Equivalent Boundary Research Articles

Research on energy transfer and vibration suppression of nonlinear energy sink with nonlinear damping

The nonlinear energy sink is a nonlinear shock absorber that provides targeted energy transfer and plays a crucial role in structural vibration suppression. In this paper, the energy transfer and dynamic characteristics of nonlinear damping nonlinear energy sink systems are analyzed. Firstly, the theoretical model of the nonlinear damping NES system is described, and secondly, the equations of the system in the free state are derived by using the complex variable average method and the multi-scale method to obtain the energy transfer efficiency equation of the system. Through the study of the slow invariant manifold and energy transfer efficiency of the system, the influence of each system parameter on the energy transfer efficiency is analyzed. Then the equations of the system under harmonic excitation are processed in the same method to obtain the boundary equations of the system, through which the saddle-node bifurcation diagram of the system is plotted to study the influence of each system parameter on the saddle-node bifurcation characteristics of the system. Finally, the slow-varying equation of the system under harmonic excitation is derived, and the influence of each system parameter on the frequency detuning parameter interval of the strongly modulated response is obtained using the phase trajectory and a one-dimensional mapping diagram of the system, and the time-mileage diagram and Poincare section are used to prove the damping effect of the strongly modulated response.

Thermal characterization of vertical interface by scanning photothermal radiometry.

In this work, scanning photothermal radiometry is used for imaging and to characterize a submicron crack. From the thermal images, the evolution of the crack is mapped in the space with micrometer resolution. A vertical contact interface at the steel-steel junction is used to represent a micro-crack with a thickness less than 0.5μm. The thermal quadrupole approach is used to model the heat transfer within the semi-infinite vertical crack. Then, using the phase mapping and that calculated from the model, the estimation of both the equivalent thermal boundary resistance of the interface and the average interface thickness was done.

Radiation of a bunch in a waveguide having areas with deeply corrugated and smooth walls

We analyze radiation from a filamentary bunch that uniformly moves in a circular waveguide and crosses the boundary between two areas: the one has a corrugated wall and another has a smooth wall. It is assumed that the corrugation period is much less than the wavelengths under consideration. However, in difference with our previous works, the corrugation depth is of the same order as the wavelength. The influence of the corrugation on the electromagnetic field is investigated using the method of the equivalent boundary conditions. At first, we study a regular corrugated waveguide. Then two cases of the waveguides with boundaries between the corrugated and smooth regions is studied: first, when the bunch flies out of the corrugated part into the smooth one, and second, when the bunch flies into the corrugated part from the smooth one. We obtain and analyze the analytical expressions for the field components in both areas and reveal the main physical peculiarities of the bunch radiation.

Temperatures of AdS2 black holes and holography revisited

In a dilaton gravity model, we revisit the calculation of the temperature of an evaporating black hole that is initially formed by a shock wave, taking into account the quantum backreaction. Based on the holographic principle, along with the assumption of a boundary equation of motion, we show that the black hole energy is maintained for a while during the early stage of evaporation. Gradually, it decreases as time goes on and eventually vanishes. Thus, the Stefan–Boltzmann law tells us that the black hole temperature, defined by the emission rate of the black hole energy, starts from zero temperature and reaches a maximum value at a critical time, and finally vanishes. It is also shown that the maximum temperature of the evaporating black hole never exceeds the Hawking temperature of the eternal AdS2 black hole. We discuss physical implications of the initial zero temperature of the evaporating black hole.

Combining statistical analyses and GIS-based approach for modeling the sanitary boundary of drinking water wells in Yaoundé, Cameroon

In slums and urban areas with unplanned housing such as in the city of Yaounde, Cameroon, poor water quality and inadequate sanitation pose significant health risks. The absence of locally-defined sanitary boundaries, tailored to hydrogeological conditions, hinders effective zoning and land use planning, exacerbating environmental degradation and health hazards. In this study, the sanitary boundary between drinking water wells and sources of pollution in the city of Yaoundé was defined using statistical analysis techniques and Geographic Information Systems (GIS). The Groundwater Quality Index (GWQI) and certain significant parameters affecting water quality notably the transmissivity of the aquifer and well depth were used to establish the sanitary boundary equation which was then interpolated in a GIS environment to obtain the sanitary boundary map of the study area. The linear equation deduced from the significant factors was defined to map the health boundaries between wells and pollution sources for a nominal value of the GWQI (GWQI = 25). Of the 112 wells analysed, 37 % had an excellent GWQI, 16 % were good while the remaining 47 % were poor. Statistical analysis showed a strong correlation between the GWQI and significant factors of groundwater pollution, such as the distance between well and pit latrines (r = −0.753), the aquifer transmissivity of the formation (r = 0.671) and the depth of the wells (r = - 0.855) but no correlation with elevation (r = 0.017) and well age (r = 0.090). Linear regression analysis confirmed the association of the GWQI with the main factors of pollution (p ≤ 0.05). A coefficient of determination of R2 = 0.85 was obtained when validating the linear regression plot based on independent data between measured and predicted GWQI. The sanitary boundary map shows that the wells in our study area should be located between 39 m and 370 m, with an average value of 215 m. New regulations on the distance between well and pit latrines are essential to prevent groundwater pollution.

