The concept of tourism economic resilience emphasizes the sustainable development level of tourism economy under uncertainty and risk. Focusing on urban agglomerations, this study aims to describe how the tourism economic resilience is developing, explore whether the resilience level is enhanced with urban agglomerations and whether spatial elements affect resilience levels. With the combination of the aggregation and diffusion effects and crowding effects of regional development, the study uses a combination of dynamic evaluation method, spatial kernel density, and mathematical models of urban agglomeration development to quantitatively analyze the spatiotemporal dynamic evolution of tourism economic resilience from 2006 to 2019, simulates and verifies its development patterns. The conclusions show that: (1) The tourism economic resilience in urban agglomerations is closely related to regional development and prosperity; (2) The development of tourism economic resilience also follows the spatial economic development pattern which moves towards equilibrium in aggregation process; (3) The tourism economic resilience of urban agglomerations has a fluctuation climbing node, generally presents as a wave-like upward trend with fluctuations and stages; (4) The evolutionary trend of tourism economic resilience in urban agglomerations presents as a slight wave-like upward curve that changes with time and co-opetition. The structure and function of China's tourism industry have always been affected by uncertainty risks during its development process, thereby threatening tourism economy’s sustainability development2. Due to its environmental sensitivity, the tourism economy is vulnerable to fluctuations in natural, social, political, and economic changes within the region, reflecting the fragility of the tourism economy under external impacts3. As a vital embodiment of the self-regulating and recovery ability of the comprehensive system, the level of resilience can not only highlight the anti-fragility level of the industry at the implicit level but also explicitly measure the sustainable development level4. Cross-discussed the concept of resilience and the tourism economy’s sustainable development, it is a valuable entry point for the tourism economy’s recovery in the post-epidemic era at the macro level and the coordinated development between regions at the meso level. With the advancement of internet technology and transportation accessibility, the economic and cultural exchanges among regions in China are getting increasingly close, the development of the tourism economy also reflects vital regional openness and industrial relevance. Under the background of regional spatial connection increase, the compatibility and integration degree between the tourism economy and regional development are also gradually rising in China5. Based on the guiding principle of the sustainable tourism economy, except the remote tourist attraction from outside of the region, potential tourism consumption demands within the area should also be valued and explored6. When uncertainty risks such as liquidity constraints emerge, the spatial transformation and substitution between remote and local tourists can provide resilient survival space for the tourism economy7. Meanwhile, urban agglomeration is not only a crucial spatial carrier for the new urbanization process but also a concentrated area for the tourism economy development and fierce market competition under the current regional development system in China8. Therefore, viewing from the point of urban agglomerations, quantitatively analysis the actual situation of tourism economic resilience, discusses the synchronous evolution process and spatiotemporal influencing factors of tourism economic resilience, which have a significant practical value for the tourism industry to transform from scale and speed-oriented growth to quality and efficiency-oriented development in the new era, then ultimately achieving the maximization of social surplus.In China, sustainable development is gradually replacing high-speed growth in the economic system. As one of the strategic pillar industries in China, achieving sustainable development transformation in the tourism economy is an inevitable choice for the tourism industry to respond to the national policy call and enhance its overall competitiveness9. Through the development process of resilience research, resilience theory was first introduced into applied economics in 2002, which believed that differences in resilience are the key explanatory factors for different outcomes under the same impact in different regions10. Since then, the definition of economic resilience has gradually become more apparent. Scholars generally agree that it refers to the ability of an economic system to adapt and restructure its internal structure to mitigate the impact of shocks, while maintaining continued development and utilizing external shocks to achieve system renewal11. Thus, the understanding of the concept has gradually shifted from resilience thinking under the framework of the ecological environment to evolutionary resilience thinking, which represents dynamic adaptation and sustainable development goals12. However, as an extension of economic resilience, the study of tourism economic resilience has appeared relatively late. Cross-disciplinary exploration of tourism economic resilience mainly focuses on crises’ external impact with natural or social attributes on the tourism economic system and the internal conditions that foster resistance against external impact13. Research topics are divided into three different frameworks: ecological environment14, socio-economic15 or political-geographical conflicts16, each related to different types of external impacts. Under the context of ecological and environmental changes, research on the resilience of tourism economies often considers the ecological environment as the foundation for the development of tourism, while climate change, ecological destruction, and environmental pollution can seriously threaten the sustainable development capacity of tourist destinations and expose their vulnerability17. As a result of excessive pursuit of short-term benefits, ecological pressure has risen dramatically, disrupting the diversity and balance of the ecological structure, which is the primary source of vulnerability for tourist destinations18. Additionally, under the context of socio-economic issues, research at the economic level mainly focused on how large-scale economic crises affect the volatility of tourism economies, and policy recommendations often emphasize the diversity and breadth of tourism products and the broadness of tourism consumption19. At the social level, sudden public health events can cause personnel mobility and have become the most discussed topic among numerous socio-economic issues20. In particular, the tourism economies stagnated after the COVID-19 pandemic, the anti-fragile properties and evaluation of the regional tourism economies resilience have gradually gained attention21. Finally, under the context of political and geopolitical conflicts, resilience research is relatively rare, and the limited research topics are mainly concerned with the impact of war conflicts or terrorism on personnel mobility, security stability, and economic activity in tourist destinations2. Such literature often takes terrorist attacks or short-term geopolitical conflicts as an entry point and proposes that conflict risks can affect tourism decision-making at the micro level but have little long-term impact on cross-regional tourism at the macro level. Besides the research topics, tourism economic resilience research methods primarily rely on qualitative studies, with relatively fewer quantitative studies. Among qualitative methods, the research use case analysis, interviews, and questionnaires. For instance, Ntounis et al. (2022) analyzed the factors affecting resilience under the impact of the pandemic using the PRISMA method. Similarly22, Quang et al. (2022) used a questionnaire survey to summarize the perceptions of the pandemic’s impact on Vietnam’s tourism industry and provided practical recommendations to enhance the tourism economy resilience further23. In terms of quantitative research, methods are more commonly used for evaluating resilience and comparing driving factors. For example, by calculating conditional value at risk, Shi et al. (2023) revealed the importance of providing tourism products, services, and infrastructure in the tourism economic resilience evaluation system24. Similarly, Zhang et al.25 explored whether the Chinese tourism economy exhibits resilience under different risk cycle contexts and ultimately identified the factors affecting tourism economic resilience through geographic detectors.Various types of uncertainty risk obstacles always accompany the economic development of human society. Using resilience criteria to represent the sustainable development ability of economic subjects is currently the mainstream and prevailing evaluation method for most of the government and academics27, did not take the economic attributes of the tourism industry into the resilience framework. Whether the existing evaluation system can accurately characterize the resilience level of the tourism economy, the application scope, and the inherent value remains to be further verified. Secondly, the current tourism economic data in China are mainly at the national and provincial levels, which is challenging to obtain tourism-related data at the city level from the statistical yearbooks. As a result, quantitative analysis of the tourism economy at the mesoscopic level is relatively few, and a complete study on spatiotemporal evolution patterns of inter-regional tourism economic resilience is lacking. As an essential spatial carrier of factor agglomeration in China at the meso scale, the stable growth of the tourism economy has great practical significance for regional employment issues and sustainable development goals. However, existing research has taken chiefly a macro or micro perspective29, with few articles choosing urban agglomerations as the entry point for analyzing tourism economic resilience, resulting in a need for more hierarchy and comprehensiveness in the existing field of tourism economic resilience research. Furthermore, scholars have yet to analyze the spatiotemporal evolution pattern of tourism economic resilience from a dynamic perspective, nor have they cross-discussed urban agglomerations development with the development law of tourism economic resilience. With the progress of regional exchanges and the gradual breaking of boundary effects, urban agglomerations have become increasingly important in Chinese regional development. But in terms of regional development, whether the resilience of the tourism economy will rise synchronously