S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant $g$, and spatial measure $d\mu$ is studied. An expression for GF $\mathcal{Z}$ in terms of the abstract integral over the primary field $\varphi$ is given. An expression for GF $\mathcal{Z}$ in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator $\hat{L}$ over the separable HS basis. The classification of functional integration measures $\mathcal{D}\left[\varphi\right]$ is formulated, according to which trivial and two nontrivial versions of GF $\mathcal{Z}$ are obtained. Nontrivial versions of GF $\mathcal{Z}$ are expressed in terms of $1$-norm and $0$-norm, respectively. The definition of the $0$-norm generator $\varPsi$ is suggested. Simple cases of sharp and smooth generators are considered. Expressions for GF $\mathcal{Z}$ in terms of integrals over the separable HS with new integrands are obtained. For polynomial theories $\varphi^{2n},\, n=2,3,4,\ldots,$ and for the nonpolynomial theory $\sinh^{4}\varphi$, integrals over the separable HS in terms of a power series over the inverse coupling constant $1/\sqrt{g}$ for both norms ($1$-norm and $0$-norm) are calculated. Critical values of model parameters when a phase transition occurs are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated. A comparison of two GFs $\mathcal{Z}$, one in the case of uncountable HS integral and one obtained using the Parseval-Plancherel identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared for the special issue "QCD and Hadron Structure" of the journal Particles; v3: minimal corrections; v4: paragraphs added related to Reviewer comment

The equation of state of a partly homogenized plasma of low-dense porous matter

The equation of state (EOS) of a low-density porous substance plasma is proposed in the form of continuous media EOS containing, as a pressure control parameter, the degree of plasma homogenization, which is function of the initial porous structure, as well as of the current values of plasma density and temperature. Using the partially-homogenized-plasma EOS an approximate analytical solution is found and numerical calculations were performed of the problem of thermal expansion of a flat layer of porous matter. The features of the obtained results are discussed in comparison with the case of a continuous substance of equivalent chemical composition. The proposed equation of state is used to analyze the experimental data on porous substance heating with laser and X-ray pulses.Comment: 20 pages, 4 figure

Structural and biochemical characterization of a novel ZntB (CmaX) transporter protein from Pseudomonas aeruginosa

The 2-TM-GxN family of membrane proteins is widespread in prokaryotes and plays an important role in transport of divalent cations. The canonical signature motif, which is also a selectivity filter, has a composition of Gly-Met-Asn. Some members though deviate from this composition, however no data are available as to whether this has any functional implications. Here we report the functional and structural analysis of CmaX protein from a pathogenic Pseudomonas aeruginosa bacterium, which has a Gly-Ile-Asn signature motif. CmaX readily transports Zn2+, Mg2+, Cd2+, Ni2+ and Co2+ ions, but it does not utilize proton-symport as does ZntB from Escherichia coli. Together with the bioinformatics analysis, our data suggest that deviations from the canonical signature motif do not reveal any changes in substrate selectivity or transport and easily alter in course of evolution

Verification and Improvement of Flamelet Approach for Non-Premixed Flames

Studies in the mathematical modeling of the high-speed turbulent combustion has received renewal attention in the recent years. The review of fundamentals, approaches and extensive bibliography was presented by Bray, Libbi and Williams. In order to obtain accurate predictions for turbulent combustible flows, the effects of turbulent fluctuations on the chemical source terms should be taken into account. The averaging of chemical source terms requires to utilize probability density function (PDF) model. There are two main approaches which are dominant in high-speed combustion modeling now. In the first approach, PDF form is assumed based on intuitia of modelliers (see, for example, Spiegler et.al.; Girimaji; Baurle et.al.). The second way is much more elaborate and it is based on the solution of evolution equation for PDF. This approach was proposed by S.Pope for incompressible flames. Recently, it was modified for modeling of compressible flames in studies of Farschi; Hsu; Hsu, Raji, Norris; Eifer, Kollman. But its realization in CFD is extremely expensive in computations due to large multidimensionality of PDF evolution equation (Baurle, Hsu, Hassan)

Автоматизированная система регулирования давления воздуха в шинах многоцелевых колесных машин

