Exact Solutions of Forced Schrödinger Equation and How to Choose the External Forces

Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.

Poroelastodynamic responses and elastic moduli of a transversely isotropic porous cylinder under forced deformation test

Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.

Experimentation of a Forced Convection Solar Dryer for Drying Sweet Potatoes at the Higher Institute of Technology of Mamou-Guinea

This study was carried out at the Mamou Higher Institute of Technology during the period from March 10 to April 15, 2022, with the aim of designing and testing a solar dryer with forced convection by drying potatoes. The dryer was designed using local materials. Its main geometric parameters are: 1) height of the drying chamber (90 cm), 2) length of the drying chamber (50 cm), 3) width of the drying chamber (43 cm), 4) surface of the racks (0.1806 m2), 5) surface of the heat accumulator (0.2537 m2). The experiment focused on the vacuum test of the dryer for two days and that of the drying of the sweet potato for three days from 8:30 a.m. to 5:30 p.m. The average vacuum test temperature values of the three environments are respectively accumulator (43°C), dryer chamber (41°C) and ambient environment (34°C). Four kilograms (4 kg) of boiled sweet potato were dried. The average temperatures in the accumulator and in the drying chamber during the three days of drying are respectively 33°C and 39°C. The final mass of the dried product is 1.2 kg, with a quantity of water extracted of 2 liters or 63% of the initial mass of the product. The average drying rate is 0.074 kg/h. The drying kinetics showed a decreasing rate in the absence of the heating period and the constant rate period.

Existence of Forced Waves and Their Asymptotic for Leslie-Gower Prey-Predator Model with Nonlocal Effects under Shifting Environment

In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails.

Insights into in-situ imbibition behavior of fracturing fluid in propped shale fractures based on nuclear magnetic resonance:A case study from Longmaxi Formation shale,Sichuan Basin,China

Shale gas is an important component of unconventional oil and gas resources.Studying the imbibition behavior is helpful to optimize flowback parameters and enhance gas recovery.Recent imbibition studies have focused on shale matrix,and the pressure conditions discussed were mostly atmospheric.The initial imbibition behavior begins from propped fractures to matrix,but there are few studies working on explaining the imbibition behavior in propped fractures or the phenomenon of many shale wells exhibit higher productivity after a“soaking”period.Therefore,propped fracture samples were designed for imbibition and migration experiments.In order to accurately study the mechanism and main influencing factors of fracturing fluid imbibition and migration in propped and unpropped shale fractures under high temperature and high pressure,a series of experiments based on nuclear magnetic resonance(NMR)were carried out.Results showed that NMR T_(2) spectra of all samples exhibited a bimodal distribution.The final imbibition volume of fracturing fluid was positively related to pressure and fracture width.The imbibition effect of fracturing fluid was more evident in matrix pores under high pressure.In the migration during soaking stage,the fracturing fluid gradually migrated from large pores to small pores and gradually displaced the shale gas from the matrix,thus allowing the water blocking in propped fractures to self-unlock to some extent.Gas permeability decreased in the imbibition stage,while it recovered in the migration stage to some extent.

Experimental and numerical simulation study on forced ventilation and dust removal of coal mine heading surface

In order to study the problems of unreasonable airflow distribution and serious dust pollution in a heading surface,an experimental platform for forced ventilation and dust removal was built based on the similar principles.Through the similar experiment and numerical simulation,the distribution of airflow field in the roadway and the spatial and temporal evolution of dust pollution under the conditions of forced ventilation were determined.The airflow field in the roadway can be divided into three zones:jet zone,vortex zone and reflux zone.The dust concentration gradually decreases from the head to the rear of the roadway.Under the forced ventilation conditions,there is a unilateral accumulation of dust,with higher dust concentrations away from the ducts.The position of the equipment has an interception effect on the dust.The maximum error between the test value and the simulation result is 12.9%,which verifies the accuracy of the experimental results.The research results can provide theoretical guidance for the application of dust removal technology in coal mine.

