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

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

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

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

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

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

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

© 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

Иммуноферментные системы и набор реагентов для определения бацитрацина в пищевых продуктах

Two test-systems for a direct and an indirect enzyme-linked immunosorbent assay (ELISA) of peptide antibiotic bacitracin (BC) were developed and studied. For the both systems, polyclonal antibodies were obtained by immunizing rabbits with a conjugate of BC with keyhole limpet hemocyanine synthesized using reaction between the peptide and the high molecular weight protein in the presence of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC). The product of BC linking to thyroglobulin which was activated with EDC and N-hydroxysulfosuccinimide served as conjugated antigen on a solid phase in the indirect ELISA. For the direct ELISA, the antibodies against BC were immunochemically immobilized onto microplate surface, while the liquid phase contained a conjugate of BC with horseradish peroxidase. This conjugate was obtained by successive reactions of antibiotic amino groups coupling to periodate oxidized carbohydrate chains of enzyme and the reducting of formed Shiff’s base with sodium borohydride. Conjugated antigens binding to anti-BC antibodies provided maximum colorimetric signals of 2.0 and 1.2 optical units for the direct and indirect ELISA, respectively, and depended on BC content in the liquid phase. Antibiotic concentration that caused the inhibition of binding by 50 % was 2.6 ng/ml in the direct ELISA and 10.0 ng/ml in the indirect ELISA. The simple and sensitive direct ELISA system was used as a prototype of the finished reagent kit and a method for measurements with technical-analytical parameters and metrological characteristics allowing the determination of BC residues in a variety of foods including 14 items in a concentration range of 9.0 to 405.0 pg/kg with proper accuracy and precision.Разработаны тест-системы для непрямого и прямого иммуноферментного анализа (ИФА) пептидного антибиотика бацитрацина (Бц). Поликлональные антитела для обеих тест-систем получены иммунизацией кроликов конъюгатом Бц и гемоцианина улитки, который синтезировали взаимодействием пептида с белком в присутствии 1-этил-3-(3-диметиламинопропил)-карбодиимида (EDC). В системе непрямого ИФА твердофазным конъюгированным антигеном служил продукт присоединения Бц к тироглобулину, предварительно активированному EDC и N-гидроксисульфосукцинимидом. Для прямого ИФА на поверхности лунок микропланшета были иммунохимически иммобилизованы антитела к Бц, а жидкая фаза содержала конъюгат Бц с пероксидазой из корней хрена, полученный путем последовательных реакций присоединения аминогрупп Бц к окисленной периодатом углеводной части фермента и восстановления образовавшегося основания Шиффа борогидридом натрия. В системах прямого ИФА и непрямого ИФА связывание конъюгированных антигенов с антителами к Бц обусловливало максимальные колориметрические сигналы около 2,0 и 1,2 единиц оптической плотности соответственно и зависело от содержания Бц в жидкой фазе. При этом концентрации антибиотика, вызывающие ингибирование связывания на 50 %, составили 2,6 нг/мл в прямом ИФА и 10,0 нг/мл в непрямом ИФА. Простая и чувствительная система прямого ИФА послужила прототипом для создания готового набора реагентов и методики выполнения измерений, технико-аналитические параметры и метрологические характеристики которых позволяют определять остаточные количества Бц в пищевой продукции животного происхождения расширенного перечня, включающего 14 наименований, в диапазоне от 9,0 до 405,0 мкг/кг с надлежащей правильностью и точностью

Propagation of uncertainty in a rotating pipe mechanism to generate an impinging swirling jet flow for heat transfer from a flat plate

In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification in the computational heat transfer by forced convection is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (Simulation 1) impinging on a flat plate (Simulation 2). This is the first probabilistic uncertainty analysis on computational heat transfer by impinging jets in the literature. The conclusion drawn from the analysis of this frequent engineering application is that the simulated system does not exhibit a significant sensitivity to stochastic variations of model input parameters, over the tested uncertainty ranges. Additionally, a set of non-linear regression models for the stochastic velocity and turbulent profiles for the pipe nozzle are created and tested, since impinging jets for heat transfer at Reynolds number of Re = 23000 are very frequent in the literature, but stochastic inlet conditions have never been provided. Numerical results demonstrate a negligible difference in the predicted convective heat transfer with respect to the use of the profiles simulated via CFD. These suggested surrogate models can be directly embedded onto other engineering applications (e.g. arrays of jets, jet flows impinging on plates with different shapes, inlet piping in combustion, chemical mixing, etc.) in which a realistic swirling flow under uncertainty can be of interest