Superposition Type Research Articles

Geochronology, in-situ elements and sulfur isotopes of sulfides from the Songjiashan cobalt-iron deposit in the Zhongtiao mountains of North China Craton: Implications for cobalt occurrence and ore genesis

The Songjiashan Co-Fe deposit in the central part of the “Tongshan skylight” on the southeastern edge of the Zhongtiao Mountains is hosted by the volcanic-sedimentary rock series of the Paleoproterozoic Songjiashan Group. The spatial distribution of the orebodies is controlled by south-north trending rock units. Based on microscopic observations, the dominant ore minerals included magnetite, pyrite, chalcopyrite, carrollite, and linnaeite, while gangue minerals comprised quartz, calcite, sericite, and chlorite. Cobalt-iron ores had massive, banded, disseminated, and veinlet texture, and alteration of the host rocks included silicification, sericitization, pyritization, carbonation, and chloritization. Mineralization processes of the Songjiashan deposit were grouped into three periods: sedimentation, metamorphism, and hydrothermal. The Co concentrations in hydrothermal pyrite (Py-III) varied from 1.05 % to 3.75 %, with an average of 2.45 %. Cobalt in pyrite was homogeneously distributed and inversely correlated to Fe, indicating that Co isomorphically replaced Fe in pyrite. The characteristic Co/Ni ratio of pyrite varied greatly, ranging from 0.1 to 1000, reflecting various genetic types of sedimentation, metamorphism, and hydrothermal mineralization, with the main mineralization period primarily related to hydrothermal activities. Zircon U-Pb geochronology of the host rock and Re-Os isochron of Co-bearing pyrites indicate that Co mineralization mainly occurred at ∼2100 Ma. In-situ S isotopic analysis of sulfides reveals two peak δ34S values of 5–9 ‰ and 12–16 ‰. We interpret that the former value reflects the mixing of volcanic and marine sulfate sources, while the latter value is mainly artributted to marine sulfate sources. All δ34S values were lower than those of Proterozoic marine sulfates (15–20 ‰). Accordingly, we infer that thermochemical sulfate reduction plays a key role in marine sulfate reduction, and that the formation of Co-rich ore bodies in the Songjiashan deposit have undergone processes of initial sedimentation, metamorphism-deformation, and subsequent hydrothermal overprinting. Genetically, we suggest that the Songjiashan deposit belongs to a sedimentary-metamorphic hydrothermal superposition type Co-Fe deposit.

Fine structure of the compound eyes of the crepuscular moth Grapholita molesta (Busck 1916) (Lepidoptera: Tortricidae).

Morphological organization, ultrastructure and adaptational changes under different light intensities (10000, 100, 1, and 0.01mW/m2) of the compound eye of the oriental fruit moth Grapholita molesta (Busck 1916) were investigated. Its superposition type of eyes consist of approximately 1072 ommatidia in males and 1029 ommatidia in females with ommatidial diameters of around 15μm. Each ommatidium features a laminated corneal lens densely covered by corneal nipples of 256nm in height. Crystalline cones are formed by four cone cells, proximally tapering to form a narrow crystalline tract with a diameter of 1.5μm. Eight retinula cells, two primary and six secondary pigment cells per ommatidium are present. The 62.3μm long rhabdom is divided into a thin 1.8μm wide distal and a 5.2μm wide proximal region. Distally the fused rhabdom consists of the rhabdomeres of seven retinula cells (R1-R7) and connects with the crystalline cone. In the proximal rhabdom region, the pigment-containing retinula cell R8 occupies a position in centre of the rhabdom while R1-R7 cells have taken peripheral positions. At this level each ommatidial group of retinula cells is surrounded by a tracheal tapetum. In response to changes from bright-light to dim-light adaptations, the pigment granules in the secondary pigment cells and retinula cells migrate distally, with a decrease in the length of crystalline tract.

Resonance Interaction Due to Quantum Coherence

AbstractThe interaction energy between two atoms is crucially dependent on the quantum state of the two‐atom system. In this paper, it is demonstrated that a steady resonance interaction energy between two atoms exists when the atoms are in a certain type of coherent superposition of single‐excitation states. The interaction is tree‐level classical in the sense of the Feynman diagrams. A quantity called quantum classicality is defined in the present paper, whose nonzero‐ness ensures the existence of this interaction. The dependence of the interatomic interaction on the quantum nature of the state of the two‐atom system may potentially be tested with Rydberg atoms.

