Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

A New HARQ Scheme for 5G Systems via Interleaved Superposition Retransmission

Within the framework of the 5G new radio(NR),we propose a new hybrid automatic repeat request(HARQ)scheme to improve the throughput performance.The difference between the proposed scheme and the conventional one lies in the first retransmission,where the erroneous coded block group is interleaved and superimposed(XORed)onto a fresh coded block group.At the receiver,an iterative message-passing decoding algorithm can be employed to recover the target erroneous code block group(CBG).Only when the superposed retransmission fails,the conventional incremental redundancy(IR)or repetition redundancy(RR)retransmission is initiated.In any case,since the first retransmission is along with but has negligible effect on the fresh CBG,it costs neither transmitted power nor bandwidth.Monte-Carlo simulation results reveal that the presented HARQ schemes can achieve throughput improvements up to 10%over block fading channels and up to 50%over fast fading channels in comparison with the original 5G CBG-level HARQ scheme but without excessively increasing the implementation complexity.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

Building color and Psychological Evaluation Based on Superposition Analysis:A case study of Pingguoyuan Street in Beijing City

China’s construction has entered the high-quality development stage,and the building color landscape as the constituent element of the quality of urban artificial landscape has attracted more and more attention.In the process of building the building color evaluation system with the appeal of“public participation”,it is necessary to absorb and adopt public opinions,and the color planning practice cannot completely match the public opinions.In this paper,Pingguoyuan Street in Beijing City was taken as an example,and factor grading was constructed based on the relevant principle of“sensitivity grading”by analyzing the coupling relationship between color and urban artificial landscape structure.GIS technology was used to integrate and analyze residents’color sensitivity data obtained by investigation and interview and form the psychological evaluation of residents’color perception of artificial landscape,so as to provide scientific basis for the color planning of Pingguoyuan Street in Beijing City from the perspective of“space justice”.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

SUPERPOSITION ABOUT THE 3D VORTEX SOLUTIONS OF THE FLUID DYNAMIC EQUATION

A class of exact general solutions of an axisymmetric flow of the fluid dynamic equations is given. Then some examples are discussed. Some vortex solutions can be superposed to give other exact solutions. It can be used to analyse the generation and evolution of the vortex ring.

Dynamic Superposition and Levitation Capability of Two Confronting Ultrasonic Waves

The superposition dynamics of two confronting ultrasonic waves and their levitation capability for centimeter-sized thin disks are investigated by numerical analyses and validated by experiments. The sound pressure simulation reveals that two opposite ultrasonic waves provide a more effective standing-wave field than a single ultrasonic wave when the diameter of disk-shaped object approaches the wavelength scale. The dynamic superposition of two confronting beams facilitates the acoustic levitation of the clay disk and aluminum disk with diameters of 0.97 and 0.90. The acoustic radiation forces exerting on these thin disks are measured experimentally, which exhibit a better levitation stability for the centimeter-sized thin disks. The equilibrium levitation positions of the two disks are located near the sound pressure node, and the maximum acoustic radiation pressure on their surfaces is less than one percent of the maximum sound pressure.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

Spatial-Modulated Physical-Layer Network Coding Based on Block Markov Superposition Transmission for Maritime Relay Communications

As an alternative to satellite communications,multi-hop relay networks can be deployed for maritime long-distance communications.Distinct from terrestrial environment,marine radio signals are affected by many factors,e.g.,weather conditions,evaporation ducting,and ship rocking caused by waves.To ensure the data transmission reliability,the block Markov superposition transmission(BMST)codes,which are easily configurable and have predictable performance,are applied in this study.Meanwhile,the physical-layer network coding(PNC)scheme with spatial modulation(SM)is adopted to improve the spectrum utilization.For the BMST-SMPNC system,we propose an iterative algorithm,which utilizes the channel observations and the a priori information from BMST decoder,to compute the soft information corresponding to the XORed bits constructed by the relay node.The results indicate that the proposed scheme outperforms the convolutional coded SM-PNC over fast-fading Rician channels.Especially,the performance can be easily improved in high spatial correlation maritime channel by increasing the memory m.

