Equilibrium State Research Articles

Noncircular Slip Surface Search on Slopes Based on Minimum Potential Energy Method and Improved SA Algorithm

ABSTRACTThe limit equilibrium method has been widely used in the study of searching the slip surface of slopes. However, the method ignores the deformation characteristics of the rock mass and assumes that the shape of the slip surface is circular, which is quite different from the actual situation of the slope. For this reason, this paper proposes a fast search method for noncircular slip surface considering the deformation characteristics of the rock mass. The method is able to calculate the compression and shear deformation energies stored in the slip surface, as well as the virtual displacement generated by the slide mass when the slope is in a critical equilibrium state. The direction of motion of the slide mass is further calculated from the magnitude of the virtual displacement. In addition, this paper improves the generation of new solutions in the simulated annealing (SA) algorithm for the structural characteristics of the slip surface of the slope, thus achieving a fast search of the slip surface. Finally, the method of this paper is compared with the test question of ACADS and the simulation results of the finite difference method (FDM) to verify the effectiveness of the method of this paper.

Extreme multi-stability and circuit implementation for a two-ReLU-memristor-based jerk oscillator

Memristor-based oscillation circuits are prone to produce coexisting infinite attractors depending on the initial conditions of memristors, leading to the appearance of extreme multi-stability. In this paper, we propose a novel memristive jerk oscillator by bringing two ReLU-type memristors in a simple jerk oscillator and investigate its dynamical behaviors associated with the coupling parameters using bifurcation plots and Lyapunov exponent plots. Further, we discuss the planar equilibrium state and its stability, and then numerically explore the coexisting infinite attractors driven by the initial conditions of two ReLU-type memristors. Because of the intervention of the two ReLU-type memristors, the memristive jerk oscillator has a planar equilibrium state whose stability closely relies on the initial conditions of two ReLU-type memristors, and different initial conditions cause different attractors to coexist, resulting in bidirectional extreme multi-stability. Finally, the memristive jerk oscillator is implemented by analog circuit and digital hardware platform, and the numerical results are confirmed by circuit simulations and hardware experiments.

On some new travelling wave solutions and dynamical properties of the generalized Zakharov system.

This study examines the extended version of the Zakharov system characterizing the dispersive and ion acoustic wave propagation in plasma. The genuine, non-dispersive field depicts a shift in plasma ion density from its equilibrium state, whereas the complex, dispersive field depicts the fluctuating envelope of a highly oscillatory field of electricity. The main focus of the analysis is on employing the expanded Fan sub-equation approach to achieve some novel travelling wave structures including the explicit, periodic, linked wave, and other new exact solutions are developed for different values of this parameter. Three dimensional graphs are utilised to examine the properties of the obtained solutions. Furthermore, ideas from planar dynamical theory are applied in this work to analyse the intricate behaviour of the analysed model. Sensitivity analysis, multistability, quasi-periodic and chaotic patterns, Poincaré map, and the Lyapunov characteristic exponent are used to analyse the dynamical features.

