EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHRDINGER SYSTEM

We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.

A study on the Antarctic circumpolar wave mode-A coexistence system of standing and traveling wave

The Antarctic circumpolar wave （ACW） has become a focus of the air-sea coupled Southern Ocean study since 1996, when it was discovered as an air-sea coupled interannual signal propagating eastward in the region of the Antarctic Circumpolar Current （ACC）. In order to analyze the mechanism of discontinuity along the latitudinal propagation, a new idea that ACW is a system with a traveling wave in the Southern Pacific and Atlantic Ocean and with a concurrent standing wave in the southern Indian Ocean is proposed in this paper. Based on the ideal wave principle, the average wave parameters of ACW is achieved using a non-linear approximation method, by which we find that the standing part and the traveling part possess similar radius frequency, proving their belonging to an integral system. We also give the latitudinal distribution of wave speed with which we could tell the reason for steady propagation during the same period. The spatial distribution of the propagation reveals complex process with variant spatial and temporal scales--The ENSO scale oscillation greatly impacts on the traveling process, while the result at the south of Australia indicates little connection between the Indian Ocean and the Pacific, which may be blocked by the vibration at the west of the Pacific. The advective effect of ACC on the propagation process should be examined clearly through dynamical method.

Standing,Periodic and Solitary Waves in (1+1)-Dimensional Caudry-Dodd-Gibbon-Sawada-Kortera System

In the paper, the variable separation approach, homoclinic test technique and bilinear method are successfullyextended to a (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera (CDGSK) system, respectively.Basedon the derived exact solutions, some significant types of localized excitations such as standing waves, periodic waves,solitary waves are simultaneously derived from the (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera systemby entrancing appropriate parameters.

The Generalized Pythagorean Comma Harmonic Powers of a Fundamental Frequency Are Equivalent the Standing Wave Harmonic Fraction System

Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system.

Existence and Stability of Standing Waves with Prescribed L2-Norm for a Class of Schrödinger-Bopp-Podolsky System

In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L2-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρwhen . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .

Study on Free-Standing Riser Under Different Working Conditions Based on 3D Co-Rotational Beam Element

When the free standing riser(FSR)is in service in the ocean,its mechanical properties are affected by various factors,including complex ocean current forces,buoyancy of the buoyancy can,and torque caused by the deflection of the upper floating body.These loads have a great influence on the deformation and internal force of the FSR.The static performance of FSR is investigated in this research under various working conditions.The finite element model of FSR is established based on the co-rotational method.The arc length approach is used to solve the model.The load is exerted in increments.The current load on the riser changes with the configuration of the riser.The accuracy of the numerical method is verified by Abaqus software.The calculation time is also compared.Then,the effects of uniform current,actual current and floating body yaw motion on FSR are studied by parameter analysis.Additionally,the influence of the FSR on the ocean current after the failure of part of the buoyancy can chamber is analyzed.The results show that the numerical model based on the co-rotational method can effectively simulate the large rotation and torsion behavior of FSR.This method has high computational efficiency and precision,and this method can quickly improve the efficiency of numerical calculation of static analysis of deep-water riser.The proposed technology may serve as an alternative to the existing proprietary commercial software,which uses a complex graphical user interface.

Assessing cutter-rock interaction during TBM tunnelling in granite:Large-scale standing rotary cutting tests and 3D DEM simulations

The widespread utilisation of tunnel boring machines(TBMs)in underground construction engineering requires a detailed investigation of the cutter-rock interaction.In this paper,we conduct a series of largescale standing rotary cutting tests on granite in conjunction with high-fidelity numerical simulations based on a particle-type discrete element method(DEM)to explore the effects of key cutting parameters on the TBM cutter performance and the distribution of cutter-rock contact stresses.The assessment results of cutter performance obtained from the cutting tests and numerical simulations reveal similar dependencies on the key cutting parameters.More specifically,the normal and rolling forces exhibit a positive correlation with penetration but are slightly influenced by the cutting radius.In contrast,the side force decreases as the cutting radius increases.Additionally,the side force shows a positive relationship with the penetration for smaller cutting radii but tends to become negative as the cutting radius increases.The cutter's relative effectiveness in rock breaking is significantly impacted by the penetration but shows little dependency on the cutting radius.Consequently,an optimal penetration is identified,leading to a low boreability index and specific energy.A combined Hertz-Weibull function is developed to fit the cutter-rock contact stress distribution obtained in DEM simulations,whereby an improved CSM(Colorado School of Mines)model is proposed by replacing the original monotonic cutting force distribution with this combined Hertz-Weibull model.The proposed model outperforms the original CSM model as demonstrated by a comparison of the estimated cutting forces with those from the tests/simulations.The findings from this work that advance our understanding of TBM cutter performance have important implications for improving the efficiency and reliability of TBM tunnelling in granite.