Identifying the dominant operating variables to evaluate the cascading failure potential in the power system by theory of mutual information

In this study, the potential of cascading failure as a result of transmission line outages through large power systems is evaluated. Transmission lines are more dispose of the outage resulting from different fault occurrences and extend the uncontrolled failures compared to other power system devices. In this case, power system dynamic security must evaluate the possibility of cascading failures using a power system control center (PSCC) in order to limit the spread of outages caused by line failures. For this issue, using the PSCC online information consisting of power system operating variables, it is possible to present a variables-based scheme to estimate power system cascading failures concerning fault events. In order to cover the issue, based on developing a set of dominant operating variables (DOVs), this paper presents an online scheme of identifying cascading failures caused by line outages in the presence of line operational diversities and communication restrictions. In this scenario, during each time interval, by evaluating the proposed DOVs, the line information consisting of dynamic securities and sensitivities to cascading failure are investigated which the lines with the potential of cascading failures are identified online. Proper DOVs are determined for this issue by studying a variety of mathematical formulations according to theory of mutual information (MI) and measuring the entropy among the variables. In a real-time environment, by using the proposed DOVs and substituting them through online boundary equations based on the Least Square Error (LSE) method, the potentials of power system cascading failures without acting any line outage are provided. The effectiveness of the suggested technique is evaluated using a typical IEEE-39 bus and IEEE-118 bus, and proper results with high accuracy are achieved by evaluating the system potential concerning large cascading failures.

Infrared radiation characteristics simulation of exhaust suppression type ships

An equivalent calculation method for the infrared-suppressed ship’s infrared radiation is carried out, which couples thermal characteristics of the ship surface and the exhaust system. Firstly, a refined physical model for the infrared suppressed exhaust system is proposed, which considers the processes of convective heat transfer and radiative heat transfer. The model generates the equivalent heat flow boundary conditions of the internal heat source through the numerical calculation of Computational Fluid Dynamics (CFD), and combines with the energy balance physical model. The energy balance model on the ship surface is developed, which considers external thermal environment conditions including itself radiation, solar radiation, atmospheric radiation, and reflective radiation among surface elements. The temperature calculation model for the ship with a jet exhaust system is formed. Subsequently, an exhaust-suppressed ship infrared radiation calculation model is formed based on the infrared radiation rendering of solid targets and the narrow spectral principle of exhaust plumes, which considers the spontaneous radiation and environmental radiation of ships. Finally, the infrared simulation results are compared and verified based on experimental data. The results indicate that the infrared radiation error on the ship’s typical parts is less than 30 %. Additionally, 90.1 % of the cabin walls using exhaust suppression systems have a temperature difference of less than 3 K under different operating conditions. It suggests that the exhaust suppression system is effective in reducing the temperature of the cabin wall. The calculation method for ship infrared characteristics constructed in this paper has reasonable results, and it can be used for infrared characteristic analysis of exhaust suppression ships.

Construction and kinematic performance analysis of a suspension support for wind tunnel tests of spinning projectiles based on wire-driven parallel robot with kinematic redundancy

This paper presents a novel suspension support tailored for wind tunnel tests of spinning projectiles based on Wire-Driven Parallel Robot (WDPR), uniquely characterized by an SPM (Spinning Projectile Model)-centered mobile platform. First, an SPM-centered mobile platform, featuring two redundant and another unconstrained Degree of Freedom (DOF), and its suspension support mechanism are designed together, collectively constructing a WDPR endowed with kinematic redundancy. Afterward, the kinematics of the mechanism, boundary equations for the redundant DOFs, and relevant kinematic performance indices are then proposed and formulated. The results from both prototype experiments and numerical assessments are presented. The capability of the support mechanism to replicate the complex coupled motions of the SPM is verified by the experimental results, while the proposed kinematics and boundary equations are also validated. Furthermore, it is revealed by numerical assessments that the redundant DOFs of the mobile platform exert a minimal impact on the kinematic performance of the suspension support. Finally, the optimal global attitude performance is obtained when these DOFs are set to zero if they are restricted to constants. However, local attitude performance can be further improved by the variable values.

