Based on the theory of acoustic waves, a circular surface radiator model is introduced as a basis for constructing a knowledge transfer model for a knowledge alliance. The three main variables in the model are chosen to be the number of enterprises in knowledge alliance, the frequency of knowledge transfer, and the relationship distances between the knowledge bodies. The internal mechanism of knowledge transfer in a knowledge alliance is studied, and the direct relationships among the internal influencing factors are explored. The results show that the number of enterprises in knowledge alliance, knowledge transfer frequency, and knowledge transfer effect are positively correlated. The “Rayleigh distance” in the knowledge field is the appropriate relationship distance measure for assessing knowledge transfer within the alliance. The Rayleigh distance is highly correlated with the number of enterprises in knowledge alliance and knowledge transfer frequency. Moreover, the number of enterprises in knowledge alliance and knowledge transfer frequency are interrelated.
With the advent of the knowledge economy era, knowledge resources have replaced traditional resources such as capital and land as the most valuable strategic resources for enterprises. Through the absorption and application of knowledge resources, enterprises can produce new products on the basis of newly developed technologies to ensure core competitiveness. With the rapid growth and evolution of the R&D costs for technology, enterprises have difficulty in achieving all of their resource development needs alone. An increasing number of enterprises are recognizing that building knowledge alliances with other enterprises can enhance each individual enterprise’s core competencies and help to sustain its long-term competitive advantage. By this means, enterprises can integrate complementary knowledge resources through communication, acquire key technical resources, and then generate new knowledge and integrate existing knowledge [
The definition of a knowledge alliance proposed by Inkpen in 1995 is still used today. He believed that a knowledge alliance is a kind of strategic alliance that creates valuable new knowledge through knowledge transfer and knowledge integration. On the basis of Inkpen’
In the process of establishing knowledge alliances to acquire knowledge to enhance core competitiveness, there are many factors that affect knowledge transfer both inside and outside an organization. Many scholars have conducted in-depth research on this topic that has yielded rich research results [
In summary, a great deal of research has been conducted on the characteristics of knowledge alliances and the motivation for their formation, the factors affecting knowledge transfer, and the mechanism and performance of knowledge transfer in knowledge alliances, and this research has yielded meaningful conclusions. The process of knowledge transfer is complicated, and it is difficult to explore the complex interactions among many influencing factors. Using theories and models of other disciplines to build metaphor models can provide new methods and inspiration for dealing with complex system problems, but the current research on knowledge transfer using metaphor research methods is rare. In addition, the current research has not paid sufficient attention to the influence of the number of enterprises within a knowledge alliance, and models are unlikely to consider multiple directions and angles in the process of knowledge transfer.
The process of knowledge transfer is affected by many factors. This paper mainly studies the influencing factors on the process of knowledge transfer from three aspects: the transfer subject dimension, the transfer behaviour dimension, and the transfer context dimension. Other influencing factors are interrelated and implicit with the three dimensions. The number of enterprises in knowledge alliance is the representation of the transfer subject dimension. Factors such as the amount of knowledge in the alliance, the level of knowledge recognition, and the complexity of the alliance relationship are all related to it. The frequency of knowledge transfer is a representation of the transfer behaviour dimension. The speed of knowledge transfer is related to the connection frequency among enterprises, and the willingness of knowledge transfer will also affect the frequency of knowledge transfer. Relationship distance is a representation of the transfer context dimension, which describes the objective state of the relationship between the subjects of knowledge transfer. The distance of the relationship also affects the methods adopted by enterprises in the transfer process, such as commissioned research, consulting, or professional meetings. At the same time, this paper uses a metaphorical research method to introduce a knowledge circular radiator model in acoustics. Besides the similarity between the research subject and the metaphorical model, the similarity between the metaphorical variables and the variables in the model should also be guaranteed. The size of sound source, the frequency of sound emission, and the distance are, respectively, metaphorized as the number of enterprises in the knowledge alliance, the frequency of knowledge transfer, and the distance of relationship, which is reasonable in physical hypothesis and metaphorical logic.
The knowledge transfer process in knowledge alliance is complicated, and the knowledge transfer system is a complex system. Each element in a complex system is interrelated and interdependent. According to the viewpoint of system science, the complex system can be simplified by abstracting the complex system and extracting the key elements in the system. Studying complex systems with the help of models from other disciplines helps to find the complex correlations among influencing factors, as well as the underlying laws in the system. This paper mainly studies the influencing factors on the process of knowledge transfer from three aspects: the transfer subject dimension, the transfer behaviour dimension, and the transfer context dimension. Through the application of metaphor and acoustic model, the knowledge transfer problem is abstracted into three dimensions of variables.