Study of the Lift Force Induced by An Interceptor on A High-Speed Mono-Hull:The Affecting Factors and Estimation Formula

To find a better way to estimate the lift force induced by an interceptor on a high-speed mono-hull ship,a series of high-speed mono-hull ship models are designed and investigated under different conditions.Different lift forces are obtained by numerical calculations and validated by a model test in a towing tank.The factors that influence the force are the interceptor height,velocity,draft,and deadrise angle.The relationship between each factor and the induced lift force is investigated and obtained.We found that the induced lift mainly depends on the interceptor height and advancing velocity,and is proportional to the square of the interceptor height and velocity.The results also showed that the effects of the draft and deadrise angle are relatively less important,and the relationship between the induced lift and these two factors is generally linear.Based on the results,a formula including the combined effect of all factors used to estimate the lift force induced by the interceptor is developed based on systematic analysis.The proposed formula could be used to estimate the lift force induced by interceptors,especially under high-speed condition.

Optimization method of fracturing fluid volume intensity for SRV fracturing technique in shale oil reservoir based on forced imbibition:A case study of well X-1 in Biyang Sag of Nanxiang Basin,China

An optimization method of fracturing fluid volume strength was introduced taking well X-1 in Biyang Sag of Nanxiang Basin as an example.The characteristic curves of capillary pressure and relative permeability were obtained from history matching between forced imbibition experimental data and core-scale reservoir simulation results and taken into a large scale reservoir model to mimic the forced imbibition behavior during the well shut-in period after fracturing.The optimization of the stimulated reservoir volume(SRV)fracturing fluid volume strength should meet the requirements of estimated ultimate recovery(EUR),increased oil recovery by forced imbibition and enhancement of formation pressure and the fluid volume strength of fracturing fluid should be controlled around a critical value to avoid either insufficiency of imbibition displacement caused by insufficient fluid amount or increase of costs and potential formation damage caused by excessive fluid amount.Reservoir simulation results showed that SRV fracturing fluid volume strength positively correlated with single-well EUR and an optimal fluid volume strength existed,above which the single-well EUR increase rate kept decreasing.An optimized increase of SRV fracturing fluid volume and shut-in time would effectively increase the formation pressure and enhance well production.Field test results of well X-1 proved the practicality of established optimization method of SRV fracturing fluid volume strength on significant enhancement of shale oil well production.

Force and impulse multi-sensor based on flexible gate dielectric field effect transistor

Nowadays,force sensors play an important role in industrial production,electronic information,medical health,and many other fields.Two-dimensional material-based filed effect transistor(2D-FET)sensors are competitive with nano-level size,lower power consumption,and accurate response.However,few of them has the capability of impulse detection which is a path function,expressing the cumulative effect of the force on the particle over a period of time.Herein we fabricated the flexible polymethyl methacrylate(PMMA)gate dielectric MoS_(2)-FET for force and impulse sensor application.We systematically investigated the responses of the sensor to constant force and varying forces,and achieved the conversion factors of the drain current signals(I_(ds))to the detected impulse(I).The applied force was detected and recorded by I_(ds)with a low power consumption of~30 nW.The sensitivity of the device can reach~8000%and the 4×1 sensor array is able to detect and locate the normal force applied on it.Moreover,there was almost no performance loss for the device as left in the air for two months.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Core-Shell Semiconductor-Graphene Nanoarchitectures for Efficient Photocatalysis:State of the Art and Perspectives

Semiconductor photocatalysis holds great promise for renewable energy generation and environment remediation,but generally suffers from the serious drawbacks on light absorption,charge generation and transport,and structural stability that limit the performance.The core-shell semiconductorgraphene(CSSG)nanoarchitectures may address these issues due to their unique structures with exceptional physical and chemical properties.This review explores recent advances of the CSSG nanoarchitectures in the photocatalytic performance.It starts with the classification of the CSSG nanoarchitectures by the dimensionality.Then,the construction methods under internal and external driving forces were introduced and compared with each other.Afterward,the physicochemical properties and photocatalytic applications of these nanoarchitectures were discussed,with a focus on their role in photocatalysis.It ends with a summary and some perspectives on future development of the CSSG nanoarchitectures toward highly efficient photocatalysts with extensive application.By harnessing the synergistic capabilities of the CSSG architectures,we aim to address pressing environmental and energy challenges and drive scientific progress in these fields.