Критерий полноты и субмаксимальные ультраклоны для линейных гиперфункций ранга 2

In recent years, the direction associated with the study of maps from a finite set A to the set of all subsets of the set A, including the empty one, has been intensively developing. Such mappings are called multifunctions on A, as well as hyperfunctions on A, if an empty subset is excluded from the subsets under consideration. It is not difficult to see that the so-called undefined or undefined functions, which are studied in many works, are most directly related to this field of research. The power of the set A is called the rank of multifunction or hyperfunction. Obviously, multifunctions and hyperfunctions generalize well-known functions of k-valued logic, however, it should be noted that the usual superposition of functions of k-valued logic is not suitable for multifunctions and hyperfunctions. Two types of superpositions are most often considered here, one of them leads to sets closed relative to the superposition, which are called multiclones and hyperclones, and for the second type of superposition, closed sets are called ultraclones and partial ultraclones. In this article, the elements of the rank 2 ultraclone lattice are considered. By now, all the maximum and minimum elements of this lattice are known. For example, Panteleev V.I. described all maximal ultraclones in the predicate language, which allowed us to prove the completeness criterion of an arbitrary system of hyperfunctions of rank 2. We managed to prove the completeness criterion in the maximal ultraclone of linear hyperfunctions of rank 2. Thus, all submaximal ultraclones of linear hyperfunctions are described.

Development of a new correlation for pre-dry out evaporative heat transfer coefficient of R290 in a microchannel

Although many correlations have and are being developed for two-phase heat transfer coefficient correlation in microchannels, none has the desired accuracy yet. This paper presents prospective improvements in the convective heat transfer coefficient correlation accuracy for the dry-out conditions; when the heat transfer coefficient drops at a certain vapor quality. An accurate heat transfer coefficient forecast is needed to minimize over or under design, conserve energy and material, and maximize the performance. R290 has been reported to be more energy efficient than R22. A new correlation relevant for R290 across 831 sets of experimental data points in a microchannel was generated by optimizing six variables in the nucleate boiling suppression factor, S, and force convective factor, F, of a selected superposition type correlation. The new correlation was optimized for saturation temperature ranging between 5 and 25 °C, diameter ranging between 1.0 and 6.0 mm, heat flux ranging between 2.5 and 60 kW/m2, and mass flux ranging between 50 and 500 kg/m2s. The MAE was reduced from 21.84 to 17.02% for pre-dry out data. The new correlation may be utilized to estimate the heat transfer coefficient of R290 in heat transfer analysis in a microchannel under the investigated operating conditions. The optimization approach utilized here has the potential of continuously improving the MAE of any heat transfer correlation for any refrigerants considered.

Functional eye rudiments in the anchialine crab Munidopsis polymorpha (Crustacea: Galatheidae)

Abstract The white crab Munidopsis polymorpha (Crustacea: Galatheidae) is the only one of a species-rich genus not occurring in the deep sea. It is endemic to marine caves, anchialine pools and groundwaters of the volcanic island of Lanzarote (Canary Islands). The eye derives from the superposition type possessing a clear zone formed by the proximal extensions of the rudimentary crystalline cones. The number of ommatidia ranges among the lowest found in decapods and the optic ganglia are strongly diminished in size. The crystalline cones are rudimentary or lost and facets with individual corneas are not discernible. The rhabdoms are tiny and irregularly arranged in the rhabdom layer. Some rhabdoms display an open arrangement of rhabdomers with microvilli that are not aligned to form orthogonal layers. The eye is one of the rare exceptions of traits that despite being rudimentary is still partially functional. The absence of stabilizing selection is probably the reason for variability or reduction of the traits necessary for image formation. In contrast, negative phototactic behaviour is present, because light is still perceived by the eyes of M. polymorpha.

Sensitivity of Wake Modelling Setups

Engineering wake modelling with single turbine wake models and wake superposition models (SupModel) requires the choice of two crucial settings: the type of wake superposition and the wake expansion rate parameter. Based on offshore wind farm measurements, the appropriate tuning of such wake modelling setups with respect to wind farm efficiency and their sensitivity to this tuning is investigated. For this purpose, universal and inflow-individual wake expansion rate parameters are optimised for different SupModels via minimising the deviation between simulated and measured power and to compare the results to simulations using a literature value. The work reveals a logarithmic, SupModel-independent sensitivity of the farm efficiency to the wake expansion rate, sufficient to allow equally accurate modelling performance for all setups if a matching parameter is chosen. The choice of the SupModel only matters in case of an unadapted wake expansion rate parameter. Beyond that, the results indicate a systematic flaw of wake models in reproducing farm power measurements for both weak and full wake situations with the same model tuning. Inflow-individual parameters obtained by this work mitigate this with a systematic pattern over wind speed and wind direction and can significantly decrease the modelling uncertainty over varying inflow conditions.