with the pace of urban agglomeration development, this question has not received sufficient attention in the field of tourism.The previous studies expanded the research perspectives on tourism economic resilience from multiple angles, providing a matter though for further innovative extensions in this paper. By affirming and using some of the above research perspectives and methods, this article also recognizes the gaps existing in the current literature. Firstly, although some scholars recently have begun the quantitative analysis of tourism resilience, the application of resilience assessment in the tourism economy is still in its infancy, and the guiding theory of the indicators selection still mainly focuses on the restorative and equilibrium aspects within the ecological resilience conceptTherefore, by taking the urban agglomerations as the research area, this paper quantitatively evaluates the tourism economic resilience based on a multi-source data structure, characterizes its spatiotemporal pattern features from a dynamic perspective, and finally combines the formation and development process of urban agglomerations with tourism economic resilience development for cross-discussion, to enrich the diversity of tourism economic resilience research in theory and help urban agglomerations plan for sustainable tourism economic development in practice.30. Effective tourism resilience management can restore the tourism products supply and the functionality of tourism services at the fastest rate possible through reasonable utilization of internal and external resources31. Using dynamic agglomeration economic theory and evolutionary economic geography theory, this article will examine a detailed analysis of the rising pattern of tourism economic resilience in urban agglomerations. Firstly, the dynamic agglomeration economic theory explains the relationship between the tourism economy and spatial expansion of cities within a regional development process from the perspectives of agglomeration and growth. The economic benefits produced by the spatial agglomeration of factors continuously attract the collaboration of surrounding cities with the central city, thereby promoting urban agglomeration’s formation and development, and the tourism economy of urban agglomeration also continuously rises under the agglomeration effect. However, when the scale of tourism economy agglomeration expands to a certain extent along with the region spatial expansion, a congestion effect will appear32. Under the combined effects of agglomeration and congestion, tourism economic resilience development will experience some fluctuations. Secondly, from a regional coordinated development perspective, integrating new cities into the development phase of the central city usually leads to a transitional stage characterized by antagonistic reactions, which is reflected as a wave-like upward trend with fluctuations and periodicity33. Therefore, under the background of regional co-opetition, there objectively exists a threshold value to determine whether the central city can integrate resources with new cities and thus enhance the tourism economy resilience. Meanwhile, the development stage and tourism economic level in urban agglomerations are quite different in China, which may lead to the deviation of the resilience development trend, and there is a certain spatial and temporal difference. In this regard, this paper will also conduct an in-depth discussion on the spatiotemporal pattern characteristics of the tourism economic resilience from the dynamic perspective.Tourism economic resilience means the ability of the tourism ecosystem to absorb or withstand disturbances and other pressures, enabling the tourism industry development to maintain its structure and function34, and propose the climbing law of the tourism economic resilience of urban agglomeration, then create a wave-like climbing curve of the tourism economic resilience. Different from the previous studies, the climbing law presented in this article intends to the developmental characteristics of tourism economic resilience. Which means, as urban agglomeration develops, there is constant co-opetition among internal tourism economies. However, during the antagonistic stage, the tourism economy is difficult to improve substantially or even experiences a fall in resilience growth. The overall development pattern presents a wave-like climbing form, similar to a series of climbing waves. This is the climbing law followed by tourism economic resilience through urban agglomerations’ development and formation. Exploring this development law, it can provide better service for the layout planning of the sustainable tourism economic development in urban agglomerations, which has important reference value for the tourism industry transformation in from scale and speed-oriented development to quality and benefit-oriented development and from extension and expansion-oriented development to core-connotation-oriented development in the new era.This article draws on the climbing mechanism and initial formula for sustainable development of urban clusters set up by Fang et al.By further considering the resilience level of core cities during the initial development, this paper has improved the climbing function curve simulation formula. Specifically, it can be expressed as follows:Variable In the formula, 35. Accurately understanding the spatiotemporal pattern characteristics and development rules of tourism economic resilience, it is valuable for promoting the sustainable development of the tourism economy and coordinated development between regions. Therefore, this paper selects 19 urban agglomerations mentioned in China's latest development plans, including National-level urban agglomerations ; Regional-level urban agglomerations; Prefecture-level urban agglomerations , with a total of 203 cities as the research object, shown in Fig. Urban agglomerations have gradually become an essential spatial carrier for tourism development in China36. In order to break through the limitations in existing research, this paper uses the vertical-horizontal stratification method to weigh the fundamental indicators, then uses the fixed base efficiency coefficient method to standardize the indicators and calculate the tourism economic resilience index at the end.37.Vertical-horizontal stratification method. The vertical-horizontal stratification method is a novel dynamic comprehensive evaluation approach characterized by its straightforward principles, clear intuitive meaning, and transparent evaluation process. It aims to determine weight coefficients based on the differences observed among evaluated objects in a temporal and spatial data tableIn the formula, it is assumed that the following set of evaluated objects is 38. The specific formula used in this study is notated as follows:Fixed base efficiency coefficient method. In order to effectively compare tourism resilience across different years, this study employs the fixed base efficiency coefficient method to standardize the original data using 2006 as the base year. It is a normalization technique that utilizes efficiency coefficients to account for changes in the level of input and output variables over timeIn the formula, indicator Linear weighting method: Combining the weight coefficient vector mentioned above with the standardized indicator values, the paper uses it to calculate the tourism economic resilience index, denoted as The traditional methods of Combinatorial evaluation typically rely on static foundations to proceed. In contrast, combinatorial dynamic evaluation introduces time factors from an emotional perspective into the combinatorial evaluation method to ensure continuity of the evaluation results39. Based on the ordinary kernel density, the paper estimates the probability density of random variables by adding time and space parameters. In the formula, Compared to traditional kernel density estimation, spatial kernel density has a broader perspective and can better reflect the spatial dynamic characteristics of the analysis object40. With the development of urban agglomeration, the intensity can appropriately reflect the competitive process of the tourism economic resilience41. According to the climbing law and the basic function model, we have developed a formula for calculating the intensity of co-opetition in urban agglomeration. The specific formula is as follows:Firstly, co-opetition intensity means the degree to which tourism economies of cities attract and integrate with each other. It is positively correlated with resilience level and negatively correlated with spatial distance42. The overall trend exhibits a wave-like fluctuation and periodicity, and there is an objective threshold value of co-opetition to determine whether the curve of the tourism economy resilience has entered the next stage due to co-opetition-induced changes in the resilience level of cities.Furthermore, during the process of tourism economic resilience enhancement in urban agglomerations, there is a transition phase in which mutual attraction and co-opetition between cities coexist in an antagonistic stateDrawing on Duan & Tang, (2022)'s method for setting threshold values in the analysis of the coordinated development process within urban agglomerations, this paper uses the mean of the co-opetition intensity as a threshold value for determining whether to unite with a new city. The formula is presented as follows:In the formula, 43. When uncertainties such as mobility restrictions arise, the transformation and substitution of remote and local tourists can provide resilience survival space for the tourism economy44. Tourism activities is the core of the tourism economy. The tourism economy is vulnerable to risks due primarily to the strong tourism demand of tourists and the high supply capacity among tourism service providers45. Furthermore, enriching the structure of the tourism economy and strengthening the government's management capacity is essential to enhance the resilience of tourism activities in response to social risk shocks46. Accordingly, this article will start from the economic attributes of the tourism industry and evaluate its resilience from four perspectives: supply, demand, structure, and management.Different from the current resilience conceptual framework, which usually based on ecological thinking, this article constructs a resilience evaluation system starting from the economic attributes of the tourism industry and proposes that tourism resilience should focus on the degree of integration and compatibility between the tourism industry and the regional economy. The sustainable development of the tourism economy not only relies on tourists from outside the region but also needs to tap into the potential demand of local residents21.In the framework, supply resilience and