Complexity science mainly focuses on the complexity phenomenon and its evolution of research objects. By exploring the commonalities of complex phenomena such as nature, society, organization, thinking, and cognition, it helps people to understand various complex phenomena more comprehensively and manage them accurately. Complexity is an objective reality. Scholars have different definitions of complexity, but their understanding of the connotation of complex systems is similar. Complexity systems are characterized by diversity, hierarchy, nonlinearity, and openness [
Metaphor is a common research approach in scientific fields of complexity. This approach can transform complex systems, through simile or analogy, into intuitive concepts expressed in simple language [
Metaphor-based scientific modelling is based on an analogy between the model and the target object. By seeking commonalities in terms of physical properties, a real physical model can be applied to better understand another real system [
First, let us consider the feature mapping between knowledge transfer in a knowledge alliance and acoustic wave transfer in an acoustic medium. Both knowledge and acoustic waves are transitive. The transmission of both knowledge and acoustic waves involves senders and receivers, and the transmitted knowledge or acoustic waves must be consistent with the receivers' capabilities. In the case of knowledge transfer in a knowledge alliance, there may be multiple knowledge senders simultaneously transferring knowledge, resulting in a superposition of knowledge transfer for a single knowledge receiving enterprise; acoustic wave transfer also has the same characteristics. The process of knowledge transfer is affected by many factors. Knowledge cannot be transmitted to a knowledge receiving enterprise completely and without distortion. Similarly, acoustic wave transfer is also subject to interference from noise. The acoustic signal received by a receiving source may be partially lost, causing attenuation during transmission.
Second, let us consider the structural mapping between knowledge transfer in a knowledge alliance and acoustic wave transfer in an acoustic medium. In the theory of acoustic waves, the vibration of a sound source is the source of acoustic waves. In the case of knowledge transfer in a knowledge alliance, a knowledge source possessing relevant knowledge is also continuously transmitting knowledge. The knowledge transfer process can be understood as a process in which a knowledge-sending enterprise continuously generates knowledge waves through constant vibration and continuously influences one or more knowledge receiving enterprises in the form of waves. In a knowledge alliance, a knowledge-sending enterprise sends knowledge waves to the knowledge receiving enterprises in the surrounding space. Similarly, a sound source also sends acoustic waves out into its surroundings. Both scenarios are consistent with the concept of a “field” [
From the above analogy between knowledge transfer and acoustic wave transmission, it can be seen that they have many similarities. Therefore, it is scientific and reasonable to use the theory of acoustic waves to construct a knowledge transfer model by mapping the concepts and research methods of acoustic wave theory to the case of knowledge transfer in knowledge alliances. The remainder of this paper will describe a metaphor model for knowledge transfer in knowledge alliances based on a circular radiator model from acoustic wave theory. The process of knowledge transfer in a knowledge alliance is a process by which a knowledge source spreads knowledge waves to surrounding target enterprises and the knowledge receiving enterprises receive and absorb these knowledge waves [
Relationship diagram of core/noncore knowledge and knowledge receiving enterprises in a knowledge alliance. 1, core knowledge; 2, noncore knowledge; 3, knowledge receiving enterprise.
As discussed in the previous section, it is reasonable and feasible to introduce a circular radiator model into research on knowledge transfer in knowledge alliances. In this section, a knowledge transfer model for a knowledge alliance is constructed using this circular radiator model, and the parameters and concepts of acoustics waves theory are introduced to explore the internal mechanism of knowledge transfer. The constructed model is called the circular knowledge radiator model. It is assumed that each point on the circular knowledge radiator is a related knowledge body involved in the knowledge transfer process and that these bodies transfer knowledge to knowledge receiving enterprises. In accordance with the principle of the superposition of waves, the knowledge wave received at the point corresponding to a knowledge receiving enterprise is a superposition of the knowledge transferred from each knowledge body in the circular knowledge radiator to the knowledge receiving enterprise.
If we wish to consider the influence of the circular knowledge radiator on any point in the knowledge field, we need to establish a spherical coordinate system with its origin at the centre of the circular knowledge radiator. This system is represented by the spherical coordinates
Coordinate frame for a circular knowledge radiator.
A polar coordinate system
Polar coordinate frame on the circular knowledge radiator.
In the circular radiator model, the function describing the sound pressure amplitude distribution at any point in the sound field can be obtained from the velocity potential of the sound source. The sound pressure amplitude reflects the intensity of the sound field at a certain point. When mapped to the case of knowledge transfer in a knowledge alliance, this amplitude can be understood as the influence of the knowledge source at a certain point in the knowledge field.