The cross-country capability of multi-purpose wheeled vehicles is one of the most important operational properties of these technical objects. In many ways, it is determined by their traction characteristics. There are a number of ways to improve traction and coupling properties of multipurpose wheeled vehicles, the main ones are the use of various kinds of traction control systems, blocking of  interaxle and interwheel differentials, the use of ballast and several others. Recently, one of the ways to improve the traction properties and cross-country ability of vehicles on soils with weak load-bearing capacity is a regulation of air pressure in the tires of the driving wheels of multi-purpose wheeled vehicles. The paper describes the process of interaction of the wheel mover with the ground surface when the air pressure in the tire changes. The influence of air pressure on the traction properties of wheeled vehicles is established. The system of automatic control of air pressure in tires of mobile cars depending on road conditions is offered. The use of the proposed regulation principle will significantly increase the cross-country ability of multi-purpose wheeled vehicles in heavy traffic conditions, eliminating the subjective factor in the person of the vehicle operator.Проходимость многоцелевых колесных машин – одно из важнейших эксплуатационных свойств данных технических объектов. Во многом она определяется их тяговыми характеристиками. Известен ряд способов повышения тягово-сцепных свойств многоцелевых колесных машин, среди которых – применение различного рода противобуксовочных систем, блокировка межосевых и межколесных дифференциалов, использование балласта и ряд других. Один из способов повышения тягово-сцепных свойств и проходимости машин по грунтам со слабой несущей способностью, который получил развитие в последнее время, – это регулирование давления воздуха в шинах ведущих колес многоцелевых колесных машин. В статье приводится исследование процесса взаимодействия колесного движителя с грунтовой поверхностью при изменении давления воздуха в шине. Установлено влияние давления воздуха на тягово-сцепные свойства многоцелевых колесных машин. Предложена система автоматического регулирования давления воздуха в шинах мобильных машин в зависимости от дорожных условий. Использование предложенного принципа регулирования позволит существенно повысить проходимость многоцелевых колесных машин в тяжелых условиях движения, исключив субъективный фактор в лице оператора транспортного средства

Structural characterization of cephaeline binding to the eukaryotic ribosome using Cryo-Electron Microscopy

The eukaryotic ribosome is emerging as a promising target against human pathogens, includ- ing amoeba, protozoans, and fungi. Among the eukaryotic-specific families of inhibitors, al- kaloids are known to bind to the eukaryotic ribosome and inhibit translocation. However, these inhibitors have varying medical indications and toxicity to humans. Structural information is available for only two of them, cryptopleurine and emetine. Aim. In our work, we aimed to elucidate the binding mechanism of another alkaloid, cephaeline, to the eukaryotic ribosome. Methods. We used cryogenic electron microscopy and cell-free assays to reveal its mechanism of action. Results. Our results indicate that cephaeline binds to the E-tRNA binding site on the small subunit of the eukaryotic ribosome. Similar to emetine, cephaeline forms a stacking interaction with G889 of 18S rRNA and L132 of the protein uS11. We propose the hypothesis of cephaeline specificity to eukaryotes by comparing the interaction pattern of cephaeline with other inhibitors binding to the E-site of the mRNA tunnel. Conclusions. The high-resolution structure of ribosome-bound cephaeline (2.45 Å) allowed us to precisely determine the in- hibitor’s position in the binding site, which holds potential for the development of the next generation of drugs targeting the mRNA tunnel of the ribosome

Structural characterization of cephaeline binding to the eukaryotic ribosome using Cryo-Electron Microscopy

The eukaryotic ribosome is emerging as a promising target against human pathogens, includ- ing amoeba, protozoans, and fungi. Among the eukaryotic-specific families of inhibitors, al- kaloids are known to bind to the eukaryotic ribosome and inhibit translocation. However, these inhibitors have varying medical indications and toxicity to humans. Structural information is available for only two of them, cryptopleurine and emetine. Aim. In our work, we aimed to elucidate the binding mechanism of another alkaloid, cephaeline, to the eukaryotic ribosome. Methods. We used cryogenic electron microscopy and cell-free assays to reveal its mechanism of action. Results. Our results indicate that cephaeline binds to the E-tRNA binding site on the small subunit of the eukaryotic ribosome. Similar to emetine, cephaeline forms a stacking interaction with G889 of 18S rRNA and L132 of the protein uS11. We propose the hypothesis of cephaeline specificity to eukaryotes by comparing the interaction pattern of cephaeline with other inhibitors binding to the E-site of the mRNA tunnel. Conclusions. The high-resolution structure of ribosome-bound cephaeline (2.45 Å) allowed us to precisely determine the in- hibitor’s position in the binding site, which holds potential for the development of the next generation of drugs targeting the mRNA tunnel of the ribosome

Flamelet Model Application for Non-Premixed Turbulent Combustion

The current Final Report contains results of the study which was performed in Scientific Research Center 'ECOLEN' (Moscow, Russia). The study concerns the development and verification of non-expensive approach for modeling of supersonic turbulent diffusion flames based on flamelet consideration of the chemistry/turbulence interaction (FL approach). Research work included: development of the approach and CFD tests of the flamelet model for supersonic jet flames; development of the simplified procedure for solution of the flamelet equations based on partial equilibrium chemistry assumption; study of the flame ignition/extinction predictions provided by flamelet model. The performed investigation demonstrated that FL approach allowed to describe satisfactory main features of supersonic H 2/air jet flames. Model demonstrated also high capabilities for reduction of the computational expenses in CFD modeling of the supersonic flames taking into account detailed oxidation chemistry. However, some disadvantages and restrictions of the existing version of approach were found in this study. They were: (1) inaccuracy in predictions of the passive scalar statistics by our turbulence model for one of the considered test cases; and (2) applicability of the available version of the flamelet model to flames without large ignition delay distance only. Based on the results of the performed investigation, we formulated and submitted to the National Aeronautics and Space Administration our Project Proposal for the next step research directed toward further improvement of the FL approach