Stagnation point slip flow of Al2O3/γ-Al2O3 nanofluids subject to Lorentz force and nonlinear thermal radiation over a stretching sheet

The flow analysis of Al 2 O 3 and γ ‐Al 2 O 3 nanofluids near a stagnating point over a stretching sheet having velocity slip at the solid–liquid interface is presented. There is a quadratic surface temperature and a linear deformation acting on the wall boundary. Due to the uniformly applied transverse magnetic flux, the Lorentz force has an impact on the flow. The effect of nonlinear TR is integrated into the heat equation. Further, water H2O and EG C2H6O2 are base fluids. The governing boundary equations are translated into dimensionless ODEs using relevant similarity variables and solved numerically using the Runge-Kutta algorithm scheme (fourth-order) and the shooting algorithm. The impacts of the parameters, that is, velocity ratio ε , velocity slip δ , nonlinear TR Rd, the temperature ratio parameter θ w , and magnetohydrodynamics M are observed for the velocity h 2 ≤ y ≤ 0 and temperature θ ( η ) fields graphically. The results of local skin friction and local Nusselt number are shown in the table. A comparative analysis of the present results and the results of previous studies has also been made in tabular form. The research indicates that water as a base fluid gives better thermal conductivity than ethylene glycol. The consequence of TR enhances the heat transfer rate of both Al 2 O 3 / γ ‐Al 2 O 3 with H2O and C2H6O2.

Discovering physics-informed neural networks model for solving partial differential equations through evolutionary computation

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on human experience or trial and error. Despite the emergence of several model searching methods, these methods primarily concentrate on optimizing the hyperparameters of fully connected neural network model based on the framework of physics-informed neural networks (PINNs), and the corresponding search spaces are relatively restricted, thereby limiting the exploration of superior models. This article proposes an evolutionary computation method aimed at discovering the PINNs model with higher approximation accuracy and faster convergence rate. In addition to searching the numbers of layers and neurons per hidden layer, this method concurrently explores the optimal shortcut connections between the layers and the novel parametric activation functions expressed by the binary trees. In evolution, the strategy about dynamic population size and training epochs (DPSTE) is adopted, which significantly increases the number of models to be explored and facilitates the discovery of models with fast convergence rate. In experiments, the performance of different models that are searched through Bayesian optimization, random search and evolution is compared in solving Klein–Gordon, Burgers, and Lamé equations. The experimental results affirm that the models discovered by the proposed evolutionary computation method generally exhibit superior approximation accuracy and convergence rate, and these models also show commendable generalization performance with respect to the source term, initial and boundary conditions, equation coefficient and computational domain. The corresponding code is available at https://github.com/MathBon/Discover-PINNs-Model.

Electromagnetic Characterization of Permanent Magnet Eddy Current Structures Based on Backplane Distance Adjustment

To address the problem of problematic spray design inside mining anchor-digging equipment, a switching seal using a permanent magnet eddy current drive is initially presented here. The layer model of the permanent magnet eddy current structure is established, the subdomain analysis model is introduced, the permanent magnet eddy current structure is divided into six regions along the axial direction, and the boundary equations are established at the interfaces of each region. The vector magnetic potential equations in each region are deduced, along with the electromagnetic torque and axial force equations. The computational results are compared and analyzed with the results of finite element simulation, verifying the accuracy of the theoretical model. The design of experiments is used to verify the feasibility of the switching seal using the permanent magnet eddy current structure.

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Screening effect of pile rows for ground vibration induced by moving loads

This study aims to predict the screening efficiency of pile rows in transversely isotropic (TI) saturated soils for ground vibrations subjected to moving loads. First, based on the fundamental solutions of TI saturated media, the boundary element method (BEM) was adopted to derive the force-deformation equation of the soil-pile boundary. The finite element method (FEM) was then applied to establish the stiffness matrix equation of the Euler-based pile rows. Subsequently, by coupling the BEM and FEM equations, the screening efficiency of the pile rows was developed according to the barrier isolation theory. The proposed approach was validated using published numerical results. Finally, the effect of soil stratification on the screening effect of pile rows in TI saturated soils was investigated.