The velocity potential of a circular knowledge radiator is known to be
Thus, according to
The knowledge wave number is an important concept. Based on the knowledge wave number, we can obtain many variables related to knowledge wave transfer to characterize the specific knowledge transfer situation, such as the knowledge wave frequency
From formula (
It can be found that formula (
Coordinate frame for the circular knowledge radiator model.
The velocity potential function in the knowledge field is known to be
From formula (
The influence on knowledge transfer within the knowledge field is equivalent to the knowledge waves. With a continuous cyclical variation over time, the influence amplitude
This function shows that the distribution function
The relationship distance reflects the relationship state of knowledge transfer subject in the process of knowledge transfer, and the relationship distance from near to far represents the state of knowledge transfer subject from intimacy to alienation. Although the relationship distance reflects a kind of gradual change, this paper uses the phased description method in the description.
When the relationship distance is close in the process of knowledge transfer, this paper holds the opinion that the subject of knowledge transfer adopts a relatively intimate transfer method, such as face-to-face teaching, commissioned research, and consultation, which is called intimate knowledge transfer. When the relationship distance is moderate in the process of knowledge transfer, this paper holds the opinion that the subject of knowledge transfer adopts a relatively stable but not very intimate transfer method, such as knowledge transfer through the Internet, personnel exchanges, professional meetings, and the establishment of research centres, which is called stable and moderate intimate knowledge transfer. When the relationship distance is far away from each other in the process of knowledge transfer, this paper holds the opinion that the degree of connection between knowledge transfer subjects is very poor. Knowledge exchange between enterprises is rare, and it is generally difficult to achieve a good knowledge transfer effect.
The knowledge wave number and knowledge wave transfer frequency can be replaced by constants (see the appendix for details). The knowledge wave number reflects the speed at which the knowledge alliance transmits knowledge waves, that is, the amount of knowledge transferred per unit time. The faster the alliance delivers knowledge, the greater the knowledge wave number. In order to facilitate discussion and understanding, in the following discussion, knowledge transfer frequency will be used to reflect the change in knowledge wave number. The radius of the circular knowledge radiator reflects the number of knowledge subjects participating in knowledge transfer in the knowledge alliance. The larger the volume of knowledge involved in knowledge transfer is, the larger the radius of the circular knowledge radiator is. Under normal circumstances, the volume of knowledge involved in knowledge transfer has a positive linear relationship with the number of knowledge sending enterprises participating in knowledge transfer. As the number of enterprises in a knowledge alliance increases, the volume of available knowledge increases. Because the knowledge volume is difficult to quantify, this paper uses the number of enterprises in the knowledge alliance instead of the knowledge volume for model construction. Different enterprises have different understanding of the same knowledge. In the process of knowledge transfer within knowledge alliance, the overlapping knowledge of all members constitutes the knowledge understanding of the alliance. The more the members the alliance have, the greater the “broadness” of knowledge will be involved in knowledge transfer.
Matlab programming was used to implement the function describing the relationship between the knowledge transfer effect of the circular knowledge radiator and the relationship distance between enterprises and to carry out a corresponding simulation analysis.
By analysing three different situations regarding the number of enterprises participating in the knowledge alliance and the frequency of knowledge transfer, the knowledge transfer process at different relationship distances will be investigated here to characterize the relationship between relationship distance and knowledge influence. For the simulations, the dimensions of the knowledge transfer frequency and the number of knowledge alliance enterprises are set to 1 to facilitate parameter setting.
To facilitate the discovery of the inherent laws relating the number of enterprises participating in the knowledge alliance, the frequency of knowledge transfer, and the distance of the relationships between the enterprises, a general knowledge alliance situation is first analysed. To represent a case in which the knowledge alliance is moderately sized and the knowledge transfer ability is also at a moderate level, the parameters are set to
Distribution of knowledge influence intensity in the knowledge field.
As shown in Figure
Based on the observed distribution pattern of the knowledge Rayleigh distance
Now, let us analyse the relationship between relationship distance and knowledge influence when the number of enterprises in the knowledge alliance is very small and the frequency of knowledge transfer is low. The relevant parameters are set to
Distribution of the influence in the knowledge field when the alliance is small and the transfer frequency is very low.
When the number of enterprises in the knowledge alliance is small, the amount of knowledge involved in the transfer is also small, the knowledge transfer speed is extremely slow, and the amount of knowledge that can be transferred simultaneously is naturally small. Figure
Figure
Finally, the relationship between relationship distance and knowledge influence is analysed for a case in which the knowledge alliance is large and the relevant knowledge transfer efficiency is high. The relevant parameters are set to
Distribution of the influence amplitude in the knowledge field when the alliance is large and the transfer efficiency is high.
