Smooth Sections Research Articles

STUDY OF THE DESIGN OF RAILWAY TRACKS OF INDUSTRIAL ENTERPRISES WITHIN THE AREAS OF SMOOTH TRACK EXPANSION

The goal. Railway sidings of industrial enterprises are the shippers and receivers of goods, which determine their main nomenclature for transportation by mainline rail transport. The length of railway sidings of industrial enterprises varies widely, from a few hundred meters to hundreds of kilometers, including the length of the siding of PJSC ArcelorMittal Kryvyi Rih exceeding 700 km. The combination of factors such as the presence of technological transportation on the sidings, the development of the industrial enterprises' transportation system over time, and the master plan of the main production facilities leads to the need to apply railway transport design standards for severe and especially severe conditions. This is mainly expressed in reducing the radii of curved track sections to the minimum possible values. When using reinforced concrete sleepers of the Sh6 type, it is possible to arrange a track gauge of 1539 mm in curved sections. But currently, there is no approved design for smooth track widening sections on reinforced concrete sleepers in front of curves with radii of less than 300 meters. There is also a reasonable need to increase the track gauge to at least 1540 mm in curves of such radii. Together with the limited service life of wooden sleepers when they are laid in areas of smooth track widening compared to reinforced concrete sleepers, this necessitates the development of a track structure on reinforced concrete sleepers within the area of smooth track widening. Methods. Methods of scientific analysis and synthesis of the track development structure, methods of analytical geometry. Results. Based on the analysis of the design of intermediate fasteners of the KB50 type, the design of a section of smooth track widening using reinforced concrete sleepers of types Sh1-1 and Sh6 and rails R50 is proposed. The track widening from 1520 to 1545 mm is achieved by developing the order of laying sleepers of different types and turning the KB50 substrates. In this case, the length of the section of smooth track widening from 1520 mm to 1545 mm is 2800 mm, and the actual deviation is 8.9‰. Practical significance. The use of the considered structure within the areas of smooth track widening, provided that the results of trial operation and testing of the established procedure are positive, will reduce the operating costs associated with the current maintenance of industrial enterprises' tracks, the parameter of which correspond to severe and especially severe design conditions.

Cohomological and motivic inclusion–exclusion

We categorify the inclusion–exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two spectral sequences of a stratified space and certain Vassiliev-type spectral sequences; we also obtain Euler characteristic analogs in the Grothendieck ring of varieties. As an application, we give an algebro-geometric proof of Vakil and Wood's homological stability conjecture for the space of smooth hypersurface sections of a smooth projective variety. In characteristic zero this conjecture was previously established by Aumonier via topological methods.

Robustness of optimal quantum annealing protocols

Abstract Noise in quantum computing devices poses a key challenge in their realization. In this paper, we study the robustness of optimal quantum annealing protocols against coherent control errors, which are multiplicative Hamlitonian errors causing detrimental effects on current quantum devices. We show that the norm of the Hamiltonian quantifies the robustness against these errors, motivating the introduction of an additional regularization term in the cost function. We analyze the optimality conditions of the resulting robust quantum optimal control problem based on Pontryagin’s maximum principle, showing that robust protocols admit larger smooth annealing sections. This suggests that quantum annealing admits improved robustness in comparison to bang-bang solutions such as the quantum approximate optimization algorithm. Finally, we perform numerical simulations to verify our analytical results and demonstrate the improved robustness of the proposed approach.

Transverse linear subspaces to hypersurfaces over finite fields

Ballico proved that a smooth projective variety X of degree d and dimension m over a finite field of q elements admits a smooth hyperplane section if q≥d(d−1)m. In this paper, we refine this criterion for higher codimensional linear sections on smooth hypersurfaces and for hyperplane sections on Frobenius classical hypersurfaces. We also prove a similar result for the existence of reduced hyperplane sections on reduced hypersurfaces.