demand resilience comprehensively consider the business anti-vulnerability of tourism destinations under the liquidity crisis, which can also refer to the integration degree between the tourism industry and the local economy47 and Prayag et al.48, this paper characterizes the tourism economy supply resilience with indicators such as the number of star hotels, number of tourist attraction, etc., which measures the ability of tourism service providers to recover to the desired state after being disturbed by risks. Taking Sharma et al.49’s study into account, this paper characterizes the tourism economy demand resilience with indicators like the scale of tourist number, tourism consumption level, etc., which measures the motivation of tourists to resume tourism activities after being disturbed by risks. Structural resilience mainly considers whether the tourism destination has the adjustment and innovation ability to form digital tourism or alternative tourism under uncertain risks such as liquidity restriction or consumption trend change20. According to the studies of Lu et al.50and Anguera-Torrell et al.51, this paper characterizes the tourism economy structural resilience with indicators such as the industrial structure rationalization index, the proportion of employees in the digital industry, etc., which measures whether tourism destinations can adjust to the formation of digital tourism instead of traditional tourism after being disturbed by risks. Management resilience is represented by the investment status and importance of tourism destinations in tourism ecological environment protection, tourism industry support, infrastructure support, and other aspects, which reflects the potential support ability of tourism destinations for the anti-vulnerability of the tourism economy52. Taking into account the findings of Wang et al.53, this paper characterizes the tourism economy managerial resilience with indicators like the intensity of environmental regulation, tourism industry attention level, etc., which measures the potential coping capacity of tourism destinations after being disturbed by risks. The specific framework and indicators are shown in Table In accordance with Calgaro et al.Since China proposed the concept of urban agglomeration construction begun from 2006, and most of the current data related to the tourism economy has been updated until 2019, this paper now selects the study period from 2006 to 2019 as the research timeframe.The spatial vector data. In this study, basic map vector data are derived from the national basic geographic information database, and uses ArcGIS software to determine the distribution of urban agglomeration.www.cnrds.com) and the Patent Retrieval and Analysis System of the National Intellectual Property Administration. This paper mainly uses indicators such as tourism volume, tourism economic income, and population density to reflect the resilience of remote and local tourism economic demand.Platform sharing data. The green innovation patents, population density, number of star-rated hotels, tourism volume, and economic income data used in this paper were obtained from the Chinese Research Data Services  believe that the differences in resilience will show an expanding trend, which differs from the conclusion of this article. This may be due to the fact that the concept of resilience emphasized by Zhang et al. (2022) were focused on the defense, recovery and reconstruction of the tourism economy after the epidemic, while the concept of resilience emphasized in this article focuses on the degree of integration and compatibility between the tourism industry and the regional economy. Under the concept of this article, the tourism economic resilience in urban agglomerations shows a gradually balanced trend among regions. The difference in the index selection and the differences in the research areas have led to a divergence in the conclusions between the two articles.After considering the spatial–temporal conditions, this paper proposed that the tourism economic resilience follows the spatial economic development law, which moves towards equilibrium in the agglomeration process. Urban agglomerations with relatively strong economic foundations, such as BTH, YRD, and PRD, exhibit higher levels of resilience, creating a significant gap compared to other urban agglomerations. This conclusion complies with the overall polarized trend of provincial tourism economic resilience evaluation in China under the impact of the COVID-19 pandemic, as summarized by Zhang et al.56. By comparing the simulation and verification results of the two articles, the trend of the development curve is relatively consistent, and the principle of climbing law has substantial similarities. It indicates that the resilience climbing law proposed in this paper conforms to the national characteristics and regional development reality in China, which is suitable for urban agglomerations development. It can provide planning reference and data support for the sustainable tourism development of urban agglomerations.After observing the fitting effect, this paper proposed that the tourism economic resilience conforms to the wave rising trend of the development law in urban agglomeration. From the perspective of urban agglomerations, Mu et al. (2022) cross-discussed urban agglomeration development and the climbing law of urban resilience curve of urban agglomerations, which also concluded that the resilience level is basically manifested as a wave climbing trendIn addition, this paper constructs a system of tourism economic resilience indicators from four aspects: supply, demand, structure, and management, which are very helpful in assessing the tourism economy resilience to the epidemic. First, the supply resilience aspect. After the outbreak of the epidemic, regions with high tourism supply resilience can quickly adapt to the new market demand to adjust tourism products and provide more health and safety protection. In this conclusion, it can mitigate the impact of supply chain disruptions and maintain the continuity of the tourism business. Second, the demand resilience aspect. Tourism demand may fall during an epidemic, but regions with high demand resilience may be able to attract different types of tourists after the epidemic. In this way, it helps mitigate the impact of demand shocks on tourism. Third, the structural resilience aspect. A diversified tourism structure will likely make urban agglomerations more resilient in their tourism economies, as they will not be exclusively dependent on one type of tourism. Fourth, the managerial resilience dimension. Highly effective tourism management and policy support can ensure that urban agglomerations adapt to future uncertainty and are more likely to energize the tourism industry after an epidemic. Assessing the resilience of tourism economies can help urban agglomerations improve their tourism economies to increase their ability to cope with epidemics or other external shocks and ensure the tourism industry's sustainability and resilience.22,25. However, these articles primarily focus on the national or provincial level, with relatively large granularity. Based on data at the city level, this article selects urban agglomerations as the research scope and aims to show the economic attributes of the tourism industry and the compatibility of the tourism economy with the regional economy, thereby reflecting the resilience and anti-fragility of the tourism economy under uncertain risks. However, compared with the national and provincial scales, there is a disadvantage of relatively insufficient data acquisition width and breadth. When major public issues such as epidemics occur, whether the tourism economic resilience development pattern of tourist destinations will deviate from the trend due to mobility restrictions and whether the previously simulated resilience level can withstand the test of special events such as epidemics, this article temporarily lacks data support to provide a more comprehensive empirical explanation. Therefore, regarding the reconstruction of tourism economic resilience development during the epidemic and even in the post-epidemic period, the author of this article hopes that more scholars in the fields of geography, data science, economic statistics, and public health management will join the discussion and conduct interdisciplinary research to provide more reference basis for research on tourism economic resilience in China or even globally.Finally, it is important to note that recent research the tourism filed has gradually begun to conduct a quantitative analysis of the epidemic impact on the tourism economic resilience and the reconstruction of the tourism economyThis article uses the method of combined dynamic analysis to measure the tourism economic resilience in urban agglomerations quantitatively. Through spatial kernel density, the spatial effects and patterns of tourism economic resilience in urban agglomerations are observed from a spatial dynamic perspective. Finally, the development curve of the resilience is scientifically verified through a simulation model of evolutionary laws, confirming the universal applicability of resilience evolution trend. Here are the main conclusions:Firstly, national-level urban agglomerations have a higher level of tourism economic resilience, while non-national-level urban agglomerations have a more robust tourism economic resilience. Upon observation, high resilience level urban agglomerations have gradually achieved stable average annual growth rates due to the more robust economic foundations and larger scales. The urban agglomerations with high growth rates are mostly limited by factors such as location factors, lack of tourism resources, or poor regional spatial development benefits, resulting in poor resilience foundation and still in the early stages of wild growth. In general, the distribution pattern and evolutionary trend of the tourism economic resilience exhibit a substantial similarity to the development laws of the current regional economy in China.Secondly, the development of tourism economic resilience in urban agglomerations also follows the spatial economic development pattern, which moves towards equilibrium in the aggregation process. Upon observation, the upward trend of regional tourism economic resilience gradually extends from national-level urban agglomerations in the eastern coastal regions to regional and prefecture-level urban agglomerations in the central and western regions. Within the regions, the development of tourism economic resilience gradually radiates from the central cities towards the surrounding cities. In general, the formation and development of urban agglomeration correlate with the rising trend of regional tourism economic resilience.Thirdly, the tourism economic resilience has a fluctuation