An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading

For the first time, the isogeometric analysis(IGA) approach is used to model and analyze free and forced vibrations of doubly-curved magneto-electro-elastic(MEE) composite shallow shell resting on the visco-Pasternak foundation in a hygro-temperature environment. The doubly-curved MEE shallow shell types include spherical shallow shell, cylindrical shallow shell, saddle shallow shell, and elliptical shallow shell subjected to blast load are investigated. The Maxwell equation and electromagnetic boundary conditions are used to determine the vary of the electric and magnetic potentials. The MEE shallow shell's equations of motion are derived from Hamilton's principle and refined higher-order shear theory. Then, the IGA method is used to derive the laws of natural frequencies and dynamic responses of the shell under various boundary conditions. The accuracy of the model and method is verified through reliable numerical comparisons. Aside from this, the impact of the input parameters on the free and forced vibration of the doubly-curved MEE shallow shell is examined in detail. These results may be useful in the design and manufacture of military structures such as warships, fighter aircraft, drones and missiles.

Nanomotion of bacteria to determine metabolic profile

In addition to their visible motion such as swimming(e.g.,with the help offlagella),bacteria can also exhibit nanomotion that is detectable only with highly sensitive instruments,and this study shows that it is possible to detect bacterial nanomotion using an AFM detection system.The results show that the nanomotion characteristics depend on the bacterial strain,and that nanomotion can be used to sense the metabolic activity of bacteria because the oscillations are sensitive to the food preferences of the bacteria and the type of surrounding medium.

A Design of Modular Interior Ferrite Magnet Fluxswitching Linear Motor for Track Transport

A novel topology of modular ferrite magnet fluxswitching linear motor(FMFSLM)use for track transport is presented in this paper,which enables more ferrite magnets to be inserted into the primary iron core.The motor has a significant low-cost advantage in long-distance linear drive.The proposed FMFSLM’s structure and working principle were introduced.Further,the thrust force expression of the motor was established.The thrust force components triggering thrust force ripple were investigated,and their expressions can be obtained according to the inductances’Fourier series expressions.Resultantly,the relationship between the harmonics of thrust force and that of self-and mutual inductances was revealed clearly.Based on the relationship,a skewed secondary should be practical to reduce the thrust force ripple.Thus,the effect of employing a skewed secondary to the proposed FMFSLM was investigated,and an optimized skewing span distance was determined.Finite element analysis(FEA)was conducted to validate the exactness of the theoretical analysis.The simulation results indicate that the strategy of suppressing thrust force ripple has a significant effect.Meanwhile,the motor maintains a good efficiency characteristic.The results of the prototype experiment are in good agreement with FEAs,which further verifies the proposed modular interior FMFSLM’s practicability.

Self-assembly of perovskite nanocrystals:From driving forces to applications

Self-assembly of metal halide perovskite nanocrystals(NCs)into superlattices can exhibit unique collective properties,which have significant application values in the display,detector,and solar cell field.This review discusses the driving forces behind the self-assembly process of perovskite NCs,and the commonly used self-assembly methods and different self-assembly structures are detailed.Subsequently,we summarize the collective optoelectronic properties and application areas of perovskite superlattice structures.Finally,we conclude with an outlook on the potential issues and future challenges in developing perovskite NCs.