Fabrication of Free Standing Nanocellulose Film via Spray Coating and its Biomedical Application: A Review

Spraying nanocellulose onto films provides a quick and scalable way to create free-standing films with exceptional consistency and customizable thickness. This method increases the application of nanocellulose films in various industries and satisfies the requirements of large-scale production. In the field of biomedicine, spray-coated free-standing nanocellulose films hold great promise for applications such as drug delivery, tissue engineering, wound healing, device coatings, and biosensing. They are excellent nanomaterials for a variety of biomedical applications due to their special qualities, including biocompatibility, high mechanical strength, porous structure, large surface area, and adaptability. This paper reviewed the detailed exposure of the spray coating process of nanocellulose suspension onto free- standing films and its biomedical applications.

Effects of Standing Time during Pretreatment on the Nitrite Concentration Detected by Spectrophotometric Method

Food safety problems caused by excessive nitrite addition have been frequently reported and the detection of nitrite in food is particularly important. The standing time during the pretreatment of primary sample has a great influence on the concentration of nitrite tested by spectrophotometric method. In this context, three kinds of food samples are prepared, including canned mustard, canned fish and home-made pickled water. A series of standing times are placed during the sample pretreatments and the corresponding nitrite contents in these samples are detected by spectrophotometric method based on N-ethylenediamine dihydrochloride. This study aims to find out a reasonable standing time during the pretreatment of food sample, providing influence factor for precise detection of nitrite.

Existence and Stability of Standing Waves for the Nonlinear Schrödinger Equation with Combined Nonlinearities and a Partial Harmonic Potential

In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L2-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.

Contact Analysis and Modeling of Standing Wave Linear Ultrasonic Motor

A contact model for describing the contact mechanics between the stator and slider of the standing wave linear ultrasonic motor was presented. The proposed model starts from the assumption that the vibration characteristics of the stator is not affected by the contact process. A modified friction models was used to analyze the contact problems. Firstly, the dynamic normal contact force, interface friction force, and steady-state characteristics were analyzed. Secondly, the influences of the contact layer material, the dynamic characteristics of the stator, and the pre-load on motor performance were simulated. Finally, to validate the contact model, a linear ultrasonic motor based on in-plane modes was used as an example. The corresponding results show that a set of simulation of motor performances based on the proposed contact mechanism is in good agreement with experimental results. This model is helpful to understanding the operation principle of the standing wave linear motor and thus contributes to the design of these types of motor.

The coppice-with-standards silvicultural system as applied to Eucalyptus plantations-a review

We review the management of Eucalyptus species under a coppice-with-standards （CWS） silvicultural system. CWS management results in product diversification, permitting production of small and large scale timber from the same stand. Eucalyptus species are suitable candidates for CWS management because： there are large worldwide plantation areas, sprouting capacity is high, and eucalypts are multipur- pose species. We discuss （1） short rotation Eucalyptus coppice manage- ment for energy and pulping and （2） Eucalyptus seedling management for solid wood products. We review the literature and discuss experi- ences with Eucalyptus managed under the CWS system. We also assess projects dealing with Eucalyptus coppice management, stand density regulation, pruning, and stand and wood quality. The growth environ- ment of the standard trees （heavy competition up to the first harvest, free growth afterwards） coupled with long rotations （〉20 years） results in high quality logs for solid wood products. Early pruning should be ap- plied to enhance wood quality. We propose a system for the silvicultural management of Eucalyptus under the CWS system, elaborating on the consequences of initial planting density, site productivity, and standard tree densities as well as timing of basic silvicultural applications.

Simulation and Implementation of Structure and Growth Visualization System of Artificial Mixed Stand

[Objective] The objective of this paper was to study the simulation and implementation of structure and growth visualization system of artificial mixed stand. [Method] The mixed stand structure visualization model and growth visualization model were built on the base of the characteristics of mixed stand structure and the relationship between growth and environment; and the C# language and MOGRE graphics engine were used to establish the mixed stand structure and growth visualization system. [Result] The mixed stand structure visualization model and growth visualization model were built, as well as the mixed stand structure and growth visualization system. [Conclusion] This paper realized the visualization simulation of the mixed stand structure and growth.

Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt

It was attempted to enhance and accelerate the separation of oxidation inclusions from magnesium alloy melt by virtue of ultrasonic agglomeration technology.In order to investigate the feasibility and effectiveness of standing waves for ultrasonic purification of magnesium alloy melt,numerical simulation and relevant experiment were carried out.The numerical simulation was broken into two main aspects.On one hand,the ultrasonic field propagations within the cells with various shapes were characterized by numerical solutions of the wave equation and with a careful choice of geometry a nearly idealized standing wave field was finally obtained.On the other hand,within such a standing wave field the agglomeration behavior of oxidation inclusions in magnesium alloy melt was analyzed and discussed.The agglomeration time and agglomeration position of oxidation inclusions were predicted with numerical simulation method.The results show that the oxidation inclusions whose apparent densities are close to the density of the melt can agglomerate at wave nodes in a short time which to a great extent enhances and accelerates the separation of oxidation inclusions from magnesium alloy melt.

A hybrid tubular standing support for underground mines:Compressive behaviour

This paper presents the development of an innovative standing support for underground mines.The main feature of this standing support is its exterior container,a combination of polyvinyl chloride(PVC)with large rupture strain and fibre-reinforced polymer(FRP)with high strength-to-weight ratio.To demonstrate the advantages of this cementitious grout filled PVC-FRP tubular(PFT)standing support,a series of compression tests were conducted.Test variables included the strength of cementitious grout infill material and the thickness of FRP jacket.Compression tests were also conducted on cementitious grout-filled PVC tubular(PT)support and cementitious grout-filled FRP tubular(FT)support.These tests showed that PFT support presents a typical strain-hardening behaviour together with an outstanding axial deformation ability(>20%of the overall height of the support).In addition,the maximum compressive strength of PFT support is much higher than that of the corresponding PT support and FT support.Furthermore,using thicker FRP jacket or high strength cementitious grout material can enhance the load carrying capacity of PFT support.These comparative results indicated that the high performance of PFT support is mainly attributed to the combination of confining constituents(i.e.PVC and FRP)and infill material.

Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.

Plant functional trait diversity and structural diversity co-underpin ecosystem multifunctionality in subtropical forests

Tree species diversity is assumed to be an important component in managing forest ecosystems because of effects on multiple functions or ecosystem multifunctionality.However,the importance of tree diversity in determining multifunctionality in structurally complex subtropical forests relative to other regulators(e.g.,soil microbial diversity,stand structure,and environmental conditions)remains uncertain.In this study,effects of aboveground(species richness and functional and structural diversity)and belowground(bacterial and fungal diversity)biodiversity,functional composition(community-weighted means of species traits),stand structure(diameter at breast height and stand density),and soil factors(pH and bulk density)on multifunctionality(including biomass production,carbon stock,and nutrient cycling)were examined along a tree diversity gradient in subtropical forests.The community-weighted mean of tree maximum height was the best predictor of ecosystem multifunctionality.Functional diversity explained a higher proportion of the variation in multifunctionality than that of species richness and fungal diversity.Stand structure-played an important role in modulating the effects of tree diversity on multifunctionality.The work highlights that species composition and maximizing forest structural complexity are effective strategies to increase forest multifunctionality while also conserving biodiversity in the management of multifunctional forests under global environmental changes.

The characteristic and prediction of scour in front of breakwaters by standing waves

In this paper bottom scours in front of vertical breakwaters by standing waves are systematically investigated, the scouring patterns, criterion for differentiating the scouring patterns and scouring mechanism are discussed ; a formula of maximum depth of scouring trough considering sediment size is given; and influence of mound foundation on bottom scours is investigated.

Physical design and cooling test of C-band standing wave accelerating tube

The physical design and cooling test of a C-band 2MeV standing wave （SW） accelerating tube are described in this paper. The designed accelerating structure consists of 3-cell buncher and 4-cell accelerating section with a total length of about 163mm, excited with 1MW magnetron. Dynamic simulation presents that about 150mA beam pulse current and 30% capture efficiency can be achieved. By means of nonlinear Gauss fit on electron transverse distribution, the diameter of beam spot FWHM （full width at half maximum of density distribution） is about 0.55mm. Cooling test results of the accelerating tube show that frequencies of cavities are tuned to 5527MHz and the field distribution of bunching section is about 3：9：10.

Room-temperature test system for 162.5 MHz high-power couplers

Fundamental power couplers are crucial components for feeding radio frequency power to accelerating cavities. Couplers must be tested and conditioned on a room-temperature test stand to evaluate and potentially improve their performance before being installed in an accelerating cavity. A new test system has been designed and is under construction at the institute of modern physics.For this test system, multiple conditioning modes, including the pulse mode, CW mode, and amplitude-sweeping mode, have been embedded in the low-level radio frequency system of the test stand. All of these conditioning modes can be run manually or automatically. In addition, a novel test cavity is proposed and has been designed, which facilitates non-contact conditioning and a multi-purpose test stand.