Influence of Entrance Geometry and Thermal Boundary Conditions on Heat Transfer in a Rectangular Channel with 45 Deg Angled Ribs on One or Two Principal Walls

The purpose of this paper is to numerically investigate the influence of the entrance geometry and thermal boundary conditions on the local and averaged heat transfer coefficient in a ribbed rectangular channel with an aspect ratio of 5. Ribs, angled at 45°, were periodically deployed on one or two opposite sides, while the remaining walls of the rectangular channel were assumed to be smooth and unheated. The effect of entrance conditions was addressed by considering either a smooth or a ribbed unheated section upstream of the ribbed heated section. The effect of the thermal boundary condition was studied by considering a uniform heat flux imposed at the inter-rib region, or at the inter-rib and the rib baseplate, or at the whole interface between the ribbed surface and the coolant. Results, presented in the form of spatially resolved and spatially averaged Nusselt numbers, show that a ribbed section preceding the heated test section affects the heat transfer coefficient, relative to a smooth entrance section, for several repetitive modules. The influence of the thermal boundary condition was found to be mainly concentrated in the surface regions immediately upstream and downstream of each rib, with small differences, in terms of spatially averaged Nusselt numbers. The presented investigation is meant to point out that heat transfer experiments on ribbed channels, massively provided by the heat transfer community according to the current technical literature, should provide an exhaustive description of the entrance and thermal boundary conditions assumed in the experiments and eventually to discuss how they could potentially affect the results.

Cavity flow characteristics of a curved hull section impacting a free surface with inclined postures

The water entry of structures is a complex gas–liquid flow. This paper studies the asymmetrical flow characteristics of a curved hull section entering water through numerical and experimental methods. The free-falling test from drop heights of 250–900 mm and inclination angles from 0° to 20° is carried out. Compared to a smooth hull section (cutting the bottom appendage), the experimental results observe some special asymmetrical flow phenomena (i.e., flow separation, jet impact, bubble flows, and bubble expansion). The physical mechanisms behind these flows are explained through combing the free surface flow and pressure distribution obtained by the numerical method. The effects of the inclination angle and impact velocities on these flow phenomena are further discussed, and they increase the degree of flow separation, bubble volume, and fragmentation. The load characteristics before and after cavity formation are analyzed based on a volume-of-fluid method. The high pressure caused by bubble closure can produce an instantaneous impulse pressure that even be 34% larger than the conventional impact pressure and is worth noting. This study clarifies some complex asymmetrical impact flow characteristics of curved hull sections and thus reveals the evolution mechanism of gas–liquid flows for complex geometries during oblique water entry.

Neutron resonance cross sections evaluation based on the phase shift deep neural network

Neutron resonance cross sections are essential in many nuclear science and application fields. Evaluated nuclear libraries usually derive neutron resonance parameters using R-matrix theory. However, determining these parameters and reconstructing the pointwise cross sections required for transport calculations is a time-consuming process. This paper presents a new method for fitting neutron resonance cross sections by using a phase shift deep neural network (PhaseDNN). The network presents resonance cross sections based on its network parameters. This approach allows for the quick calculation of cross section values from the given network parameters. Additionally, PhaseDNN can fit network parameters to experimental data to obtain a smooth resonance cross section curve. Therefore, it has the potential to be an alternative to R-matrix theory.

Spectral asymptotics of elliptic operators on manifolds

The study of spectral properties of natural geometric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global analysis, differential geometry and mathematical physics. Instead of studying the spectrum of a differential operator [Formula: see text] directly one usually studies its spectral functions, that is, spectral traces of some functions of the operator, such as the spectral zeta function [Formula: see text] and the heat trace [Formula: see text]. The kernel [Formula: see text] of the heat semigroup [Formula: see text], called the heat kernel, plays a major role in quantum field theory and quantum gravity, index theorems, non-commutative geometry, integrable systems and financial mathematics. We review some recent progress in the study of spectral asymptotics. We study more general spectral functions, such as [Formula: see text], that we call quantum heat traces. Also, we define new invariants of differential operators that depend not only on the eigenvalues but also on the eigenfunctions, and, therefore, contain much more information about the geometry of the manifold. Furthermore, we study some new invariants, such as [Formula: see text], that contain relative spectral information of two differential operators. Finally, we show how the convolution of the semigroups of two different operators can be computed by using purely algebraic methods.

O razreshimosti lineynykh differentsial'nykh operatorov na vektornykh rassloeniyakh nad mnogoobraziem

Necessary and sufficient condition is established for the closedness of the rangeor surjectivity of a differential operator acting on smooth sections of vector bundles. For connectednoncompact manifolds it is shown that these conditions are derived from the regularityconditions and the unique continuation property of solutions. An application of these results toelliptic operators (more precisely, to operators with a surjective principal symbol) with analyticcoefficients, to second-order elliptic operators on line bundles with a real leading part, and to theHodge–Laplace–de Rham operator is given. It is shown that the top de Rham (respectively, Dolbeault)cohomology group on a connected noncompact smooth (respectively, complex-analytic)manifold vanishes. For elliptic operators, we prove that solvability in smooth sections impliessolvability in generalized sections.