DIVERSITY-AND-MULTIPLEXING TRADEOFF AND THROUGHPUT OF SUPERPOSITION CODING RELAYING STRATEGY

While the Network Coding cooperative relaying (NC-relaying) has the merit of high spectral efficiency,Superposition Coding relaying (SC-relaying) has the merit of high throughput. In this paper,a novel concept,coded cooperative relaying,is presented,which is a unified scheme of the NC-relaying and SC-relaying. For the SC-relaying strategy which can be considered one-way coded relaying scheme with multi-access channel,the close-form solution of the outage probabilities of the basic signal and additional signal are obtained firstly. Secondly,the Diversity-and-Multiplexing Tradeoff (DMT) characteristics of basic signal and additional signal are investigated entirely as well as the optimal close-form solutions. The compared numerical analysis shows the evaluation error of throughput based on the close-form solution is about 0.15 nats,which is within the acceptable error range. Due to the mutual effect between the both source signals,the available maximal values of the two multiplexing gains are less than 1.

APPLICATION OF TIME-TEMPERATURE SUPERPOSITION PRINCIPLE TO EVALUATION OF SCATTERING INTENSITY EVOLUTION IN PHASE SEPARATION FOR PMMA/SAN BLENDS

Spinodal phase separation behavior of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile)(PMMA/SAN)blends was investigated by the time-resolved small angle light scattering (SALS) technique. It was found that the influence oftemperature on the scattering intensity evolution followed the time-temperature superposition principle. The relationshipbetween temperature and the relaxation time of scattering intensity I(t) can be well described by the Williams-Landel-Ferry(WLF) function.

Superposition of Coherent States in a Mesoscopic Josephson Junction with Dissipation

A mesoscopic Josephson junction with dissipation is considered. Usually the dissipation in the system is described as a consequence of its coupling to a reservoir. By solving the master equation we show that the state of the junction can evolve in a quantum superposition of two coherent states even when the dissipation is present.

A superposition scheme for downlink multicell processing with finite backhaul capacity

In the scenario of downlink multicell processing withfinite backhaul capacity in the case of two base stations andtwo mobile users, by regarding the channel as a multipleaccess diamond channel with two destinations, an achievabilityscheme that sends correlated codewords through the multipleaccess channel with common data is proposed. By consideringthe superposition structure, fully correlated codewords can besupported by the proposed scheme, which can benefit thesystem throughput in the case of a relatively-large-capacitybackhaul. First, an achievable region for the achievable theoryis given and it is proved from the perspective of informationtheory. Then, in the Gaussian scenario, a simulationcombining dirty-paper coding and power allocating is providedfor the achievable region. Simulation results demonstrate thatwhen the backhaul capacity is relatively large, the proposedscheme outperforms the existing achievability scheme withoutthe SUlaerlaosition structure.

Generalized Block Markov Superposition Transmission over Free-Space Optical Links

In free-space optical(FSO) communications, the performance of the communication systems is severely degraded by atmospheric turbulence. Channel coding and diversity techniques are commonly used to combat channel fading induced by atmospheric turbulence. In this paper, we present the generalized block Markov superposition transmission(GBMST) of repetition codes to improve time diversity. In the GBMST scheme, information sub-blocks are transmitted in the block Markov superposition manner, with possibly different transmission memories. Based on analyzing an equivalent system, a lower bound on the bit-error-rate(BER) of the proposed scheme is presented. Simulation results demonstrate that, under a wide range of turbulence conditions, the proposed scheme improves diversity gain with only a slight reduction of transmission rate. In particular, with encoding memory sequence(0, 0, 8) and transmission rate 1/3, a diversity order of eleven is achieved under moderate turbulence conditions. Numerical results also show that, the GBMST systems with appropriate settings can approach the derived lower bound, implying that full diversity is achievable.

Numerical study on the separation and superposition of the influences from up-and downstream rotors

A three-dimensional Navier-Stokes solver is used to investigate the separation and superposition of the influences from upstream and downstream rotors in an axial-radial combined compressor for unsteady design applications.The data from rotor/stator and stator/rotor configurations show that the unsteady flow response in axial stator passage is caused only by one rotor.The results from the rotor/stator/rotor configuration revealed the superimposed characteristic of influences from upstream and downstream the rotor.The impact of the superimposed characteristic was studied by analyzing the virtual relative flow angle at the stator exit.The results show that the axial velocity in the passage of axial stator can be influenced by wake from upstream axial rotor and potential field of downstream radial rotor.While they are coupled to have an effect on the unsteady flow in axial stator passage,the excitation or suppression phenomena appear and lead to different levels of deterministic fluctuation kinetic energy.Their locations are determined by the frequencies of the involved influences.In addition,the variability of superimposed characteristic(excitation and suppression)at the stator exit modulates the inlet flow angle for downstream rotor.