climbing node, generally presenting as a wave-like upward trend with fluctuations and stages. Upon observation, national-level urban agglomerations benefit from advantages in geographic location, economic structure, and the depth and breadth of tourism economies, resulting in the highest level of stability in resilient development. However, the regional-level and prefecture-level urban agglomerations are prone to negative spillover effects and easily encounter the development bottlenecks when the resilience level reaches a certain level. This is the change node where the tourism economic resilience of urban agglomeration fluctuates.Fourthly, the evolutionary trend of tourism economic resilience in urban agglomerations presents a slight wave-like upward curve that changes with time and co-opetition. Upon observation, all the evolutionary curves of the tourism economic resilience have a good fitting effect. In terms of the overall trend, it complies better with the wave-like rising trend of urban agglomeration development law, which shows a slight wave-like rising trend. Through fitting, the evolutionary rising law of tourism economic resilience in urban agglomerations has been verified, which is suitable for developing urban agglomerations.Considering the above research conclusions and the tourism economy resilience development, the following policy recommendations are offered in order to realize the transformation of the tourism economy’s sustainable development and enhance the comprehensive competitiveness of the tourism industry in Chinese urban agglomerations.Firstly, multiple parties should work together to enhance the tourism economy resilience of urban agglomerations. To begin with, it should improve the tourism economy resilience of urban agglomerations from the supply side. For example, strengthen the construction of hotels and tourist attractions, especially star-rated hotels and scenic spots. In this way, it can create more jobs in the tourism economy industry and improve the quality of public services. Next, it should understand and satisfy consumer expectations and energize tourism consumption from the demand side. Then, continuously optimize the structure of the tourism industry and form the industrial layout with complementary advantages between cities. Strengthen the construction of tourism digitization, such as applying virtual digital person technology to digital tour guides. Finally, strive to form the organic unity of the market and t the government, which can promote the high-quality development of tourism economic resilience. The two are complementary and work together to encourage each other.Secondly, cross-city cooperation and linkages can jointly improve the overall tourism economic resilience to reduce social risks’ impact. When a liquidity crisis or epidemic occurs, the spatial shift between long-distance and short-distance tourists can provide a resilient living space for the tourism economy. In the post-epidemic era, the forming of cross-city cooperation and linkage mechanisms is the key to the spatial shift of long-distance and short-distance tourists. On the one hand, establish a tourism cooperation mechanism for urban agglomerations. It creates cross-city tourism cooperation platforms and establishes joint websites or digital platforms. As a result of these approaches, cities are able to exchange information and resources so that they can respond to emergencies quickly and collaboratively. On the other hand, promote online tourism to digitize tourism. During liquidity crises or epidemics, provide tourism content online to maintain interaction with tourists and mitigate the extent of physical tourism.Thirdly, establish a crisis management mechanism and formulate a comprehensive crisis management plan to enhance the risk-resistant capacity of the tourism economy of urban agglomerations. This mainly responses to public health emergencies and natural disasters. In the first instance, formulate a joint crisis response plan. Urban agglomerations should develop joint crisis response plans in advance, clarify each city’s responsibilities and concerted actions, as well as ensure an orderly response in times of crisis. Alternatively, promote joint insurance programs and establish emergency assistance funds. Tourism enterprises within an urban agglomeration can work together to promote a coordinated insurance program to share the losses caused by the crisis and improve the overall tourism economic resilience. Create an emergency assistance fund for urban agglomerations in the event of a problem to ensure tourists’ immediate financial assistance, and tourism enterprises in times of crisis.


Under the different temperature environment, the precast pile-soil interface characteristics has an important impact on the safety and long-term stability for pile foundation. A large precast pile-soil shear experimental device is used to carry out the direct shear test of concrete-loess interface with different moisture contents under different freezing temperatures. The variation laws of shear strength parameters are revealed with influencing factors, and the shear mechanism of interface is discussed. The stress-strain constitutive equation of interface is proposed, and the shear strength criterion is established with considering the effects of temperature and moisture content on cohesion and internal friction angle. The results show the curve of shear stress and shear displacement can be divided into three stages: elastic deformation stage, plastic deformation stage and sliding failure stage, which macroscopically reflects the shear failure mechanism of the frozen soil-concrete interface. The shear strength of the interface is affected by the test temperature, sample moisture content and normal stress. The lower the test temperature, the greater the shear strength of the interface; With the increase of normal stress, the shear strength of interface increases; With the increase of moisture content, the shear strength of the interface increases and then decreases. The relationship of shear stress and shear displacement of frozen soil-concrete interface can be well described by the piecewise combination of hyperbolic function and linear function. Pile foundation has been widely used in highway, railway, bridge and high-rise building projects, and its function is to transfer the superstructure load to the rock or soil layer with high strength and low compressibility through the pile body, which provides higher bearing capacity and reduces foundation settlement. The stress and deformation between soil and structure are mainly transmitted through their interface . BecauseThe model pile test can effectively simulate the action of the different types of pile-soil under different loads, and can evaluate the limit states of failure and deformation , 6. BecaUnder the influence of ground temperature, Yavari et al.  and Li eIn the freezing environment, Zhao et al.  adopted Although many scholars have done a lot of research on the frozen soil-structure interface, there is no in-depth and systematic research on the influence factors of its shear properties. Therefore, in this paper, the mechanical relationship of frozen soil-concrete interface is simplified as a two-dimensional contact surface between frozen soil and structure. The mechanical properties of frozen soil-concrete interface are analyzed through the direct shear tests, which are carried out under different test temperatures, sample moisture content and normal stress. The shear stress mechanism of interface is discussed, the stress-strain constitutive equation of interface is proposed, and the shear strength criterion is established with considering the effects of temperature and moisture content.The stress and strain of the precast pile-soil interface is observed during the pile-soil interface shear simulation test, the generation and development mechanism of the shear characteristics are analyzed to discuss the stability of the pile foundation under the high and low temperature environment.At the beginning of the shear test, the pile-soil test box is placed on the pile simulation box, the soil is filled and compacted, and a loading plate is covered, then a vertical load is applied on loading plate to simulate the earth pressure. The horizontal thrust is applied to the pile simulation box to make the pile simulation box slide between the operation platform and the precast pile-soil test box, and the precast pile-soil interface produces relative displacement and shear failure until the horizontal thrust tends to be stable. During the test, the displacement and horizontal thrust of the pile simulation box are measured and recorded.Because the concrete slab is located at the lower part of compacted soil, while the horizontal thrust acts on the concrete slab along the interface direction, the concrete slab is also subjected to the vertical pressure transmitted by the vertical load through the compacted soil. The mechanical response of precast pile-soil interface occurs along the horizontal thrust direction. When shear displacement occurs, the pile-soil contact interface generates friction to balance the horizontal thrust. Assuming that the friction at the interface is evenly distributed, the interface friction corresponding to the maximum horizontal thrust is the ultimate friction (shear strength) at the precast pile-soil interface.Low temperature laboratory  and moisture content (θ). It can be seen from τ) of frozen soil-concrete interface can also be expressed as,The direct shear test data of frozen soil-concrete interface show that the shear strength is affected by normal stress (σ), freezing temperature (c) and internal friction angle (φ) are the functions of freezing temperature and moisture content. If the relationship of shear strength parameters, moisture content and freezing temperature is found out, the strength criterion of frozen soil-concrete interface can be obtained.Where, the shear strength parameters cohesion  criteria of frozen soil-concrete interface can be obtained as,Substituting the fitting parameters in Tables According to the shear stress and shear displacement curve, the relationship of shear stress and shear displacement can be divided into elastic deformation stage, plastic deformation stage and sliding failure stage. In order to establish the whole process expression of shear stress and shear displacement relationship, the hyperbolic model is used to approximately describe the elastic-plastic development stage, and the shear strength is used to represent the failure stage, so the hyperbolic function of shear stress and shear displacement is expressed as,τ = τp), then the shear stress and shear displacement is expressed as,When the shear stress reaches the shear strength . With the increase of moisture content, the unfrozen water film thickens, and the pore ice cementation