Non-trivial Bundles and Algebraic Classical Field Theory

Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e., appropriate smooth functions on them. The kinematics will be further specified by means of the Peierls brackets, which in turn are defined via the causal propagators of linearized field equations. We shall compare the formalism we use with the more traditional ones.

Reynolds Number Dependency of Wall-Bounded Turbulence Over a Surface Partially Covered by Barnacle Clusters

The settlement of barnacles on a ship hull is a common form of marine biofouling. In this study, the Reynolds number dependency of turbulent flow over a surface partially covered by barnacle clusters is investigated using direct numerical simulations of turbulent channel flow at friction Reynolds numbers ranging from 180 to 720. Mean flow, Reynolds and dispersive stress statistics are evaluated and compared to the corresponding results for a generic irregular rough surface with a Gaussian height distribution. For the barnacle surface, distinctive features emerge in the velocity statistics due to the interplay between the barnacle clusters and the large, connected smooth-wall sections surrounding them. This aspect is further investigated by applying a rough-smooth decomposition to the local time-averaged flow statistics for the barnacle surface. Using this decomposition, the partial recovery of smooth-wall behaviour over the smooth sections of the barnacle surface can be observed in the Reynolds stress statistics with the streamwise Reynolds stresses exhibiting a similar behaviour as previously found for boundary layers over surfaces with a rough to smooth transition.

Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 on S3

We construct and give a complete classification of all the differential symmetry breaking operators [Formula: see text], between the spaces of smooth sections of a vector bundle of rank [Formula: see text] over the [Formula: see text]-sphere [Formula: see text], and a line bundle over the [Formula: see text]-sphere [Formula: see text]. In particular, we give necessary and sufficient conditions on the tuple of parameters [Formula: see text] for which these operators exist.

Effects of superfine grinding sweet potato leaf powders on physicochemical and structure properties of sweet potato starch noodles.

Sweet potato leaves (SPLs) containing abundant functional components are consumed primarily as fresh vegetables worldwide. This study investigated the physical properties of superfine grinding SPLs powder, and their effects on cooking, texture, and sensory properties, micro- and molecular structures of starch noodles were also explored. The results showed that the bulk and tapped density (from 0.34 to 0.28 g/mL3 and from 0.69 to 0.61 g/mL3), repose and slid angle (from 42.15 to 30.96° and from 48.67 to 22.00°), water-holding capacity and swelling capacity (from 8.66 to 4.94 g/g and from 10.03 to 7.77 mL/g) of SPLs powders were decreased with milling time increased. The cooking loss, swelling index, texture, and sensory properties of SPLs sweet potato starch noodles (SPLSNs) were improved as the particle size of SPLs decreased. XRD and FT-IR showed that SPLSNs contained less complete crystallites (from 28.85% to 14.19%) and lower proportion of crystalline region (R 1047/1017 from 0.96 to 0.81, R 1017/994 from 0.41 to 0.43). SEM revealed that SPLSNs exhibited fewer ordered arrays and smooth cross sections. Our findings provide a foundation for utilizing SPLs and developing functional starch noodles.

Forecast Study on the Overall Coefficient for Passage of Single-Phase and Passage of Single-Phase in an Annular to Plain Tubes Heat Stream

Abstract To prevent buoyancy effects from increasing the overall heat transfer coefficient due to low heat flux, smooth vertical circular tubes require forced convection conjectures. Previous research has focused on mixed convection in turbulent regions and has limited studies on forced convective heat transfer. This study aims to investigate the predictable overall coefficients of heat transfer performance under specific conditions of forced convection, considering both vertical up flow and down flow through the smooth circular test section. The recommended Reynolds numbers for water are (7201.6–14577.4) and (3186.7–6396.75) for single-phase and single-phase annular passages, respectively, with a heat application range of (50–500 W). The overall coefficient of heat transfer is (333.91 - 432.95 W/m2.K) and (169.76 - 251.20 W/m2.K) for single-phase and single-phase annular passages, respectively. The flow was turbulent for all heat fluxes.