Reshaping force for deformed casing repairing with hydraulic rolling reshaper and its influencing factors

Hydraulic rolling reshaper is an advanced reshaping tool to solve the problem of casing deformation,which has been widely used in recent years.When it is used for well repair operation,the reshaping force provided by ground devices is generally determined by experience.However,too large reshaping force may destroy the deformed casing,and too small reshaping force may also prolong the construction period and affect the repairing effect.In this paper,based on Hertz contact theory and elastic-plastic theory,combined with the process parameters of shaping,and considering the structural characteristics of the deformed casing and reshaper,we propose a mathematical model for calculating the reshaping force required for repairing deformed casing by hydraulic rolling reshaper.Meanwhile,the finite element model and numerical method of hydraulic rolling reshaper repairing deformed casing are established by using the finite element method,and the reliability of the mathematical model is verified by several examples.On this basis,the control variable method is used to investigate the influence of each parameter on the reshaping force,and the influence degree of each parameter is explored by orthogonal simulation test and Pearson correlation analysis.The research results not only provide an important theoretical basis for the prediction of reshaping force in on-site construction,but also provide a reference for the subsequent improvement of the shaping process.

Diatom-induced impact on shear strength characteristics of finegrained soils

Diatomaceous soils,composed of diatom microfossils with biological origins,have geotechnical properties that are fundamentally different from those of conventional non-diatomaceous fine-grained soils.Despite their high fines content,diatomaceous soils typically exhibit remarkably high shear resistance,approaching that of sandy soils.However,the exact role that diatoms play in controlling the mechanical properties of fine-grained soils and the underlying mechanisms remain unclear.In light of this,the shear strength response of diatomaceous soils was systematically investigated using consolidated undrained triaxial compression tests on diatomekaolin mixtures(DKMs)with various diatom contents and overconsolidation ratios.The micro-and nano-scale structures of the soil samples were characterized in detail using scanning electron microscope(SEM)and atomic force microscope(AFM)to interpret the abnormal shear strength parameters of diatomaceous soils.The results indicated that the presence of diatoms could contribute to significantly higher strength,e.g.the friction angle of DKMs was improved by 72.7%to 37and the value of undrained shear strength tripled with diatom content increasing from 20%to 100%.Such significant improvement in soil strength with diatom inclusion could be attribute to the hard siliceous skeleton of diatoms and the interlocking between particles with rough surfaces,which were quantitatively analyzed by the surface roughness parameters with AFM.Furthermore,a conceptual model established based on the macro-mechanical tests and microscopic observations portrays a microstructural evolution of soils with increasing diatoms.The microstructure of soils was gradually transformed from the matrix-type to the skeletal one,resulting in a continual augmentation in shear strength through mutual interactions between diatom microfossils.This paper provides new insights into the multi-scale structural properties of diatoms and significantly advances our understanding of the mechanical behavior of diatomaceous soils.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Predicting impact forces on pipelines from deep-sea fluidized slides:A comprehensive review of key factors

Deep-sea pipelines play a pivotal role in seabed mineral resource development,global energy and resource supply provision,network communication,and environmental protection.However,the placement of these pipelines on the seabed surface exposes them to potential risks arising from the complex deep-sea hydrodynamic and geological environment,particularly submarine slides.Historical incidents have highlighted the substantial damage to pipelines due to slides.Specifically,deep-sea fluidized slides(in a debris/mud flow or turbidity current physical state),characterized by high speed,pose a significant threat.Accurately assessing the impact forces exerted on pipelines by fluidized submarine slides is crucial for ensuring pipeline safety.This study aimed to provide a comprehensive overview of recent advancements in understanding pipeline impact forces caused by fluidized deep-sea slides,thereby identifying key factors and corresponding mechanisms that influence pipeline impact forces.These factors include the velocity,density,and shear behavior of deep-sea fluidized slides,as well as the geometry,stiffness,self-weight,and mechanical model of pipelines.Additionally,the interface contact conditions and spatial relations were examined within the context of deep-sea slides and their interactions with pipelines.Building upon a thorough review of these achievements,future directions were proposed for assessing and characterizing the key factors affecting slide impact loading on pipelines.A comprehensive understanding of these results is essential for the sustainable development of deep-sea pipeline projects associated with seabed resource development and the implementation of disaster prevention measures.