Potential Theory Research Articles

Bayesian machine learning framework for characterizing structural dependency, dynamics, and volatility of cryptocurrency market using potential field theory

Identifying the structural dependence between the cryptocurrencies and predicting market trend are fundamental for effective portfolio management in cryptocurrency trading. In this paper, we present a unified Bayesian machine learning framework based on potential field theory and Gaussian Process to characterize the structural dependency of various cryptocurrencies, using historic price information. The following are our significant contributions: (i) Proposed a novel model for cryptocurrency price movements as a trajectory of a dynamical system governed by a time-varying non-linear potential field. (ii) Developed a Bayesian machine learning framework for inferring the non-linear potential function from observed cryptocurrency prices. (iii) Proposed that attractors and repellers inferred from the potential field are reliable cryptocurrency market indicators, surpassing existing attributes in the literature. (iv) Analysis of cryptocurrency market during various Bitcoin crash durations shows that attractors captured the market trend, volatility, and correlation. In addition, attractors aids explainability and visualization. (v) The proposed cryptocurrency market indicators (attractors and repellers) was used to improve the prediction performance of state-of-art deep learning price prediction models.

Rayleigh–Taylor instability in a Casson fluid layer with heat and mass transfer

This study investigates the stability of the interface between two fluids, a Casson fluid on top and a viscous fluid below, with heat and mass transfer occurring between them. We used the potential flow theory, which simplifies the problem by ignoring tangential stresses and focusing on normal stress balance. We did not consider no-slip conditions at the boundaries, assuming zero normal velocity at these rigid boundaries instead. A second-order polynomial equation was developed to calculate the growth rate of instabilities and solved numerically using the Newton–Raphson method. The results showed that heat and mass transfer improved the stability of the interface, even though the Atwood number, a measure of instability, remained high.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

Performance assessment of a Triple Coaxial-Cylinder Wave-Energy Converter (TCWEC)

We propose a novel Triple Coaxial-cylinder Wave-Energy Converter (TCWEC) system, as an evolution of the commonly deployed dual-coaxial cylinder WEC (DCWEC). TCWEC consists of one inner cylinder and two concentric outer cylinders, characterized by two coupled resonant frequencies, improving wave power absorption. A semi-analytical model, based on potential flow theory and matched eigenfunction expansions, is developed to analyze the 3-Degrees of Freedom (DOF) system. The viscous drag coefficients are determined by Computational Fluid Dynamics (CFD) simulations and employed as equivalent linear damping. Analysis of impact of the viscous flow-separation factor fvis on the capture width indicates that the higher energy-absorption capability of TCWEC is not merely attributed to a smaller fvis value, but rather a planned split of the outer cylinder in DCWEC design into two cylinders in TCWEC, so as to produce an effectively broader resonance property. Under identical sea conditions, it is found that, compared to DCWEC, the optimal capture width of TCWEC is increased by as much as 77% in regular waves. In irregular waves, the optimal capture width is increased up to 40% across the entire frequency range. These findings suggest that the energy absorption efficiency of TCWEC is promising and its potential for real-world applications.

Comparative study of analytical models with linear and quadratic pressure drop conditions on a perforated plate in water waves

Proper pressure drop conditions are essential in predicting hydrodynamic performance of perforated structures in the framework of a potential flow theory. In this study, we investigate water waves passing through a perforated plate with various pressure drop models to examine how pressure drop conditions affect the hydrodynamic performance of perforated structures. We derive the analytical solutions of waves across the perforated plate by adopting three commonly pressure drop conditions, including one linear pressure drop condition (LPDC), and two quadratic pressure drop conditions (QPDCs). A series of laboratory experiments are conducted to validate the present theoretical results. We compare the hydrodynamic performance between the experimental data and the theoretical solutions with the three different pressure drop models, typically for wave reflection coefficients, dynamic pressures, and velocity fields measured by the technique of particle image velocimetry in the experiments. It is found that the existing pressure drop models can predict well wave reflection coefficients, dynamic pressure, and velocity profiles at certain conditions. However, the linear wave solutions associated with LPDC or QPDCs generally underpredict the amplitude of particle velocity near the free surface on the perforated plate. This underestimation increases largely as the wave steepness increases. The LPDC performance relies much on the selection of empirical coefficients. For the QPDCs, the analytical models show deviated results from the experimental data for wave reflection coefficients when the wave steepness is relatively low.