Characteristics of Seepage Barriers in Fluvial Reservoirs of Meandering Rivers and Their Impacts on Water Injection Development: A Case Study of Neogene Guantao Formation in Block M, Gudao Oilfield

To deepen our understanding of reservoir heterogeneity, seepage barriers in the study area were divided into interlayer, intralayer, and planar levels based on their spatial distribution characteristics and then investigated by taking the third member of the Neogene Guantao Formation in the block M of the Gudao oilfield as an example. Based on their genesis characteristics, the interlayer seepage barriers were divided into the overbank sand-overbank sand type, overbank sand-channel type, isolated channel superposition type, and channel shallow-cut type. The planar seepage barriers were categorized into the channel boundary type, abandoned channel type, channel-overbank sand type, and floodplain mudstone type. The intralayer seepage barriers were classified into the mudstone type and physical property type. Classifying multiple levels of different types of seepage barriers led to the refinement of their spatial characteristics. The strength of seepage barriers was characterized using the “seepage barrier coefficient” and “reservoir quality coefficient,” and the small-valued coefficients of the interlayer and intralayer seepage barriers indicated that these seepage barriers are characterized by large thickness, high mudstone content, poor physical properties, and weak seepage ability. The strength of the planar seepage barriers was dependent on the sedimentary facies types and channel stages, and the difference between planar seepage barriers was characterized using the reservoir quality coefficient. The seepage barriers were described based on the multilevel classification of seepage barrier categories, the intralayer seepage barriers with a lateral accretion pattern in the meandering river point bars were identified and described, and the distribution characteristics of seepage barriers were summarized at multiple levels. The method of “hierarchical analysis, skeleton construction, and category fitting” was used to establish 3D models of different levels of seepage barriers, and a modeling method based on the characteristics of intralayer seepage barriers under the constraint of architecture pattern was used to model intralayer seepage barriers with a lateral accretion pattern. In the monitoring of water injection profiles, it was found that the extent of blockage achieved by seepage barriers affects the water injection volume and thus controls the fluid transport pattern. Due to the development characteristics of the seepage barrier in the formation, there are some differences in injection production efficiency under different well pattern matching modes. The research on the distribution characteristics of different levels of seepage barrier categories provides a reliable geological basis for improving the injection-production relationship.

Fine Depiction of the Single Sand Body and Connectivity Unit of a Deltaic Front Underwater Distributary Channel: Taking the Third Member of the Dongying Formation in the Cha71 Fault Block of the Chaheji Oilfield as an Example

By taking the third member of the Dongying Formation in the Cha71 fault block of the Chaheji oilfield as an example, the single sand body of the deltaic front underwater distributary channel is meticulously depicted by using the data of well logging and performance production. Portrays the vertical separation model, total lateral separation type, vertical type, lateral superposition type, 4 types of single sand body vertical superimposed and bay type, bank contact between docking, instead of four kinds of single sand body lateral contact type, and summarizes its logging facies identification. The quantitative prediction model of the single sand body was established, the characteristics of single sand body plane distribution were summarized, and the identification of the oil-water layer and the lower limit of reservoir effective thickness were studied. And we got the conclusion that based on the fine characterization of the single sand body and the lower limit standard of effective reservoir thickness, the distribution range of the effective reservoir and connecting unit is determined. Finally, the connectivity of the connecting unit is verified by dynamic data.

Superposition type coherent states in all dimensional loop quantum gravity

We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is given by constructing proper superposition over quantum numbers of the spin-networks with vertices labelled by the coherent intertwiners. Such superposition type coherent states are labelled by the so-called generalized twisted geometric variables which capture the geometric meaning of discretized general relativity. We study the basic properties of this kind of coherent states, i.e., the completeness and peakedness property. Moreover, we show that the superposition type coherent states are consistent with Thiemann's coherent state for $SO(D+1)$ gauge theory in large $\eta$ limit.