Thermodynamic modeling of liquid binary alloys of the Al–Er system

The paper presents the results of a study of the thermochemical properties of the Al–Er system. The thermodynamic characteristics were evaluated (△fH0298, S0298, (H0298−H00), Cp(T) and Cp(liq)) for the intermetallic compounds Al3Er, Al2Er, AlEr, Al2Er3, AlEr2. The values of△fH0298 calculated based on the semiempirical Miedema model adapted for the group of Al–REM alloys were taken for calculations and amounted to –47.7, –58.4, –63, –55.2, –46.8 kJ/mol∙at, respectively. The mixing characteristics of liquid alloys of this system were evaluated by Terra software package for modeling the equilibrium states of heterogeneous inorganic systems with an extensive database of properties of individual substances. The model of ideal solutions of interaction products was used as a computational model. Modeling of equilibrium composition and properties of melts was carried out in the temperature range of 1900–2100 K, in an argon atmosphere at a total pressure of 0.1 MPa in the system. Comparison of the obtained results with the simulation results in the approximation of an ideal solution, allowed us to determine the excess integral thermodynamic properties of liquid alloys (Gibbs energy, enthalpy, and entropy). It is shown that in the studied temperature range, with an increase of temperature, there is a natural, though not significant, decrease in the values of these parameters by absolute value. It is established that the formation of liquid alloys of the Al–Er system is accompanied by significant heat release: the value of the integral enthalpy of mixing at a temperature T = 2100 K is –58.9 kJ/ mol∙at. When comparing the thermochemical properties of the Al–Er system with the binary systems Al–Y and Al–Sc studied by the same methods, it is shown that all energy curves pass through the extremum at XSc,Y,Er ≈ 0.5. The strongest interaction of the components is observed in the Al–Y system, (ΔHmix = –58.9 kJ/mol∙at), which is close enough to the maximum modulo value of the enthalpy of mixing in the Al–Er system. The weakest interaction is observed in the Al–Sc system (ΔHmix = –44.8 kJ/mol·at). The results obtained in this work provide a theoretical basis for further experimental study of erbium–containing aluminum alloys.

Self-Inhibition Phenomena in Cu3Pt Oxidation by CO2.

This study investigates the oxidation behavior of Cu3Pt(100) in CO2 using a combination of ambient-pressure X-ray photoelectron spectroscopy, mass spectroscopy, and density functional theory modeling. Our in situ measurements reveal the simultaneous oxidation and reduction of Cu2O due to the opposing effects of atomic oxygen and CO generated from dissociative CO2 adsorption, leading to a dynamic equilibrium state of simultaneously occurring redox reactions. Complementary atomistic calculations elucidate the inhibitory effects of subsurface Pt enrichment and the counteracting roles of CO2 and CO in surface oxidation and reduction. These results provide mechanistic insights into the dissociative pathway of CO2 molecules and dynamic evolution of surface composition and reactivity of Cu-based alloy catalysts in CO2-rich environments, with broader implications for tuning gas-surface reactions by manipulating gas reactants or solid surface composition.

Microstructure and strength of cold-drawn large strain Fe35Ni35Cr20Mn10 high-entropy alloy

The Fe35Ni35Cr20Mn10 high-entropy alloy wires can achieve a large strain of 8.73 and a section reduction ratio of 99.98 %,and possess a high strength of 1868 MPa via traditional wire drawing. The microstructure evolution and mechanical properties of cold-drawn Fe35Ni35Cr20Mn10 high-entropy alloy are characterized by microstructure observation and tensile test. The results showed that The Fe35Ni35Cr20Mn10 HEA has excellent plastic forming capacity and excellent phase stability during plastic deformation. The Fe35Ni35Cr20Mn10 HEA has excellent continuous drawing ability, the main deformation mechanism is the plane slip and cross slip of the dislocation and the dynamic recovery of the sublamellar layer make the lamellar structure maintain a dynamic equilibrium state, and the lamellar thickness is basically unchanged to support the continuous plastic deformation under high strain conditions. The dynamic balance of coarsening and refining of lamellar structure in the process of plastic deformation is mainly due to the merging of HEA lamellar caused by the movement of trigeminal node induced by strain. Texture evolution showed that the <111> and <100> fiber textures were the stable texture component and the texture component content remained unchanged even under further increased strain. The Fe35Ni35Cr20Mn10 high-entropy alloy wire with high strain of 8.73 possesses excellent strength, and its tensile strength is 1868 MPa at room temperature, which has the largest strain. The dislocations proliferation, lamellar structure refinement and texture strengthening lead to high strength of the Fe35Ni35Cr20Mn10 high-entropy alloy wire.

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

The impact of quantum correlations on parameter estimation in a spin reservoir

We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.