Effects of shearing processing on the quality and magnetic properties of electric steel sheet

Mechanical manufacturing process of electric motor induces a residual stress, which increases the iron loss, and affects the efficiency and performance of machine. In this paper, a shear test was carried out on a non-oriented electrical steel sheet with a thickness of 0.50 mm and a relative clearance range of 2–12% of the thickness, and the shear force was detected during shearing process. The sheared surface morphology, microhardness distribution and magnetic properties after the shearing processing were also tested. The obtained experimental results indicate that: as the shear clearance increases, the shear force increases, the plastic deformation zone enlarges, and the flow of microstructure becomes intense. In addition, as the shear clearance increases, the depth and work-hardening degree of the work-hardened layer increase, resulting in degraded magnetic properties of the electrical steel. Moreover, when the lateral clearance is 5%, a complete and smooth shear section can be obtained.

Gauss‐Prym maps on Enriques surfaces

AbstractWe prove that the kth Gaussian map is surjective on a polarized unnodal Enriques surface with . In particular, as a consequence, when , we obtain the surjectivity of the kth Gauss‐Prym map , with , on smooth hyperplane sections . In case , it is sufficient to ask .

Numerical Simulation Study on Influence of a Structural Parameter of D Bolt, an Energy-Absorbing Rock Bolt, on its Stress Distribution

A D bolt, an energy-absorbing rock bolt, is a smooth steel bar with a number of anchors along its length. The anchors, which can be spaced evenly or unevenly along its length, are firmly fixed within a borehole using either cement grout or resin, while the smooth sections of the bolt between the anchors may freely deform in response to rock dilation. A series of numerical simulations have been conducted using the finite difference method to investigate the effects of D bolt on the displacement increase of rock mass around a roadway in comparison with normal fully encapsulated rebar. As a result, the displacement of 49 mm at the top of roadway roof in the D bolts supported model is much larger than 30.08 mm in the fully encapsulated rebar bolts supported model so that the former is capable of absorbing potential deformation energy of rock mass around a roadway to tolerate the large deformation of rock. Plans of spacing arrangement of D bolt’s anchor have a significant effect on stress redistribution of the bolt. The numerical simulation result shows that for the D bolt with its whole length of 2.4 m, the length of its exposed section of 0.1 m, and the 4 anchors with the length of 0.1 m, the maximum tensile stress of 3.25 GPa generated in the D bolt with the ratio of the spacing between anchors (RSA) of 30 : 40 : 50 : 70 is lower about 1.13–1.31 times than the other D bolts with different ratio of spacing, and the changing range of stress is also the smallest, where the ratio of 30 : 40 : 50 : 70 indicates a ratio of lengths of deformable sections which is determined by turns from the innermost section of rock mass around roadway to the outermost section of roadway space. This study demonstrates that it is reasonable to employ the RSA of D bolt which makes it bring out its energy-absorbing capability to the full.

Anti-infective characteristics of a new Carbothane ventricular assist device driveline

ObjectivesDriveline infections are a major complication of ventricular assist device (VAD) therapy. A newly introduced Carbothane driveline has preliminarily demonstrated anti-infective potential against driveline infections. This study aimed to comprehensively assess the anti-biofilm capability of the Carbothane driveline and explore its physicochemical characteristics. MethodsWe assessed the Carbothane driveline against biofilm formation of leading microorganisms causing VAD driveline infections, including Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa and Candida albicans, using novel in vitro biofilm assays mimicking different infection micro-environments. The importance of physicochemical properties of the Carbothane driveline in microorganism-device interactions were analyzed, particularly focusing on the surface chemistry. The role of micro-gaps in driveline tunnels on biofilm migration was also examined. ResultsAll organisms were able to attach to the smooth and velour sections of the Carbothane driveline. Early microbial adherence, at least for S. aureus and S. epidermidis, did not proceed to the formation of mature biofilms in a drip-flow biofilm reactor mimicking the driveline exit site environment. The presence of a driveline tunnel however, promoted staphylococcal biofilm formation on the Carbothane driveline. Physicochemical analysis of the Carbothane driveline revealed surface characteristics that may have contributed to its anti-biofilm activity, such as the aliphatic nature of its surface. The presence of micro-gaps in the tunnel facilitated biofilm migration of the studied bacterial species. ConclusionThis study provides experimental evidence to support the anti-biofilm activity of the Carbothane driveline and uncovered specific physicochemical features that may explain its ability to inhibit biofilm formation.

Planning Queen Elizabeth II’s Visit to Bondi Beach in 1954

Planning Queen Elizabeth II’s Visit to Bondi Beach in 1954

On the structure group of an infinite dimensional JB-algebra

We extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with structure group S1.