weakens for soil particles and concrete particles. This is because the thickness of unfrozen water film determines the cementation strength of ice-soil particles and ice-concrete particles. And the thickness of unfrozen water film is approximately linear with freezing temperature. The lower the freezing temperature, the thinner the unfrozen water film . The iceThe interface friction includes the surface friction of soil-concrete particles, the surface friction of soil particles and the bite force caused by the embedding and interlocking among particles. The friction among soil particles, the surface friction between soil-concrete particles is affected by the normal stress. The greater the normal stress is, the more obvious the friction effect is. The bite force generated by the embedding and interlocking between particles is obviously affected by the initial moisture content. When the initial moisture content is smaller, the soil sample freezes into pore ice, the volume expansion of water-ice phase transition has little effect on the soil skeleton, and the friction force on the interface is larger. As moisture content exceeds the saturated moisture content, more water is frozen into ice resulting in larger volume expansion, which affects the bite force formed by the embedding and interlocking among particles, and reduces the friction force of the interface.Loess and high-strength plain concrete are made into soil-concrete samples with different moisture content, then the direct shear test of frozen soil-concrete interface is carried out under different freezing temperature, normal stress and moisture content by using a large pile-soil shear experimental device in cryogenic Laboratory. the influence law of different factors on the shear strength of interface is revealed, the stress displacement constitutive equation is proposed, and the shear strength criterion is established with considering the effects of freezing temperature and moisture content on cohesion and internal friction angle. The following conclusions can be obtained as,The curve shape of shear stress and shear displacement of the interface in the direct shear test shows obvious segmentation, it divided into elastic deformation stage, plastic deformation stage and sliding failure stage successively.The shear strength of frozen soil-concrete interface is affected by normal stress, freezing temperature and moisture content. The shear strength increases linearly with the increase of normal pressure, the shear strength increases linearly with the decrease of freezing temperature, and the shear strength increases and then decreases with the increase of moisture content.The shear strength parameters of the interface are affected by freezing temperature and moisture content. With the decrease of freezing temperature, the cohesion increases linearly, while the internal friction angle decreases and then increases. With the increase of moisture content, the cohesion first increases and then decreases, while the internal friction angle decreases and then increases. The shear strength criterion is obtained by multiple regression method.The shear stress and shear displacement relationship of frozen soil-concrete interface can be well simulated by using the piecewise combination of hyperbolic function and linear function.The direct shear failure mechanism of frozen soil-concrete interface can be attributed to the strength of ice, the ice cementation, the cohesion of soil particles, the surface friction of soil-concrete particles, the surface friction among soil particles, the biting force caused by the embedding and interlocking among particles, etc.S1 Table(DOCX)Click here for additional data file.S1 Dataset(XLS)Click here for additional data file.


Hepatocellular carcinoma (HCC) is the most common primary liver cancer. High-risk patients should undergo semi-annual surveillance. Management of HCC is complex and requires multidisciplinary team evaluation and the consideration of patient’s goals of care. Early HCC is best managed by curative-intent treatment with liver resection, transplantation, or ablation. Intermediate-stage disease may be treated with transarterial therapies. Advanced-stage disease should be treated with systemic therapy. There are many therapies and therapy combinations currently under investigation.Hepatocellular carcinoma (HCC) ranks fourth in cancer-related deaths worldwide. Semiannual surveillance of the disease for patients with cirrhosis or hepatitis B virus allows for early detection with more favorable outcomes. The current underuse of surveillance programs demonstrates the need for intervention at both the patient and provider level. Mail outreach along with navigation provision has proven to increase surveillance follow-up in patients, while provider-targeted electronic medical record reminders and compliance reports have increased provider awareness of HCC surveillance. Imaging is the primary mode of diagnosis in HCC with The Liver Imaging Reporting and Data System (LI-RADS) being a widely accepted comprehensive system that standardizes the reporting and data collection for HCC. The management of HCC is complex and requires multidisciplinary team evaluation of each patient based on their preference, the state of the disease, and the available medical and surgical interventions. Staging systems are useful in determining the appropriate intervention for HCC. Early-stage HCC is best managed by curative treatment modalities, such as liver resection, transplant, or ablation. For intermediate stages of the disease, transarterial local regional therapies can be applied. Advanced stages of the disease are treated with systemic therapies, for which there have been recent advances with new drug combinations. Previously sorafenib was the mainstay systemic treatment, but the recent introduction of atezolizumab plus bevacizumab proves to have a greater impact on overall survival. Although there is a current lack of improved outcomes in Phase III trials, neoadjuvant therapies are a potential avenue for HCC management in the future. Hepatocellular carcinoma (HCC) is the dominant type of primary liver cancer, and the fourth most common cause of cancer-related deaths worldwide. This is the case despite the development and implementation of hepatitis C treatment and hepatitis B vaccination and antiviral therapy ,2,3. MosThe implementation of surveillance programs for chronic liver disease, cirrhosis, and HCC allows for earlier tumor detection, curative treatment, and longer overall survival, as compared to when patients present symptomatically with the advanced disease ,19. The The goal of surveillance programs is to identify early-stage HCC in at-risk patients , when curative-intent treatment is an option . The AmeAlthough the HCC surveillance of patients with cirrhosis has been found to increase survival, surveillance is underused in clinical practice . BarrierDue to the continued underuse of surveillance programs, it is recommended that interventions be implemented to improve HCC surveillance rates ,37. A vaImaging plays a critical role in the diagnosis of HCC , making The Liver Imaging Reporting and Data System LI-RADS,  is a comPer EASL and AASLD guidelines, the diagnosis of HCC in cirrhotic patients should be based on non-invasive criteria and/or pathology, while in non-cirrhotic patients, it should be confirmed by pathology. While US is the primary surveillance modality, in the case of diagnosis, CT or MRI should be used due to higher sensitivity. These organizations also advise against routine biopsy, unless a timely diagnosis is required, the image-based diagnosis is inconclusive, or for the diagnosis of HCC in patients without cirrhosis ,27.HCC is different from other malignancies in that liver function plays an important role in prognosis along with tumor stage ,48,49,50The BCLC staging system was originally developed for the stratification of patients with cirrhosis and HCC with their respective treatment recommendations, and is now also applied in patients without cirrhosis  58]. Al. Al58]. The three curative-intent treatment modalities are resection, transplant, and local ablation, and should be utilized whenever feasible . The decSurgical resection is the treatment of choice in non-cirrhotic patients with a non-fibrotic liver, no underlying hepatitis, and no vascular invasion . EASL anLiver transplantation (LT) is indicated for patients who are not candidates for surgical resection but are within the Milan criteria. The Milan criteria were introduced after a 1996 study defined selection criteria for transplant patients that led to superior survival, and it has since become the standard of care for early HCC ,76. MacrLocoregional therapies are commonly used in the management of HCC, comprising treatment in 50–60% of cases. The goal of locoregional therapies is to reduce tumor viability, progression, and extend overall survival in patients with HCC . When HCOther methods take advantage of the hypervascularity of tumors and their unique reliance on blood supply from the hepatic artery, whereas hepatic parenchyma blood supply is largely from the portal vein, allowing transarterial therapies to be target selective . TransarThe advent of novel agents for systemic therapy in HCC gives promise to treatment in advanced stages of disease . In 2007Neoadjuvant therapies involve local or systemic treatment applied prior to the surgical treatment of HCC to prevent dropouts during LT waiting periods, to shrink tumors to meet LT criteria, to increase the liver resection rates, and to prevent recurrence . This thThere is no currently approved adjuvant therapy after curative-intent treatment for HCC. The efforts to find an adjuvant therapy to reduce the risk of recurrence and prolong survival are still ongoing but none have been significant enough to be implemented in the guidelines. Interferon was tested as an adjuvant therapy in viral-related HCC in the Asian population with promising results showing a survival benefit and reduced recurrence rate when compared to controls ,156. TheThe significant role of locoregional therapies in the treatment of HCC requires a method of determining the response of disease to treatment . The WorEarly detection followed by surgical resection or transplant offers the best outcomes for patients with HCC. The implementation and execution of surveillance programs are crucial to detect HCC before advanced stages of the disease. For intermediate HCC, locoregional therapies such as TACE or TARE allow for targeted treatment of the lesion without systemic side effects. Systemic therapies are reserved for the cases of advanced unresectable HCC. Combined approaches are a more recent addition to the treatment of HCC as are neoadjuvant and adjuvant therapies, which allow downstaging of the disease prior to transplant or resection and help to prevent recurrence.