Global existence of solutions for a free‐boundary tumor model with angiogenesis and a necrotic core

In this paper, we study a free‐boundary problem modeling the growth of spherically symmetric tumors with angiogenesis and a necrotic core, where the Robin boundary condition is imposed for the nutrient concentration. The existence of a global solution is established by first reducing the free‐boundary problem into an equivalent initial boundary value problem for a nonlinear strongly singular parabolic equation on a fixed domain, then proving that an approximation problem admits a unique solution by the Schauder fixed point theorem combined with the estimates for parabolic equations, and finally taking the limit. Compared with the Dirichlet boundary value condition problem, the Robin condition causes some new difficulties in making rigorous analysis of the model, particularly on the uniqueness of solutions to the approximation problem.

Aerodynamic performance and wind-induced response of carbon fiber-reinforced polymer (CFRP) cables

To study the aerodynamic performance and wind-induced response of carbon fiber-reinforced polymer (CFRP) cables, CFRP cable was designed by replacing a steel cable in a tied arch bridge based on stiffness, strength and area equivalent criteria, respectively. The aerodynamic performance and wind-induced response of CFRP cable and steel cable were studied and compared by computational fluid dynamics (CFD) model. Based on the computational results, optimal cable replacement criterion was proposed for CFRP cable to replace steel cable. In addition, surface modification was conducted by engrooving vertical symmetric (VS), vertical asymmetric (VA) and helical symmetric (HS) V-shaped grooves to improve the aerodynamic performance and wind-induced response of CFRP cable. Results showed that CFRP cables exhibited inferior aerodynamic performance and wind-induced response in most cases. However, CFRP cable based on stiffness equivalent criterion exhibited better aerodynamic performance and wind-induced vibration properties compared to the other two cable replacement criteria, thus is regarded as the optimal substitute for steel cable. In addition, HS grooves generated symmetric disturbances and caused approximately equivalent boundary layer separation delays uniformly and continuously along the cable length, thus exhibiting better effect in decreasing the reverse flow region, the maximum negative flow velocity, the vortex shedding frequency and the wind-induced vibration amplitude of CFRP cable. Hence, the stiffness equivalent criterion combined with surface modification with HS V-shaped grooves was proposed to replace steel cable with CFRP cable. This study can provide insights into the aerodynamic performance and wind-induced response of CFRP cable and instructions for cable replacement practice.

End of the world branes from dimensional reduction

We consider dimensional reduction of cigar geometries which are obtained by a Wick rotation of black hole solutions. Originally the cigar geometry is smooth around the tip, but after the dimensional reduction along the Euclidean time direction, there appears an end-of-the-world brane (ETW brane). We derive the tension of the brane by two methods: bulk equations of motion and boundary equations of motion.In particular, for AdS7-soliton ×S4 and AdS4-soliton ×S7 backgrounds in M-theory, we find that the tension of the emerging ETW branes behaves as t(Φ) ~ e−3Φ in the string frame. This indicates the existence of such ETW branes in the strongly coupled regime of type 0A string theory.

ON THE UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS WITH PARAMETER

A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.

Characteristics of Perimeter Rock Damage in a Bottom-Pumping Roadway under the Influence of Mining Activities and Rational Location Studies: A Case Study

With the aim of determining the damage characteristics and a reasonable positional arrangement of the surrounding rock in a bottom-pumping roadway influenced by mining in a high-gas mine, the boundary equation for the plastic zone of the surrounding rock in a circular roadway under an unequal compressive stress field was adopted to analyze the relationship between the distribution characteristics of the plastic zone of the bottom-pumping roadway and the stability of the rock surrounding the bottom-pumping roadway under different bidirectional stress ratios. This was carried out in the bottom-pumping roadway of the working face of Licun coal mine 3301 as the engineering background, where the nature of the coal seams mined is bituminous coal, and the absolute gas outflow is 0.5 m3/min−1. A numerical simulation was used to analyze the distribution characteristics of the surrounding rock stress and the bidirectional stress ratio, as well as the deformation and damage characteristics of the surrounding rock at different positions in the bottom-pumping roadway. A numerical simulation was applied to analyze the distribution characteristics of the surrounding rock stress and the two-way stress ratio, as well as the deformation and damage characteristics of the rock surrounding the bottom-pumping roadway when the bottom-pumping roadway was arranged in different locations. The results show that, with an increase in the bidirectional stress ratio, the plastic zone of the perimeter rock in the bottom-pumping roadway shows nonuniform “butterfly” distribution characteristics, which seriously affects the stability of the rock on the perimeter of the roadway; the stress on the bottom plate of the working face after excavation can be divided into four areas according to the size of the bidirectional stress ratio and the stress loading and unloading states. In addition, the size of the perimeter rock deformation can be sorted into four areas according to the damage range of the perimeter of the rock plastic zone in the bottom-pumping roadway. The size of the deformation in the surrounding rock can be sorted as follows: unpressurized high-stress ratio > unpressurized stress ratio stable area > pressurized low-stress ratio area > original rock stress ratio area. Accordingly, we found that the reasonable location of the bottom-pumping roadway is arranged at the 15 m position outside the hollow area below the coal pillar, along the limestone upper medium-grained sandstone layer along the bottom. The study’s results were applied to the field. The industrial experiments on the site show that the deformation of the surrounding rock is reasonable when the bottom-pumping roadway is dug along the limestone roof and arranged 15 m outside the fault of the mining hollow area below the coal pillar.