An Analytical Method to Test Elastic Rock Mass Parameters Based on a Macro-Joint Model

The measurement of rock joint parameters is a hotly debated and difficult problem in rock mechanics. Joints have great influence on the propagation of stress waves in rock mass. Since the multiple reflections of stress waves propagating inside the joints is not considered accurately, the reflection wave shape cannot be obtained by using a discontinuous displacement model to describe the deformation characteristics of joints. A joint is regarded as a rock using the first analysis of the stress wave transmission in the course of a single joint and the propagation law of a reflection wave. For rocks orientated in the same direction with the same type of wave superposition, stress wave parameters can be established through the multiple reflection effect of a single-joint analysis model. Further to this, analysis using an extended single-joint model can estimate a stress wave under the condition of a vertical incidence group parallel strata analysis model. Taking a single macro-joint as an example, a measuring line is arranged in the normal direction of the joint, and two measuring points on both sides of the joint are arranged in a line to record the waveforms of the incident and transmitted waves. According to the established single-joint analysis model, the calculated waveform of the incident side measuring point is calculated by using the measured waveform of the transmission side measuring point, and the measured waveform of the incident side measuring point is compared with the measured waveform of the incident side measuring point, and the joint elastic parameters with the minimum error are obtained by using the principle of least square method. Six tests were carried out through joints with a thickness of 0.04 m. The results show that the primary wave (P-wave) and secondary vertical wave (SV wave) velocity of joints obtained from many tests have good consistency, which indicates that the joint analysis model has good stability, and the test solution of joint elastic parameters based on the model is reliable.

Navigating the Hilbert space of nonseparable elastic states in arrays of periodically coupled one-dimensional waveguides

A planar array of three one-dimensional elastic waveguides mutually coupled periodically along their length and driven externally is shown theoretically and numerically to support nonseparable superpositions of states. These states are the product of Bloch waves describing the elastic displacement along the waveguides and spatial modes representing the displacement across the array of waveguides. For a system composed of finite length waveguides, the frequency, relative amplitude, and phase of the external drivers can be employed to selectively excite specific groups of discrete product modes. The periodicity of the coupling is used to fold bands enabling superpositions of states that span the complete Hilbert space of product states. We show that we can realize a transformation from one type of nonseparable superposition to another one that is analogous to a nontrivial quantum gate. This transformation is also interpreted as the complex conjugation operator in the space of the complex amplitudes of individual waveguides.

Approximate Minimax Estimation of Functionals of Solutions to the Wave Equation under Nonlinear Observations

The authors consider the problem of minimax estimation of a functional of the solution to the wave equation with rapidly oscillating coefficients. The observation (output signal) is nonlinear (has the operator of superposition type). For the small parameter e > 0, the existence of the solution of the original problem is proved using the traditional minimax approach. Transition to a homogenized parameter problem allows us to remove the nonlinearity in the observation. The main result of the paper is that the minimax estimate of the problem with homogenized parameters is an approximate minimax estimate of the original problem.

POD analysis of passage-layout effect on unsteady internal flow in a realistic blade serpentine coolant channel with low aspect ratios

Internal serpentine ribbed coolant channel with low aspect ratio (AR) has been widely employed to provide excellent thermal protection for advanced first-stage turbine blades. Various height differences (ΔHs) of adjacent passages along pressure side can be generated under the restriction of actual blade profile. The present work made an attempt to acquire detailed influences of ΔH on the time-averaged and transient secondary motions near sharp bends of low-AR coolant channels. An actual blade ribbed three-pass coolant channel with two ΔHs was chosen as experimental model. Planar time-resolved particle image velocimetry technique was applied to capture the transient flow fields in 21 typical cross sections. Time-averaged results were validated by standard PIV measurements and flow visualizations. Snapshot proper orthogonal decomposition was employed to extract the dominant flow structures and identify the underlying small-scale flow patterns in time-resolved velocity fields. The experimental results indicated the low-AR channel with real blade profile induces a new type of the secondary-vortex superposition downstream of bends, in comparison with the large-AR channels in open literature. The crucial reason is the ΔH along pressure side leads to an intensive impingement on the bend wall, which weakens the effects of bend, rib and curvature of suction side. Another new discovery is the effect of ΔH on unsteady internal flow. In the small ΔH case, the oscillatory frequency of the secondary vortices is nearly similar with the counter-rotating Dean-vortices; however, in the large ΔH case, the oscillatory frequency is much lower, and the rotating direction of vortices is same and unchanged in a period. Increasing inlet Reynolds number can significantly change the underlying small-scale flow patterns and improve the oscillatory frequency of large-scale structures, although the basic time-averaged flow patterns are nearly same. Effect of injection from auxiliary-hole (AH) on unsteady internal flow is obvious and the optimum mass flow ratio of AH-to-inlet is 5%.