Analyzing and predicting the urbanization and ecological resilience coupling and coordination of Guangdong Province

Taking 21 cities in Guangdong Province as the research object, this study quantitatively analyzes the spatiotemporal evolution of urbanization and ecological environment coupling from 2000 to 2020 using a coupling coordination model, and predicts the coordinated development of urbanization and ecological resilience coupling from 2000 to 2020 using an LSTM deep learning model. Analysis of the geographical data conveys the following observations: (1) Remotely sensed night-time luminosity data indicate a precipitous escalation in the urbanization quotient within Guangdong, with the Pearl River Delta, featuring Guangzhou and Shenzhen as hubs, exhibiting high levels of nocturnal radiance, in stark contrast to the lower and more dispersed illumination in the province’s northern latitudes. (2) Indices of ecological resilience suggest a progressive enhancement across Guangdong, with Maoming exhibiting the utmost resilience, succeeded by Jiangmen, Dongguan, Shenzhen, and Zhongshan in terms of ecological robustness. (3) The synergistic relationship between urbanization dynamics and ecological resilience metrics in Guangdong has been incrementally enhanced, with Qingyuan and Shaoguan exemplifying optimal coupling and coordination, while Zhongshan has experienced the most pronounced increment in these interdependencies. (4) The proportional advancement of urbanization and ecological resilience in the province is approaching a theoretical equilibrium state. (5) Projections based on spatiotemporal models forecast a gradual upgrade in the urban-ecological systems’ coupling and coordination coefficients from 2021 to 2025, with a general trend of incremental progression among the majority of the province’s urban centers towards a moderate level of integrated development.

Financial Development and Foreign Direct Investment Impact on Economic Growth: Evidence from Nepal

The interplay among financial development, foreign direct investment (FDI), and economic growth has been a subject of keen interest among scholars, both from a theoretical standpoint and through empirical research. Focusing on Nepal, this study examines the distinctive connections among economic expansion, the influx of foreign capital, and the evolution of the financial sector. Given the lack of a definitive metric for financial development, this research adopts the financial development index, along with the financial institution index and financial market index, as alternative indicators. It also considers additional variables that could influence economic growth beyond financial development and FDI. Utilizing the Autoregressive Distributed Lag (ARDL) bounds testing method and the Error Correction Model (ECM), the analysis uncovers a robust positive link between financial development and FDI in enhancing Nepal's economic output. Furthermore, both the short-term and long-term analyses prove to be reliable, devoid of issues like heteroscedasticity, autocorrelation, and multicollinearity. Importantly, the findings indicate that in the face of short-term disruptions, the dynamics between these variables adjust back to a long-term equilibrium state.

Thermodynamic equilibrium of [formula omitted] Ising model on square lattice

We constructed a theoretical magnetic phase diagram in an external magnetic field T(P+), making it possible to determine the conditions for the existence of ferromagnets, antiferromagnets, and spin glass phases. The high-performance CUDA software package was used to the complete enumeration of all configurations of finite number spins in the ±J Ising model. We performed the rigorous numerical calculation of the partition function of N=8×8 systems of interacting spins with open boundary conditions. We used Monte Carlo methods like the Metropolis algorithm to calculate the critical temperatures for N=40×40 spins. The results of the Monte Carlo experiments are consistent with rigorous calculation data. The transition from the spin glass to the induced ferromagnetic state in an external field occurs without any critical change in the heat capacity. We used the ±J Ising model to calculate the instability line (AT—line) for the heat capacity of spin glass in the H−T diagram in an external magnetic field and the behavior of magnetic susceptibility in an external magnetic field. A rigorous calculation of the partition function allowed us to calculate all possible states and their thermodynamic probability. The calculation of the partition function meant that the model’s physics was obtained in an equilibrium state. The instability line was calculated for spin glass in the equilibrium state.

Effect of repulsive interaction and initial velocity on collective motion process.