Introduction to loop quantum gravity. The Holst’s action and the covariant formalism

We review Holst formalism and dynamical equivalence with standard GR (in dimension [Formula: see text]). Holst formalism is written for a spin coframe field [Formula: see text] and a Spin(3,1)-connection [Formula: see text] on spacetime [Formula: see text] and it depends on the Holst parameter [Formula: see text]. We show the model is dynamically equivalent to standard GR, in the sense that up to a pointwise Spin(3,1)-gauge transformation acting on (uppercase Latin) frame indices, solutions of the two models are in one-to-one correspondence. Hence, the two models are classically equivalent. One can also introduce new variables by splitting the spin connection into a pair of a Spin(3)-connection [Formula: see text] and a Spin(3)-valued 1-form [Formula: see text]. The construction of these new variables relies on a particular algebraic structure, called a reductive splitting. A weaker structure than requiring that the gauge group splits as the products of two sub-groups, as it happens in Euclidean signature in the selfdual formulation originally introduced in this context by Ashtekar, and it still allows to deal with the Lorentzian signature without resorting to complexifications. The reductive splitting of [Formula: see text] is not unique and it is parameterized by a real parameter [Formula: see text] which is called the Immirzi parameter. The splitting is here done on spacetime, not on space as it is usually done in the literature, to obtain a Spin(3)-connection [Formula: see text], which is called the Barbero–Immirzi connection on spacetime. One obtains a covariant model depending on the fields [Formula: see text] which is again dynamically equivalent to standard GR. Usually in the literature one sets [Formula: see text] for the sake of simplicity. Here, we keep the Holst and Immirzi parameters distinct to show that eventually only [Formula: see text] will survive in boundary field equations.

Mechanical and vibration characteristics investigation of the elastic ring squeeze film damper-rotor considering oil film sealing and leakage

Elastic ring squeeze film damper (ERSFD) is extensively used in industrial rotating systems due to its excellent noise control and vibration suppression characteristics. However, the oil film sealing and leakage has a profound effect on the mechanical and vibration characteristics of the ERSFD and the ERSFD-rotor during operation. The sealing and leakage reduce the axial flow of the oil film, leading to changes in the initial boundary conditions of the flow field, which in turn affects the oil film pressure and damping coefficient of ERSFD. Meanwhile, the sealing causes an increase in the oil film force of ERSFD, which in turn affects the response of the rotor system. But there is relatively little research on the impact of sealing and leakage on the dynamic performances of ERSFD-rotor. In this paper, a mathematical model of ERSFD under different sealing conditions (no end seal, complete end seal, piston ring seal, O-ring seal) is established by changing the initial boundary equations of the flow field of ERSFD and the coupled solution of the Reynolds equation of ERSFD with different sealing and leakage boundary equations is realized. Then, the characteristics of oil film pressure and force of ERSFD under different sealing conditions is studied. After that, an ERSFD-rotor model considering oil film sealing and leakage is established based on displacement compatibility conditions and force balance principles. Meanwhile, the impact of sealing and leakage on the amplitude-frequency relation and sudden imbalance of an ERSFD combined support rotor is researched. The research results reveal that good sealing can significantly increase the damping of the system, thereby reducing the vibration amplitude of the ERSFD-rotor system. In addition, good sealing conditions can also shorten the transient process of sudden unbalanced excitation. Finally, the effectiveness of some simulation results was verified through experiments on the ERSFD rotor test bench.