This article introduces the main mechanisms of friction noise generated by submarine rubber-based propeller bearings and analyzes their respective scope of application and limitations. Then, the research on suppressing friction noise through the optimization of the structure and improvement of materials of rubber-based propeller bearings is discussed. Finally, the article summarizes a promising research direction aimed at eliminating friction noise in submarine rubber-based propeller bearings. By improving the structure and materials, the friction noise of propeller bearings can be effectively suppressed, thereby improving the deterrence and stealth performance of submarines. Submarines possess extremely strong stealth and assault capabilities and are recognized as one of the most intimidating and aggressive weapons. All major maritime nations are committed to developing submarines. As shown in However, rubber-based propeller bearings still have problems, such as the production of abnormal friction noise during start-up and shut-down, during low-speed and heavy-load operation, or poor lubrication. Once there is abnormal friction noise in the submarine propeller bearing, the submarine’s noise level will suddenly increase, greatly weakening the submarine’s stealth capabilities, reducing its deterrence, and even posing a serious threat to the submarine’s survival. To eliminate the friction noise of submarine rubber-based propeller bearings, many scholars have investigated the mechanism and suppression methods of friction noise.After decades of research and experimentation following the end of World War II, the U.S. Navy resolved many key technical problems of rubber bearings, such as their material, structure, and lubrication theory. In addition to the United States, countries such as Russia, the United Kingdom, Germany, Japan, Canada, and China have also been conducting in-depth research on noise-reduction technology for submarine propeller bearings. Regarding the friction noise of submarine rubber-based propeller bearings, a large number of research results has been obtained, but due to the complexity of the problem, most of the issues remain in the research stage. This article first discusses the mechanism of friction noise generation in submarine rubber-based propeller bearings, then introduces noise-suppression methods, and finally summarizes and suggests directions for further research on friction noise in submarine rubber-based propeller bearings.The approximate process of vibration generated by friction is shown in Stick-slip occurs between two elastic surfaces that are sliding relative to each other. The motion is usually not continuous but intermittent, with a sawtooth waveform for the variation of the FF. It is generally believed that the stick-slip mechanism is caused by the static FC being greater than the dynamic FC. Sinclair et al.  proposedd et al.  proposedBhushan  investigYao et al.  proposedMeziane  proposedStick-slip motion usually occurs under working conditions that are less than ideal, such as low speed and poor lubrication. Typically, every friction system has a critical relative sliding velocity, and stick-slip motion disappears when the actual relative sliding velocity exceeds the critical value. However, experiments have shown that for high-frequency noise, the location of noise generation does not coincide with the location of stick-slip motion. In practice, high-frequency friction noise usually occurs when the relative sliding velocity is high, which contradicts the concept of the critical velocity of stick-slip motion. Therefore, the mechanism of stick-slip motion cannot reasonably explain the phenomenon of high-frequency friction noise.The theory of sprag-slip was proposed by Spurr in 1961 . Its basThe simplified model of the sprag-slip mechanism is shown in In Equation (1), As can be seen from Equation (2), when Sprag-slip is a type of low-frequency self-excited vibration caused by friction. When the contact state is in a certain specific situation, the FF at the contact interface increases rapidly, causing the relative motion between the friction pair to stop and resulting in a self-locking phenomenon. The theoretical foundation of the sprag-slip mechanism is weak, and many friction noise phenomena cannot be reasonably explained by this theory. An example is friction noise, which often occurs in places where the FC is relatively large. In such a case, there is often vibration not only along the friction direction but also perpendicular to the friction direction . Therefore, this theory is relatively less accepted.Under insufficient lubrication, such as mixed lubrication, boundary lubrication, and even dry friction states, with the increase in relative sliding velocity between the friction pair, the FF between the two sliding surfaces decreases, and vibration often occurs during this sliding process, resulting in noise. The relationship between FC and relative sliding velocity is shown in For a single-degree-of-freedom friction vibration system under the action of negative slope FC, as shown in In Equation (3), Perform Taylor expansion on the expression of the FF:If it is a small-amplitude vibration, higher-order terms can be neglected, and by substituting into the equation, we obtain the following:Let Let Solving the equation, we obtain the following:When the slope of the Krauter  conducteThe theory of negative friction–velocity slope mechanism has been widely accepted in the academic community. However, this theory cannot explain many friction noise phenomena, such as the friction noise sometimes appearing in regions where the slope of the friction–relative sliding velocity is non-negative. In addition, this theory is based on a simple external characteristic model and seriously neglects the stochasticity and temporal variation of friction characteristics. Therefore, it can neither fully explain the complex structure and friction characteristics of brake squeal phenomena nor meet the requirements of design and prediction. Consequently, limitations persist when using this theory to explain the generation of friction noise.Modal coupling ,25 is onAs shown in Here, Now, assuming that the above system is subjected to excitation forces The system neglects its own damping and adopts a displacement-controlled force. Substituting it into Equation (9), we obtain the motion equation of the system:To summarize,Assuming To determine the stability of the system, suppose the general solution of the equation is The condition for the above system of equations to have a non-zero solution is given:Expanding further, we obtain the following:Suppose This equation is called the characteristic equation. Solving for it using Equation (18), we obtain the following:Equation (19) has four roots, which determine the stability and degree of stability of the system.Let When When When Taking the square root of both sides, we obtain the following:In Equations (20) and (21), A, B, C, and D in the equation above are determined by the initial conditions of the system. The first two terms are self-excited vibration terms. Over time, the self-excited vibration terms will tend toward infinity, indicating that the system is unstable. This is the explanation of the modal coupling theory.The coefficients Mihajlovic et al.  analyzedIn addition, deformable bodies have several modal shapes, each with its own frequency. When friction occurs on the surface of an object, coupling phenomena can lead to structural instability, and modes with similar frequencies can couple and produce friction noise at that frequency. However, not all modes with similar frequencies will produce this noise, so this is merely a method for predicting friction noise. Moreover, this theory is based on certain assumptions and special conditions, and it does not take into account nonlinear factors such as the characteristics of the friction interface, which affects friction noise. Therefore, the modal coupling theory can only serve as a linear theory method in the frequency domain, and it cannot analyze time–domain signals or contact behavior of the system during friction motion, which means it offers little help in explaining the underlying mechanism of squealing.There are many factors that can cause friction noise in the shaft and propeller bearing, such as water temperature, water quality, bearing structure, bearing materials, surface conditions of the shaft and bearing, alignment between the shaft and bearing, and so on. To suppress abnormal noise in submarine rubber-based propeller bearings, many scholars have conducted related research. This article mainly discusses improvements in the structure and materials of rubber-based propeller bearings.Optimizing the bearing structure and improving the contact state of the bearing surface can enhance the surface lubrication characteristics of the bearing, thereby reducing the generation of abnormal friction noise.Daugherty et al.  investigZhou  analyzedZhou et al.  studied Since the 1960s, the development of the propeller bearing structure on U.S. nuclear submarines has gone through three stages. The first stage used metal-backed strip bearings under the MIL-B-17901A standard ,38, and In recent years, scholars have found that the FC is not necessarily smaller when the surface is smoother. When the friction pair surface presents a certain structure, it has stronger wear resistance and lower surface FC instead ,42,43. BWhen rubber-based propeller bearings are under low-speed and heavy-load conditions, it is difficult for the bearing surface to form hydrodynamic lubrication, and boundary lubrication exists on the friction interface, which can easily generate friction noise. By introducing hydrostatic lubrication in the contact area, the surface lubrication performance of the bearing can be improved. Hydrostatic lubrication does not require relative motion between the journal and the bearing