Self-propelled collective motion is a highly complex phenomenon, necessitating advanced practical and theoretical tools for comprehension. The significance of studying collective motion becomes apparent in its diverse applications. For instance, addressing evacuation challenges in scenarios with multiple agents can be achieved through an examination of collective motion. Research indicates that the transition of individuals (such as birds, fish, etc.) from a state of rest to equilibrium constitutes a phase transition. Our interest of the issue is to delve into the nature of this transitional phase and elucidate the parameters that shape it. Hence, the primary aim of this paper is to grasp the kinetic phase transition by examining how initial velocity and repulsive interactions impact the dynamics of the system. To gain insight into the complex behavior of multi-agent systems, we apply an extended version of the classical Vicsek model. This extension includes an additional interaction zone, the repulsive zone, where particles repel each other at close range to avoid collisions. Our study uses numerical simulations to explore the system's behavior under various conditions. The focus of this study is the impact of initial velocity on the collective movement of particles. The importance of this research lies in comprehending how velocity affects the overall movement. The conclusion we can draw from these results is that the initial velocity affects both the noise and the density. The novelty of the work is the transition phase, yet it lacks universal characteristics because the critical noise depends on the initial velocity system and the repulsion radius zone. Notably, the repulsion radius and particle density play pivotal roles in achieving a phase transition from one equilibrium state to another aligned equilibrium state.

A dynamic analysis of a tourism-based socioecological system

The study proposes a dynamic analysis regarding interactions between the resources provided by the forest, the wildlife present inside or in the proximity of that environment and visitors revolving around the before mentioned socioecological framework. The mathematical model is described by a nonlinear system with three differential equations. The discrete time delay is introduced to illustrate the entire past impact of tourists on forest resources and wildlife. The basic assumption is that the wildlife species which inhabit the area are relying entirely on forest resources to meet their needs for food, shelter, and to attract tourists. Also, there is a positive correlation between ecotourism activities and the presence of forest resources and wildlife. The equilibrium states are determined, and they are subjected to a stability and bifurcation analysis. The study employs a Hopf bifurcation analysis in the neighborhood of the equilibrium states by choosing the time delay as the bifurcation parameter. The critical values of the time-delay that lead to oscillatory behavior are determined. Numerical simulations are carried out to show the system’s qualitative behavior in the vicinity of the equilibria.

A High-Order Well-Balanced Discontinuous Galerkin Method for Hyperbolic Balance Laws Based on the Gauss-Lobatto Quadrature Rules

In this paper, we develop a high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules. Important applications of the method include preserving the non-hydrostatic equilibria of shallow water equations with non-flat bottom topography and Euler equations in gravitational fields. The well-balanced property is achieved through two essential components. First, the source term is reformulated in a flux-gradient form in the local reference equilibrium state to mimic the true flux gradient in the balance laws. Consequently, the source term integral is discretized using the same approach as the flux integral at Gauss-Lobatto quadrature points, ensuring that the source term is exactly balanced by the flux in equilibrium states. Our method differs from existing well-balanced DG methods for shallow water equations with non-hydrostatic equilibria, particularly in the aspect that it does not require the decomposition of the source term integral. The effectiveness of our method is demonstrated through ample numerical tests.

Thermodynamics and kinetics of evaporation and thermal decomposition of 1-ethyl- and 1-butyl-3-methylimidazolium methanesulfonate ionic liquids: Experimental and computational study

Knudsen cell mass spectrometry was used to study the evaporation of two ionic liquids, 1-ethyl-3-methylimidazolium methanesulfonate ([EtMIm][MS], MS = CH3SO3) and 1-butyl-3-methylimidazolium methanesulfonate ([BuMIm][MS]), accompanied by thermal decomposition (thermolysis). The independent occurrence of evaporation and thermolysis reactions made it possible to determine their thermodynamic and kinetic characteristics under identical experimental conditions. The saturated vapor pressures were measured and the standard enthalpies of vaporization of [EtMIm][MS](l) and [BuMIm][MS](l) were obtained. The standard thermodynamic functions of formation in the liquid and gaseous states at 298.15 K were estimated from the available experimental data and the results of quantum chemical calculations. The gaseous decomposition products of ionic liquids were identified and the pressures of the thermolysis products of [EtMIm][MS](l) were determined. According to the experimental data and quantum chemical calculations, the thermolysis of [EtMIm][MS](l) occurs through heterogeneous reactions far from the equilibrium state. The kinetics of the reactions is described in two ways. When the degree of sample conversion is used as a variable, the constant reaction rates at the initial stage of thermolysis correspond to a pseudo-zero order reaction with a monotonic increase in the degree of conversion. In the proposed alternative approach, the reaction rates are estimated from the fluxes of thermolysis products and are expressed in terms of ionic liquid concentration.

