value at 20 K

    Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

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    Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154316/1/nme6268.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154316/2/NME_6268_novelty.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154316/3/nme6268_am.pd

    Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

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    We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

    Методики расчета продолжительности запекания изделий из мясного фарша при тепловой обработке в конвекционных печах

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    Saving energy resources, optimizing production processes and ensuring high quality of finished products are important tasks facing the food industry of the Republic of Belarus at the present stage of social and economic development. From this point of view, the current direction of scientific activity is development of methods for predicting duration of heat treatment of food products, which will allow to increase the level of production planning, implement production processes rationally, ensure production of finished products with high consumer parameters with no underheating or overheating of material of the processed bodies, and decrease the cost of energy resources for thermal processes. The paper proposes the method for theoretical calculation of baking duration for minced meat products in direct contact of the heating medium with the processed body in modern convection units. When developing a theoretical calculation, heat transfer processes are divided into internal and external. When describing internal heat transfer processes, changes in the thermal and physical characteristics of the material of the processed body are considered, determined by mass transfer processes and physical and chemical changes in structural elements with conversion of raw minced meat into finished product with baked crust. The processes of external heat exchange are described according to the operating parameters of modern convection ovens used in small and medium-sized enterprises of food industry and public catering. The values of duration of heat treatment on the example of products made of chicken mince at different temperatures of the heating medium are obtained. Special rod cassettes with a rigid thermocouple attachment design have been developed to ensure correct experiment. Deviations of baking duration values between the theoretically calculated and experimentally obtained values range from 1.49 to 4.44 % for different temperatures of heating medium, which indicates the efficiency of the developed technique. The proposed technique for calculating the duration of baking process for minced meat products when heated will allow optimizing production processes, saving energy resources and obtaining finished products with high consumer parameters. Acknowledgments. The research was carried out as part of the state program of scientific research “Quality and Efficiency of Agroindustrial Production”.Экономия энергетических ресурсов, оптимизация производственных процессов и обеспечение высокого качество готовой продукции – важные задачи, стоящие перед пищевой промышленностью Республики Беларусь на современном этапе социально-экономического развития. С этой точки зрения актуальным направлением научной деятельности является разработка методик прогнозного определения продолжительности тепловой обработки пищевых продуктов, применение которых позволит повысить уровень планирования производства, рационально осуществлять производственные процессы, обеспечить получение готовой продукции с высокими потребительскими характеристиками без недогрева или перегрева материала обрабатываемых тел, оптимизировать затраты энергетических ресурсов на проведение тепловых процессов. В работе предлагается методика теоретического расчета продолжительности запекания изделий из мясного фарша при прямом контакте греющей среды с обрабатываемым телом в современных конвекционных аппаратах. При разработке теоретического расчета процессы теплообмена разделены на внутренние и внешние. При описании процессов внутреннего теплообмена учтены изменения теплофизических характеристик материала обрабатываемого тела, обусловленные протекающими массообменными процессами и наличием физико-химических изменений структурных элементов с преобразованием сырого фарша в готовый продукт с запеченной коркой. Процессы внешнего теплообмена описаны согласно режимным параметрам современных конвекционных печей, применяемых в малых и средних предприятиях пищевой промышленности и общественном питании. Получены значения продолжительности тепловой обработки на примере изделий из куриного фарша при различных температурах греющей среды. Разработаны специальные стержневые кассеты с конструкцией жесткого крепления термопар, обеспечивающие проведение корректного эксперимента. Отклонения значений продолжительности запекания между теоретически – рассчитанными и полученными экспериментально составляют от 1,49 до 4,44 % для различных температур греющей среды, что свидетельствует о эффективности разработанной методики. Предложенная методика расчета продолжительности процесса запекания изделий из мясного фарша при нагревании позволит оптимизировать производственные процессы, обеспечить экономию энергетических ресурсов и получать готовую продукцию с высокими потребительскими характеристиками. Благодарности. Работа выполнена в рамках государственной программы научных исследований «Качество и эффективность агропромышленного производства»

    The effect of the condensed-phase environment on the vibrational frequency shift of a hydrogen molecule inside clathrate hydrates

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    © 2018 Author(s). We report a theoretical study of the frequency shift (redshift) of the stretching fundamental transition of an H 2 molecule confined inside the small dodecahedral cage of the structure II clathrate hydrate and its dependence on the condensed-phase environment. In order to determine how much the hydrate water molecules beyond the confining small cage contribute to the vibrational frequency shift, quantum five-dimensional (5D) calculat ions of the coupled translation-rotation eigenstates are performed for H 2 in the v=0 and v=1 vibrational states inside spherical clathrate hydrate domains of increasing radius and a growing number of water molecules, ranging from 20 for the isolated small cage to over 1900. In these calculations, both H 2 and the water domains are treated as rigid. The 5D intermolecular potential energy surface (PES) of H 2 inside a hydrate domain is assumed to be pairwise additive. The H 2 -H 2 O pair interaction, represented by the 5D (rigid monomer) PES that depends on the vibrational state of H 2 , v=0 or v=1, is derived from the high-quality ab initio full-dimensional (9D) PES of the H 2 -H 2 O complex [P. Valiron et al., J. Chem. Phys. 129, 134306 (2008)]. The H 2 vibrational frequency shift calculated for the largest clathrate domain considered, which mimics the condensed-phase environment, is about 10% larger in magnitude than that obtained by taking into account only the small cage. The calculated splittings of the translational fundamental of H 2 change very little with the domain size, unlike the H 2 j = 1 rotational splittings that decrease significantly as the domain size increases. The changes in both the vibrational frequency shift and the j = 1 rotational splitting due to the condensed-phase effects arise predominantly from the H 2 O molecules in the first three complete hydration shells around H 2
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