Sloshing in a tank with elastic side walls and a membrane cover

The coupled problem of liquid sloshing in a tank with a membrane cover and elastic side walls is investigated. The velocity potential theory is used for the flow and the linear elastic theory for the cover and side walls. For the former, the vertical mode expansion is used, in which all the roots of the dispersion relationship are first found. The expansion automatically satisfies the governing equation, the tank bottom, and the tank cover conditions. The deflections of the side walls are expanded into a cosine series together with a four term polynomial, which is vital for the procedure to succeed. These expansions are then matched through the dynamic and kinematic equations of the plates, and the problem is completed by imposing the edge conditions of the plate and membrane. Through the combined matrix equation, the natural frequencies of the system are obtained. In addition, the nature of the dispersion relationship of the membrane is analyzed. Explicit solutions are obtained for some special cases, and the link with the free surface sloshing is established. Extensive numerical results are provided, and their physics is analyzed.

Large-signal stability analysis of an islanded DC microgrid with constant power loads based on mixed potential function

Abstract In DC microgrids, power electronic converters are widely used to connect loads and renewable energy sources to generate different voltages. These loads operate as constant power loads (CPL) within a closed control loop. When voltage fluctuates, these loads display negative impedance characteristics, potentially leading to system instability. Therefore, the analysis of the impact of CPL on DC microgrids during large disturbances is crucial. This paper employs mixed potential theory to study the large disturbance stability of DC microgrids under CPL. Deriving the stability criterion for the system under significant perturbations reveals the impact of load types and control parameters on system stability and provides a detailed analysis of how specific system parameters affect stability. Consequently, the stability criterion can ensure the system’s stability under large disturbances without the need for repeated calculations and simulations. Simulation results verify the correctness of this stability criterion.

Stabilization Mechanisms of Traveling Crossflow Mode in Hypersonic Swept Wing Flows

Momentum potential theory (MPT) is employed to establish a physics-based interpretation of the traveling crossflow mode and analyze the underlying stabilization mechanisms of associated control methods, such as wall cooling, wall suction, and grooves. The traveling crossflow mode over a swept wing with a Mach number of 6 is first solved using direct numerical simulations. The MPT decomposition illustrates the vortical nature of the traveling crossflow mode, with the vortical component having a higher magnitude than the acoustic and thermal components. The vortical source makes the greatest contribution to the mode instability, whereas the response of the source terms depends on the control method used. Wall cooling primarily impacts the thermal component, thus decreasing the thermal source and subsequently changing the vortical source. Wall suction influences the vortical component directly, and only the vortical source undergoes a small reduction. The acoustic and vortical components are sensitive to grooves. The compression waves induced by grooves are identified as the source of the stabilization effect.

Effect of step bottom and waterway on flexural gravity wave scattering

Flexural gravity wave scattering by two semi-infinite non-identical ice sheets, which are separated by a clean water surface, is investigated in the presence of a step bottom topography. The problem is investigated in the cases of (i) intermediate water depth and (ii) shallow water. The effect of two edge conditions, (i) simply supported edge and (ii) free edge, on wave scattering is also analyzed. Employing linear velocity potential theory, the problem is studied in the frequency domain. The physical phenomenon is modeled as a boundary value problem having the Laplace equation as the governing equation, and it is solved using the eigenfunction expansion method. Considering the bottom topography and upper boundary, the fluid domain is divided into three regions, and in each region, velocity potential is expressed in terms of infinite Fourier series. Velocity and pressure are matched at the intermediate surface of two regions, and a system of algebraic equations with unknown coefficients is obtained. The complete solution of the present problem is recognized by solving the system of equations numerically. The energy relation is derived using Green's theorem. The reflection and transmission coefficients are computed and compared with the energy relation to check the accuracy of the present method. For different parameters (depth ratio, clean waterway, and different ice properties), reflection coefficient and transmission coefficient are computed and presented as a function of angular frequency. The value of the reflection coefficient ranges from zero to unity, whereas at certain frequencies, the transmission coefficient attends value more than unity.

Influence of Composition on Mechanical Properties and Sound Speed of AlAs1−xPx for Various Pressures

The mechanical properties of AlAs1−xPx alloy under the influence of composition have been determined. The sound speed of AlAs1−xPx has been determined at various compositions. The studied properties were obtained with the effect of composition at various pressures. The predicted values were consistent with the available experimental results. The investigation used empirical method calculations based on empirical pseudo potential theory (EPM) with the virtual crystal approximation (VCA) to broaden the applications of ternary alloys and better investigate their potential as novel materials. AlAs1−xPx is a material that shows promise for usage in multi-junction solar cell designs because its properties can potentially be adjusted. The mechanical stability of AlAs1−xPx alloys was obtained according to these conditions C11 + 2C12 > 0, C44 > 0, and C11-C12 > 0. The obtained anisotropy factor was not equal to 1, indicating the presence of elastic anisotropy in the studied alloy in the applied composition range. The AlAs1−xPx alloy is a ductile material throughout the entire composition range at various pressures due to the Bu/Cs values exceeding 1.75.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.

Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth

We prove the Wolff potential estimates for nonlocal equations with Orlicz growth. As an application, we obtain the Wiener criterion in this framework, which provides a necessary and sufficient condition for boundary points to be regular. Our approach relies on the fine analysis of superharmonic functions in view of nonlocal nonlinear potential theory.

On the Bulk Photovoltaic Effect in the Characterization of Strained Germanium Microstructures

Strain engineering serves as an effective method for optimizing electronic and optical properties in semiconductor devices, with applications including the enhancement of optical emission in Ge and GeSn‐based devices, improvement of carrier mobility, and second harmonic generation in silicon photonics structures. Current methods for deformation characterization in semiconductors, such as X‐ray diffraction and Raman spectroscopy, often require bulky and expensive setups and are limited in vertical resolution. Consequently, techniques capable of measuring lattice strain while overcoming these drawbacks are highly desirable. This study proposes a proof of concept for a cost‐effective, compact, fast, and non‐destructive approach to probe non‐uniform strain fields and additional material properties by exploiting the bulk photovoltage effect. The method is benchmarked with an array of silicon nitride stripes deposited under varying pressure conditions on a germanium substrate. Initially, their surface strains are verified through Raman spectroscopy. The deformations are replicated in a finite element method platform by integrating mechanical simulations with deformation potential theory, thereby estimating the band edge energy landscape. Finally, the study discusses the theoretical behavior of the photovoltage signal, considering semiconductor properties, defects, doping, and deformation. The findings offer insights into the development of advanced techniques for strain and transport analysis in semiconductor materials.

Thermoelastic fracture of two-dimensional hexagonal quasicrystal media weakened by a penny-shaped crack subjected to uniformly antisymmetric heat fluxes

This study focuses on the thermoelastic fracture behavior of quasicrystals, a class of solids that exhibit unique properties between traditional crystals and amorphous materials. The complex atomic structure of quasicrystals poses challenges in understanding their fracture mechanisms under thermoelastic loading conditions. Central to our investigation is an analytical examination of a penny-shaped crack in an infinite three-dimensional body composed of two-dimensional hexagonal quasicrystals, where the upper and lower crack surfaces are applied to a pair of uniformly antisymmetric heat fluxes. This crack problem requires simultaneous consideration of thermal-phason-phonon multiple field coupling. According to the symmetry of field variables with respect to the crack plane, the thermal-phason-phonon coupled crack problem is transformed into a mixed boundary value problem in the upper half space. The extended displacement discontinuities, encompassing both phonon and phason displacement discontinuities, as well as the temperature discontinuity, are chosen as the basic unknown variables to construct the boundary integral-differential equations governing the mixed boundary value problem. Based on these boundary governing equations and Fabrikant's potential theory method, the problem with the crack surface subjected to uniform antisymmetric heat fluxes is solved. The solutions of thermal-phason-phonon fields on the crack plane, and in the full space are given in closed-form. Numerical results are employed to validate the obtained analytical solutions and visually illustrate the spatial distribution of thermal-phonon-phason coupling fields in the vicinity of the crack. The study provides fundamental insights into the behavior of cracks in quasicrystals under thermal loading, with potential implications for the design of new materials and structures.

Dynamic analysis of multi-module floating photovoltaic platforms with composite mooring system by considering tidal variation and platform configuration

Floating Photovoltaics (FPV) are emerging as an innovative technology to utilizing solar energy which advances the exploration of renewable energy technologies in the deep sea. This investigation proposes a novel methodology to verify the feasibility of the designed models in time-domain analysis via the motion responses, the mooring analysis based on the finite element method (FEM) and the airgap analysis, considering a comparison of dynamic responses between the regular hexagon shape and rectangle shape semi-submersible floating photovoltaic platform (FPVP) both combinate the cables and the tensioners mooring system to adapt the tidal variation. Initially, the response amplitude operators (RAOs) of the two configurations of the FPVP numerical models established in AQWA are derived from the frequency-domain analysis. Then, the method of rectifying the RAOs by incorporating additional damping essential to compensating the fluid viscosity due to the limitation of the potential flow theory is verified through comparison with the Computational Fluid Dynamics (CFD) solver. Subsequently, the motion responses of the two conceptualized FPVPs with the composite mooring system under different depths of water are assessed in time-domain analysis through OrcaFlex which regards the cables and tensioners as Morison type based on the FEM theory. Simultaneously, the variations in the air gap of platforms with dissimilar stiffness tensioners are compared to assess the safety of FPV systems under different water depths. The long-term extreme forecast of effective tension force for various return periods derived from the Weibull distribution model is verified. Finally, considering the factors that influence the design and safety of multi-module floating photovoltaics in variable-depth water, this study provides essential guidance for the safe construction technology of semi-submersible FPVPs, serves as a valuable reference for promoting reliable and cost-effective FPV technologies for offshore environments.