Resource theories of communication

A series of recent works has shown that placing communication channels in a coherent superposition of alternative configurations can boost their ability to transmit information. Instances of this phenomenon are the advantages arising from the use of communication devices in a superposition of alternative causal orders, and those arising from the transmission of information along a superposition of alternative trajectories. The relation among these advantages has been the subject of recent debate, with some authors claiming that the advantages of the superposition of orders could be reproduced, and even surpassed, by other forms of superpositions. To shed light on this debate, we develop a general framework of resource theories of communication. In this framework, the resources are communication devices, and the allowed operations are (a) the placement of communication devices between the communicating parties, and (b) the connection of communication devices with local devices in the parties’ laboratories. The allowed operations are required to satisfy the minimal condition that they do not enable communication independently of the devices representing the initial resources. The resource-theoretic analysis reveals that the aforementioned criticisms on the superposition of causal orders were based on an uneven comparison between different types of quantum superpositions, exhibiting different operational features.

On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

Improvement of two-phase heat transfer correlation superposition type for propane by genetic algorithm

The prediction accuracies of the two-phase heat transfer coefficient for the flow in a small channel, which are usually based on the mean absolute error (MAE) between the correlation and experimental data, have remained unsatisfactory. Conventionally, the regression method has been used to determine the correlation that best represents the experimental data. In this paper, an improved heat transfer correlation for the evaporation of propane is developed by applying the genetic algorithm method. A total of 789 data points from 4 sources with circular diameters ranging from 1.0 to 6.0 mm are used to minimise the MAE while searching for the optimum conditions for the suppression factor, S, and convective factor, F, in a selected superposition correlation for two different vapour quality ranges. The optimisation can minimise the MAE at 33% and 25% for Case I and Case II, respectively. The proposed method assists in attaining a precise empirical prediction that fits well with the experimental data.

Poincaré Bessel beams: structure and propagation

Non-separable superpositions of polarization and spatial modes in Gaussian beams have shown rich patterns of spatially-variable polarization encoded in the transverse mode of the light, with the potential for many applications. In this work, we investigate encoding similar types of superpositions in Bessel beams. We find that analogously to what is observed in Poincaré–Gaussian beams, Poincaré–Bessel beams can be produced by Bessel-mode superpositions. They show polarization patterns with disclinations in the orientation of the polarization ellipse and mappings of the Poincaré sphere onto the transverse mode. We report on the observation of lemons, stars and monstar disclinations in the multi-ringed profile of Bessel modes. By manipulating the angular spectrum of the component Bessel beams, we are able to impart linear rotation of the patterns along the non-diffracting range due to a linearly increasing propagation phase difference.

Orbital-Angular-Momentum Multiplexed Continuous-Variable Entanglement from Four-Wave Mixing in Hot Atomic Vapor.

Multiplexing is crucial for the data-carrying capacity of information communication systems. Orbital angular momentum (OAM) with a topological charge ℓ (ℓ integer) provides a degree of freedom to realize multiplexing. In this Letter, we report an experimental implementation of OAM multiplexed continuous variables (CV) entanglement based on a four-wave mixing (FWM) process, in which 13 pairs of entangled Laguerre-Gauss (LG) modes, LG_{ℓ,pr} and LG_{-ℓ,conj}, are simultaneously and deterministically generated, where ℓ (ℓ integer) is the topological charge corresponding to the OAM mode and pr (conj) indicates a probe (conjugate) beam. In the meanwhile, we experimentally show that there is no entanglement between the modes of LG_{ℓ,pr} and LG_{ℓ,conj} (ℓ≠0). These results clearly confirm the conservation of OAM in the FWM process from the viewpoint of a CV system. In addition, we investigate the entanglement properties of three types of coherent superposition of OAM modes. In the end, we also study the effect of the pump beam radius on the number of OAM multiplexing. Such OAM multiplexed CV entanglement provides a new perspective and platform to study CV quantum information protocols.

Approximate minimax estimation of functional from the solution of parabolic boundary-value problem with rapidly oscillating coefficients under nonlinear observations

The article deals with the problem of the minimax estimation of a functional from the solution of a parabolic boundary-value problem with rapidly oscillating coefficients. We measure not the value that describes the investigated process, but some value from the solution with an operator, which determines the way of measurement. The problem is complicated not only due to the rapidly fluctuating coefficients and unknown functions that are included in the equation and initial conditions, but also due to the observation being nonlinear (it has a superposition type operator). At a value of the small parameter, the solution existence for the original problem is established using the traditional minimax approach. The transition to a problem with averaged parameters allows us to get rid of nonlinearity in the observation. The main result of the work is to prove that the minimax estimate of the problem with averaged coefficients is an approximate minimax estimate of the original problem.