Horizontal and vertical dispersion in a wind-driven oceanic gyre model

This study addresses the horizontal and vertical dispersion of passive tracers in idealized wind-driven subtropical gyres. Synthetic particles within a closed basin are numerically advected to analyze their dispersion under different theoretical velocity fields. Horizontal dispersion simulations incorporate the classic wind-driven Stommel circulation along with (i) surface Ekman drift associated with the Stommel wind field and (ii) inertial effects due to particle size and buoyancy. Results reveal that the Ekman drift inhibits particle dispersion across the entire domain leading to tracer concentration in a quasi-stable distribution skewed toward the western side of the basin. Similar behavior is observed with inertial particles. The equilibrium state is quantified for different diffusivity values, particle sizes, and buoyancies. For vertical dispersion, simulations incorporate the three-dimensional Ekman velocity, which includes a negative vertical component, while ignoring inertial effects. Initially, surface particles accumulate around the gyre center while slowly sinking, but they disperse across the basin once they surpass the Ekman layer and are free from surface effects. Tracers sink more on the western side of the basin, regardless of horizontal diffusivity. On average, ignoring inertial effects, particles sink less with higher diffusivity and more with lower diffusivity, suggesting a potential for high horizontal distribution of sunken tracers in the ocean.

Simulating irregular symmetry breaking in gut cross sections using a novel energy-optimization approach in growth-elasticity

Growth-elasticity (also known as morphoelasticity) is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to the push-and-pull from their neighbors, the shape of the growing structure is determined from a state of mechanical equilibrium. As mechanical loads continue to be added to the system through growth, many interesting shapes, such as smooth wavy wrinkles, sharp creases, and deep folds, can form on the tissue surface from a relatively flatter geometry.Previous numerical simulations of growth-elasticity have reproduced many interesting shapes resembling those observed in reality, such as the foldings on mammalian brains and guts. In the case of mammalian guts, it has been shown that wavy wrinkles, deep folds, and sharp creases on the interior organ surface can be simulated even under a simple assumption of isotropic uniform growth in the interior layer of the organ. Interestingly, the simulated patterns are all regular along the tube’s circumference, with either all smooth or all sharp indentations, whereas some undulation patterns in reality exhibit irregular patterns and a mixture of sharp creases and smooth indentations along the circumference. Can we simulate irregular indentation patterns without further complicating the growth patterning?In this paper, we have discovered abundant shape solutions with irregular indentation patterns by developing a Rayleigh–Ritz finite-element method (FEM). In contrast to previous Galerkin FEMs, which solve the weak formulation of the mechanical-equilibrium equations, the new method formulates an optimization problem for the discretized energy functional, whose critical points are equivalent to solutions obtained by solving the mechanical-equilibrium equations. This new method is more robust than previous methods. Specifically, it does not require the initial guess to be near a solution to achieve convergence, and it allows control over the direction of numerical iterates across the energy landscape. This approach enables the capture of more solutions that cannot be easily reached by previous methods. In addition to the previously found regular smooth and non-smooth configurations, we have identified a new transitional irregular smooth shape, new shapes with a mixture of smooth and non-smooth surface indentations, and a variety of irregular patterns with different numbers of creases. Our numerical results demonstrate that growth-elasticity modeling can match more shape patterns observed in reality than previously thought.