The thermoelectric properties of the two-dimensional Nowotny-Juza material NaBeX (X = P, As, and Sb)

The two-dimensional β-type Nowotny-Juza phase-filled tetrahedral compound has excellent electrical conductivity, low thermal conductivity and outstanding thermoelectric properties. This study investigated the stability and electronic properties of NaBeX (X = P, As, and Sb) through first-principles calculations. The results demonstrate that these materials are structurally stable and are direct bandgap semiconductors with bandgaps of 0.6542 eV, 0.6549 eV, and 0.6686 eV, respectively. The electrical and thermal transport properties of NaBeX are investigated by combining the deformation potential theory and Boltzmann transport theory. Subsequently, the thermoelectric properties of NaBeX are evaluated at temperatures ranging from 400 to 800 K. The n-type NaBeX materials exhibit large ZT values of 2.48, 2.62, and 1.72. The results of the present study indicate that n-type NaBeX has the potential to be used as a thermoelectric candidate material at temperatures ranging from 400 to 800 K.

Research on dynamic responses of multi-float systems during wet towing

Very large floating structures (VLFS) are substantial in scale, typically comprising dozens to hundreds of interconnected modules. This paper utilizes a multi-float towing approach to enhance transport efficiency. A numerical model of multi-float system, based on potential flow theory and multi-body hydrodynamic interaction, is developed and validated. The dynamic responses for six towing configurations under various wave periods and environmental load directions are investigated by using this model. In addition, a selection method is proposed to determine the optimal towing configuration that meets the towing stability criteria while maximizing efficiency, cost-effectiveness, and minimizing environmental impact. Results indicate that during towing multi-float systems, the rear module's vertical motion caused by the combination of heave and pitch is significantly greater than that of the front module, especially in long wave periods. When the number of longitudinal tandem modules reaches four, the low-frequency motion modes with sway and yaw as the main motions are excited, leading to a significant lateral displacement and horizontal rotation of the multi-float system. This also results in uneven tensions of the symmetrical cables. Additionally, the dynamic behaviors of the towing configurations are more pronounced in oblique or lateral waves than in forward waves. As the current direction shifts from forward to lateral, the sway amplitude of the system with four longitudinal tandem modules decreases. Furthermore, an optimal towing configuration is determined by the selection method, which has good stability in moderate sea conditions. The findings of this paper provide valuable insights for towing multi-float systems and have implications for future VLFS construction.

Experimental and numerical study of a hinged floating bridge under waves and moving loads

ABSTRACT As an important means of water transportation, floating bridges have broad application prospects. In this paper, a numerical calculation model of the floating bridge considering the combined actions of waves and moving loads is established based on the potential flow theory, and model tests are carried out to verify the accuracy of the numerical method. The effects of motorcade loads and wave parameters on the dynamic responses of the floating bridge were further investigated. The results show that the larger vertical displacements of the floating bridge are affected by both the increase in the number of vehicles and the decrease in vehicle distances. The wave frequency and wave amplitude ranges dominated by the waves and vehicle loads were provided. The extreme dynamic responses of the hinged floating bridge under the combined effect of the waves and moving loads are less than the linear superposition of the individual effect.

A review of research progresses on potential flow theory of single-mode fluid interfacial instabilities

A review of research progresses on potential flow theory of single-mode fluid interfacial instabilities

Hydrodynamic Performance of an Inverted Trapezoidal Breakwater with Permeable Retrofit

Abstract The scattering of incident waves by a surface-piercing inverted trapezoidal breakwater (SPTB) encircled by retrofit is numerically examined based on the assumptions of potential flow theory. The dual boundary element method is adopted to evaluate the hydrodynamic performance of the retrofitted SPTB breakwater. The scattering coefficients (i.e., wave transmission, wave reflection, energy loss), and force coefficients acting on the inner SPTB and outer retrofit are reported against relative water depth for various input values of breakwater and incident waves. The SPTB with 10% porosity, spacing S/h=0.25, width varied within 1.5≤B/W≤2, and depth d/h=0.2 is suggested against the incident waves to secure the coastal infrastructure.