surface but rather only for lubricating fluid to be pumped into the bearing clearance at a certain pressure to separate the journal from the bearing forcing hydrostatic lubrication.For hydrostatically lubricated bearings, hydrostatic lubrication is achieved mainly by opening a cavity structure on the bearing surface. Narendra et al.  studied Due to the gravity of the propeller, the local specific pressure of the propeller bearing is relatively high. In order to reduce the local specific pressure and suppress the generation of friction noise, Li et al.  designedFor some time, a large number of scholars have been committed to developing rubber-based propeller bearing materials with excellent friction and wear performance and low noise. Currently, the main methods for suppressing the frictions and vibration from rubber-based materials include changing the material hardness, surface treatment, and filling reinforcement, imparting self-lubricating properties, and improving hydrophilicity.The hardness of the rubber strip can have an impact on the friction noise of propeller bearing. Bhushan et al.  investigSurface treatment is a method of depositing materials with excellent friction performance on the surface of rubber or altering the surface morphology of rubber through chemical means. This can help avert direct contact between the rubber and the friction pair to a certain extent, effectively improving the friction and wear performance of the rubber. Common coating materials include polytetrafluoroethylene (PTFE), diamond-like carbon (DLC), and silicon nitride. Jiang et al.  used eleFilling reinforcement is a method of improving the mechanical properties of composite materials by adding fillers to achieve the purpose of improving rubber friction and wear performance. Commonly used reinforcing fillers include zinc oxide , carbon Introducing solid lubricants with low FC into rubber can give the rubber materials self-lubricating properties. This is because as the composite material wears, the solid lubricant gradually appears and forms a lubricating layer on the worn surface, to a certain extent, avoiding direct contact between the rubber and the friction pair, thereby improving the friction and wear performance of the composite material. Some commonly used solid lubricants with excellent performance include graphite, graphene, PTFE, and molybdenum disulfide. Adding a single self-lubricating material alone may not significantly improve the friction or wear performance of the rubber, so two or more self-lubricating materials are often added at the same time, and some self-lubricating materials also have a synergistic effect when added simultaneously.Wang et al.  inventedSome self-lubricating materials have excellent properties themselves, but due to their poor dispersibility in the NBR matrix, their excellent properties cannot be fully realized, such as graphene and CNTs with a high specific surface area. Jia et al.  used solThe degree of difficulty for the formation of the lubricating water film between the stern shaft and the bearing is a key factor affecting the FC between them during start/stop and low-speed conditions. Improving the hydrophilicity of the surface of the rubber-based composite material makes it easier for the bearing and the friction pair to form lubricating water film, which can reduce the FC and friction noise of the rubber-based propeller bearing under start/stop and low-speed conditions. He et al.  proposedRubber-based propeller bearings are widely used in the submarine field due to their many advantages. However, the drawback is that abnormal friction noise can occur during start-up, shut-down, low speed, heavy load, and poor lubrication. In order to suppress the friction noise of submarine rubber-based propeller bearings, many scholars have conducted research on the friction noise mechanism of rubber-based propeller bearings and have successfully suppressed the friction noise by optimizing the bearing structure and improving the bearing material.The currently matured noise mechanisms include mainly the stick-slip mechanism, the sprag-slip mechanism, the negative friction–velocity slope mechanism, and the modal coupling mechanism. Each mechanism has a complete theoretical system, and the various theories are closely related, but they also have significant differences due to the assorted research objects. In the research field of friction noise from submarine rubber-based propeller bearings, directly adopting a certain mechanism cannot comprehensively explain how friction noise is generated. Therefore, in such research, it is necessary to fully consider all aspects of the actual situation of the friction system to explain the generation mechanism of different friction noises. Then, according to the specific generation mechanism of different friction noises, researchers can optimize the bearing structure and improve the bearing materials to achieve sufficient friction noise suppression.Connect the research on the friction noise mechanism of propeller bearings with the molecular structure of materials to explore the relationship between composite material properties and friction noise at the molecular level;Study the relationships among contact interface micro-asperities, impurities in lubricating water, and friction noise;Study the mechanism of abnormal friction noise of propeller bearings under fluid–solid–heat multi-field coupling and multi-boundary conditions;Research real-time monitoring technology for propeller bearing load distribution, wear status, and friction noise as well as design composite intelligent bearings and develop real-time monitoring and warning diagnostics for the state of propeller bearing;Carry out research on the structural design and control technology of permanent magnet–electromagnetic bearings.To further eliminate the friction noise of submarine rubber-based propeller bearings, it is suggested to conduct research in the following five areas:Eliminating friction noise of submarine propeller bearings is of great significance for improving the stealth performance of submarines. With continuous deepening of research, mankind will eventually develop virtually silent submarine propeller bearing.


Abnormal retro patellar stress is believed to contribute to patellofemoral complications after total knee arthroplasty (TKA), but the causal link between TKA and patellofemoral contact stress remains unclear. By reviewing the relevant studies, we found that both TKA implantation and additional patellar resurfacing increase retro patellar pressure. The rotation and size of the femoral component, thickness and position of the patellar component, installation of the tibial component, prosthesis design and soft tissue balance further influence patellofemoral stress. Specific measures can be applied to reduce stress, including the installation of the femoral prosthesis with an appropriate external rotation angle, placing the tibial component at a more posterior position and the patellar button at a more medial position, avoiding over-sized femoral and patellar components, selecting posterior-stabilized design rather than cruciate-retaining design, using gender-specific prosthesis or mobile-bearing TKA system, and releasing the lateral retinaculum or performing partial lateral facetectomy. Despite these measures, the principle of individualization should be followed to optimize the patellofemoral biomechanics. Total knee arthroplasty (TKA) is becoming an increasingly common procedure for severe knee diseases. Although both the surgical technique and the patient satisfaction rate have been improving in recent decades, some patients still developed patellofemoral complications following TKA, such as persisting anterior knee pain, patellar subluxation or dislocation, patellar component wear or loosening, and even patella fracture –3. The iPatellofemoral contact force, area, and pressure are the biomechanical parameters of the patellofemoral joint, and the pressure is defined as the patellofemoral reaction force divided by the contact area between the patella and the surface of the trochlea . PreviouWe reviewed the consistently reported factors in TKA affecting the patellofemoral contact force, area, and pressure, with the aim of providing information for individualized osteotomy and prosthesis installation in TKA and for the diagnosis and treatment of patellofemoral joint complications following TKA.As the largest sesamoid bone, the patella functions to force the extensor muscles away from the rotational center of the knee, so as to increase the lever arm of the quadriceps, rendering knee extension more effective , 21  increases the outward tension applied to the patella, resulting in greater stress on the lateral patellofemoral joint than on the medial facet . In addiRollback of the femoral condyles on the tibial plateau with knee flexion is one of the characteristic features of normal knee kinematics, and is largely attributed to the increasing tension of the posterior cruciate ligament (PCL) during flexion . The ranTKA reduces the patellofemoral contact area and elevates the pressure, compared with the normal knee, resulting from the lowered congruence between the femoral and patellar components after TKA , 29, 30.Malrotation of the femoral component could contribute to anterior knee pain and accelerate the wear of the patellar component . Some auAlthough higher medial stress is induced by external rotation of the femoral component, easing the lateral force benefits patients , which mOf note, for the TKA with the patella resurfacing, although the average retro patellar pressure reported in some studies was not up to 20 MPa, malrotation of the femoral component aggravated the malalignment between the patellar button and trochlear groove prosthesis, with the pressure on certain contact points even exceeding the yield stress of ultra-high molecular weight polyethylene (UHMWPE), which