Quantifying the Temperature Dependence of the Multi-Species, Multi-Reaction Model. Part 1: Parameterization for a Meso-Carbon Micro-Bead Graphite

In this work, the temperature impact on the Multi-Species, Multi-Reaction (MSMR) model is studied. This is accomplished by acquiring data from slow rate lithiation and delithiation of a meso-carbon micro-bead (MCMB) graphite. The MSMR model is used to simulate linear-sweep voltammetry data of a porous electrode composed of graphite, and because the electrode is close to a state of dynamic equilibrium, the peaks in the differential voltage spectroscopy plot can be analyzed. Through this analysis, the temperature impact on the total fraction of available host sites in a particular MSMR gallery (Xj), the impact on the reference potential (U°j), and the impact on the parameter detailing the deviation from Nernstian behavior (ω j) can be found. This is the first time the temperature dependence of the MSMR parameters have been experimentally analyzed. In Part 2, the impact of the temperature dependence of the MSMR parameters on the entropy coefficient of an intercalation material will be studied.

Stability analysis of a vertical cantilever pipe with lumped masses conveying two-phase flow

This study investigates the vibration behavior of a vertical cantilever pipe conveying gas-liquid two-phase flow, focusing on the influence of lumped masses attached to the vertical cantilevered pipe. The governing motion equation based on small deflection Euler–Bernoulli beam theory is solved by using the generalized integral transforms technique. The proposed solution approach was first validated against available numerical and experimental results in the literature. The effects of the mass ratios, number and position of lumped masses on the stability of the pipe are investigated. Numerical results show that the parameters of the lumped masses affect significantly the stability of the pipe conveying two-phase flow, by altering the fluid–structure interaction dynamics and impacting natural frequencies and vibration modes of the pipe. Specifically, as the position of a single lumped mass moves downward from the fixed end to the free end, the critical flow velocity initially increases and subsequently decreases, thereby reducing the stability of pipe. Moreover, increasing the number of lumped masses significantly impacts the critical flow velocity due to the mass ratios and locations. Notably, modal “jumping” phenomena are observed, which demonstrate continuous shifts between equilibrium and non-equilibrium states in the cantilever pipes. These findings are crucial for ensuring the safe operation of pipes with discrete masses across various engineering applications.

Experimental investigation of the swirling steam jet condensation at low mass flux

Swirling steam jet condensation holds significant applications in industrial processes such as nuclear safety and gas–liquid mixing in the oxygen transmission pipeline of the liquid rocket engine. However, due to its involvement with complex flow and phase-change heat transfer, the application and optimization of related condensation technologies still face challenges. Therefore, this paper aims to investigate the condensation characteristics of the swirling steam jet by numerous experiments. The steam mass flux is 15–45 kg/(m2·s), and the water temperature ranges from 40 to 85 °C. A novel X-type swirl pressure nozzle is selected to achieve the swirling flow of the steam jet. A comparative analysis is conducted on the interface behavior and evolution of condensation parameters of the non-swirling and swirling steam jets during condensation processes. Results show that the swirling jet condensation includes three flow patterns, namely, chugging regime, smooth grown bubble regime, and rough grown bubble regime. Compared with the non-swirling steam jet condensation, swirling steam jets exhibit a 10.36% increase in the smooth grown bubble regime region and a 14.63% decrease in the rough grown bubble regime. Swirling bubble morphology evolves steadily, and the surface is smoother and more rounded. Simultaneously, irregular deformation behaviors can also occur in the swirling bubble condensation process, such as spiral growth of jet bulge, neck torsion, and the corolla pattern. This deformation helps to increase the contact area and prolongs the bubble lifetime, allowing for more adequate heat transfer at the steam–water interface. The swirling motion of the steam jet will reduce the bubble collapse frequency. As the water temperature rises from 60 to 80 °C, the bubble condensation rate and collapse frequency decrease. The bubble radius increases and the condensation time is extended. With the increasing steam mass flux, the collapse frequency gradually increases. The condensation rate and the bubble radius vary nonlinearly. At the higher steam mass flux, the swirling motion can effectively release the heat that accumulates inside the bubble after reaching the condensation equilibrium state.