Quantum metrology with coherent superposition of two different coded channels

We investigate the advantage of coherent superposition of two different coded channels in quantum metrology.In a continuous variable system,we show that the Heisenberg limit 1/N can be beaten by the coherent superposition without the help of indefinite causal order.And in parameter estimation,we demonstrate that the strategy with the coherent superposition can perform better than the strategy with quantum switch which can generate indefinite causal order.We analytically obtain the general form of estimation precision in terms of the quantum Fisher information and further prove that the nonlinear Hamiltonian can improve the estimation precision and make the measurement uncertainty scale as 1/N^(m) for m≥2.Our results can help to construct a high-precision measurement equipment,which can be applied to the detection of coupling strength and the test of time dilation and the modification of the canonical commutation relation.

A Novel Artificial Superposition Compound Eye

A new artificial superposition compound eye model is presented based on micro-lens array. In all compound eyes,it has the advantages of small volume,light weight,wide FOV,high sensitivity and much higher energy utilization ratio. Nevertheless,its structure is relatively complicated,especially the GRIN medium in the crystalline cone. Therefore,the modeling,analysis and fabrication for it are burdensome. In the established model,the GRIN is replaced by a curved micro-lens array. Thus,the modeling,analysis and optimization process are simple,and the components of artificial superposition compound eye are easy to be fabricated. The system is modeled by ZEMAX software. With the help of raytracing,its principle is analyzed,and the sensitivity comparison between the superposition compound eye and the apposition compound eye is done. The model's validity is proven.

Classification and exploration potential of sedimentary basins based on the superposition and evolution process of prototype basins

Classification,superimposed evolution and sedimentary filling of prototype basins are analyzed based on the Wilson cycle principle of plate theory,by dissecting the evolution history of 483 sedimentary basins around the world since the Pre-cambrian,combined with the three stress environments of tension,compression and shear.It is found that plate tectonic evo-lution controls the superimposed development process and petroleum-bearing conditions of the prototype basins in three as-pects:first,more than 85%of the sedimentary basins in the world are developed from the superimposed development of two or more prototype basins;second,the superposition evolution process of the prototype basin takes Wilson cycle as the cycle and cycles in a fixed trajectory repeatedly.In each stage of a cycle,a specific type of prototype basin can be formed;third,each prototype basin can form a unique tectonic-sedimentary system,which determines its unique source,reservoir,cap conditions etc.For hydrocarbon accumulation,the later superimposed prototype basin can change the oil and gas accumulation conditions of the earlier prototype basin,and may form new petroleum systems.Based on this,by defining the type of a current basin as its prototype basin formed by the latest plate tectonic movement,14 types of prototype basins can be classified in the world,namely,intracontinental growth rift,intr acontinental aborted rift,intercontinental rift,passive continental margin,interior craton,trench,fore-arc rift,ba ck-arc rift,back-arc de pression,back-arc small ocean,peri pheral foreland,back-arc foreland,strike-slip pull-apart,and strike-slip flexural basins.The classification scheme can ensure the uniqueness of the types of in di-vidual sedimentary basin,and make it possible to predict their oil and gas potential scientifically through analogy.

Macroscopic Quantum Superposition States in a Model of Photon-Supersonic Phonon Interaction

A model of photon-hypersonic phonon interaction is proposed. The evolution of macroscopic quantum superpo sition states is analyzed, including the wave function and number distribution. It is shown that a superposition state of hypersonic phonon modes can be generated in the case of nondetuning and no losses.

Quantum State Engineering by Superpositions of Coherent States along a Straight Line in Cavity Quantum Electrodynamics

A scheme is proposed for generating the superpositions of several coherent states in a cavity field with dispersive cavity quantum electrodynamics(QED).In the scheme,a sequence of atoms interact dispersively with the cavity field,connected with a microwave source,and is manipulated by classical fields,followed by state-selective measurements.In this way,the cavity field is collapsed onto a superposition of several coherent states along a straight line with controllable coefficients.This scheme provides the possibility for quantum state engineering via coherent-state superpositions in cavity QED for the first time.