exacerbated the wear of the patellar component . MoreoveIn TKA, the osteotomy amount of femoral condyles and the size of the femoral prosthesis affect the patellofemoral stress as well. Inadequate cutting of the anterior femur  or upsized femoral component causes overfilling of the patellofemoral joint, increasing the tension within the patellar tendon and the retro patellar contact force , 17, 36.A common issue in TKA, namely, the decision on whether to resurface the patella, remains controversial , 25. Xu For TKA with patella resurfacing, the thickness of the patellar button is the focus of attention. Similar to the impact of femoral component size on patellofemoral stress, a thicker patellar button is expected to lead to patellofemoral overfilling, flexion deficit, and higher patellar tendon tension and retro patellar force. On the other hand, excessive osteotomy is often needed to obtain a smaller overall patellar thickness. It effectively reduces the patellofemoral force, but puts the patella at a greater risk of stress fracture, with increased postoperative complications such as extension weakness and patellar instability , 41. TanThe geometry of the patellar facet varies with populations. In an in vivo study on TKA with patellar resurfacing performed on 129 knees, Assi et al.  found thWith patella-retaining TKA, scholars tend to reduce or even cut thin the patella besides removing the peripatellar osteophytes. Similar to the effect of the thickness of the patellar button, this operation contributed to a more friendly retro patellar pressure, in theory, despite the lack of support by relevant studies. Meanwhile, reconstructing a more medial highest point of the native patella seems to reduce the already greater pressure of the lateral patellofemoral joint. However, Senioris et al.  noted thCompared with the general location of the tibial component in TKA, its anterior displacement increases the patellofemoral force, while its retrodisplacement unloads the patellofemoral joint , 51. On As to whether and how the rotation of the tibial component affects patellofemoral stress, no reports are available to date. However, in an in vivo study, Nicoll and Rowley  stated tTo date, a wide array of prostheses have been available for TKA, with different sagittal radii, depths and orientations of the trochlear groove of the femur as well as the geometry of the patellar component surface in the patellofemoral design . The impThe selection of tibiofemoral implants also influences the patellofemoral biomechanics. A few studies believed that after implantation of the PS prosthesis, average patellofemoral contact force and pressure were significantly lower in comparison to the posterior CR design , 14, 21.In TKA, the mobile-bearing design showed evidently lower patellofemoral contact stress than its fixed-bearing counterpart , 60. ThiIntraoperative soft tissue balance also influences retro patellar stress . For insFor patients with patellar instability, the lateral retinaculum release is a common surgical technique. It has been proven that lateral retinaculum release was able to decrease the retro patellar contact force and pressure , 62, 63,In addition, lateral facetectomy can reduce patellofemoral contact pressure in non-patella-resurfacing TKA by improving the alignment between the native patella and trochlear groove prosthesis . LaksteiDespite numerous approaches available to reduce patellofemoral stress, not all are applicable to specific individuals, and the appropriate strategies should be used. For instance, for patients with dysplasia of the distal femur , increasing the external rotation angle properly during osteotomy might be a better choice to improve patellofemoral biomechanics. One example is that, for a patient with preoperative patellar maltracking, the surgeon could balance the soft tissues around the patella  to optimize patellar movement patterns and decrease retro patellar stress. Additionally, it is necessary to combine two or more methods to achieve the goal at times. At present, however, literature remains scanty on individualized treatments, and further researches are urgently needed.Both TKA implantation and additional patellar resurfacing significantly influence retro patellar pressure. The rotation and size of the femoral component, thickness and position of the patellar component, installation of the tibial component, prosthesis design, and soft tissue balance further affect patellofemoral stress. Specific measures can be applied to reduce stress, including the installation of the femoral prosthesis with an appropriate external rotation angle , placing the tibial component at a more posterior position and the patellar button at a more medial position, avoiding over-sized femoral and patellar components, selecting PS design rather than CR design, using gender-specific prosthesis or mobile-bearing TKA system, and releasing the lateral retinaculum or performing partial lateral facetectomy. Despite these alternatives, an individualization principle should be followed to optimize the patellofemoral biomechanics. Additionally, most of the previous studies on patellofemoral stress were in vitro studies or finite element model analysis, lacking direct evidence of the relationship between abnormal retro patellar stress and postoperative complications. Therefore, it will be valuable to investigate the patellofemoral stress during TKA with subsequent follow-up of patellofemoral joint complications such as anterior knee pain after TKA, which will contribute to the improvement of its clinical results.


In recent decades, vaccines have been extraordinary resources to prevent pathogen diffusion and cancer. Even if they can be formed by a single antigen, the addition of one or more adjuvants represents the key to enhance the response of the immune signal to the antigen, thus accelerating and increasing the duration and the potency of the protective effect. Their use is of particular importance for vulnerable populations, such as the elderly or immunocompromised people. Despite their importance, only in the last forty years has the search for novel adjuvants increased, with the discovery of novel classes of immune potentiators and immunomodulators. Due to the complexity of the cascades involved in immune signal activation, their mechanism of action remains poorly understood, even if significant discovery has been recently made thanks to recombinant technology and metabolomics. This review focuses on the classes of adjuvants under research, recent mechanism of action studies, as well as nanodelivery systems and novel classes of adjuvants that can be chemically manipulated to create novel small molecule adjuvants. The use of adjuvants in vaccine development takes advantage of the many benefits these substances can offer, such as reducing the amount of antigen required for each vaccination dose and the frequency of booster vaccinations or improving the stability of the antigen component by lengthening its half-life and, consequently, enhancing its immunogenicity antigens .Escherichia coli, yeasts (Saccharomyces cerevisiae and Pichia pastoris), Baculovirus, mammalian cells, plant cells, or cell-free systems [Virus-like particles (VLPs) are icosahedral nanoparticles of similar size to viruses (ranging from 20 to 800 nm) , which p systems . The his systems . Another systems ,208. In  systems ,210,211. systems .Saccharomyces cerevisiae is the vector currently employed for the expression of L1 proteins. The combination of VLPs and adjuvants (AlP) results in a strong immune response and 90% protection from cervical cancer [In the HPV vaccine, instead, non-enveloped HPV virions contain double-stranded DNA (dsDNA). The L1 and L2 proteins compose the major and minor structural proteins of the capsid, which has icosahedral symmetry . Saccharl cancer .Virosome is a drug-delivery system that consists of the viral envelope and components of the virus or another pathogen. They are formed by reconstituted influenza virus envelopes and contain hemagglutinin (HA), neuroamidase (NA), and phospholipids and they are lacking viral genetic material, such as VLPs . The firThe presence of HA in the virosome structure allows the maintaining of the receptor-binding capability, increasing the immunogenicity, and membrane fusion activity, but virosomes cannot induce infection in cell after binding because of the lack of viral RNA . AntigenAs listed before, novel classes of immune-activating adjuvants have been discovered in the last 20 years, able to boost immune response in fragile populations such as immunocompromised and elderly people. Several classes of adjuvants are available, each of them with its own strengths and weaknesses. Delivery systems such as oil-in-water emulsions are effective and safe systems, nevertheless, suffer from the possibility to create local or systemic adverse effects. Recent studies demonstrate that PRR signaling can be altered in several populations, reducing the protective effect of vaccine formulation. As an example, the immunological mechanisms that prevent fetal rejection as well as the dysregulation of TLR pathway in elderly people or the presence of genetic polymorphisms . For allAdjuvants are a large family of key components of vaccine formulations. Their use has been fundamental during the most important vaccination campaigns of history, including Polio, swine flu, and the last COVID-19 pandemic. Even if good results have been already obtained, other efforts are fundamental to increase vaccine protection against resistant viruses and reduce the necessity of additional booster shots. Recombinant technology, DNA screening, and bioinformatic research have clarified novel mechanisms of action and key players of the immune signaling pathways. Other efforts are necessary to identify more potent adjuvants able to counteract future pandemics and increase the chance of success against cancer.