When the knowledge alliance is large and the knowledge transfer frequency is high, the number of enterprises participating in the alliance is relatively large, the knowledge volume is also large, and the knowledge transfer is greater. In this case, the knowledge transfer capabilities of the knowledge alliances are strong, and the interaction with noncore knowledge is consequently exacerbated. Figure
This paper discusses the knowledge transfer performance of knowledge alliances when the number of enterprises and the frequency of knowledge transmission are moderate, low, and high. We find that the vicinity of the knowledge Rayleigh distance is a region with a good knowledge transfer effect and that the knowledge field can be divided into a near-field region and a far-field region based on the knowledge Rayleigh distance. The knowledge transfer process follows different rules in the near field and the far field. Knowledge transfer to the knowledge receiving enterprises in the near field is very unstable, whereas the knowledge influence in the far field is monotonically attenuated as the relationship distance increases. From a comparison of the three cases, it can be seen that when the number of enterprises and the frequency of knowledge transmission are greater, the knowledge Rayleigh distance is larger, and the influence of the knowledge alliance on the knowledge transfer to knowledge receiving enterprises varies more slowly in the far field.
In the previous section, we discussed three kinds of conventional knowledge alliances for which the number of enterprises and the frequency of knowledge transmission are moderate, low, and high and found that these alliances show different knowledge influence trends at different distances. Next, we will further discuss the impact of these two indicators (number of enterprises and frequency of knowledge transfer) on the knowledge transfer by evaluating the impact of changes in either
The results for
Distributions of the influence amplitude in the knowledge field when
Distributions of the influence amplitude in the knowledge field when
In other words, when the frequency of knowledge transfer becomes higher and the knowledge Rayleigh distance of knowledge transfer is larger, the knowledge alliance needs to maintain a more stable, relatively far relationship distance to ensure the best knowledge transfer effect. This is because when increasing frequency of knowledge transfer, the amount of knowledge transferred per unit time will increase. According to the theory of strong ties and weak ties, if the knowledge transfer enterprises keep strong association with each other, external factors will disturb the process of knowledge transfer, which is easy to cause deviation in knowledge content in knowledge transfer. Keeping weak association can produce better knowledge transfer effect.
When the number of enterprises in the knowledge alliance increases, the knowledge alliance needs to be stable, and a relatively far relationship distance can produce good knowledge transfer effect. This is because in the process of knowledge transfer, the larger the number of enterprises in the alliance, the more the level of knowledge will be. Receiving enterprises can deepen their understanding of knowledge by receiving different levels of knowledge, but they are also vulnerable to multi-level knowledge. When there are many members in the alliance, the knowledge receiving enterprise should keep a certain relationship distance with the knowledge sending enterprise. If the relationship distance is too close, knowledge will be accepted without hesitation, which may lead to the deviation and distortion of understanding due to the multilevel understanding of knowledge in the alliance. Only by keeping a certain distance and selectively accepting and integrating the received knowledge, can enterprises understand and absorb the multilevel knowledge objectively.
This is consistent with the view of knowledge network and technology innovation network. According to the knowledge network theory, the organizational scale of knowledge network can be regarded as the number of members in social network. There is a positive correlation between the number of enterprises in knowledge alliance and the complexity of the cooperation relationship among the members of knowledge alliance. The close relationship among enterprises will cause expensive communication costs, coordination costs, and supervision costs. According to the technological innovation network theory, maintaining a stable relationship within an organization helps to improve the efficiency of knowledge transfer and thus promote knowledge innovation. When the number of enterprises in knowledge alliance is large, it is difficult to maintain a stable intimate relationship, so it is better to keep the appropriate relationship distance when the organization scale is large.
This paper sets
This paper explores the specific impacts of these two influencing factors on knowledge transfer and the relationship between these two factors through an investigation of knowledge alliances with different numbers of participating enterprises and different frequencies of knowledge transfer. The number of enterprises and the frequency of knowledge transfer in a knowledge alliance are both important factors influencing knowledge transfer. The effects of these two influencing factors are similar. As the number of enterprises or the frequency of knowledge transfer increases, the instability of knowledge transfer in the near field increases. At the same time, the knowledge Rayleigh distance increases, and the rate of change in knowledge transfer in the far field slows down. These two influencing factors also mutually affect each other, with a change in one factor enhancing the effect of the other. However, the knowledge influence is more sensitive to changes in the number of enterprises, and correspondingly, the number of enterprises also exerts a more obvious effect on the influence of a change in the frequency of knowledge transfer.
In this paper, the theory of acoustic wave transfer is introduced, the circular knowledge radiator model is introduced as a model of knowledge transfer in a knowledge alliance, and the relationships among the factors affecting knowledge transfer are studied. Based on this research, the following conclusions can be drawn. First, the effect of knowledge transfer in a knowledge alliance is affected by the number of enterprises in the knowledge alliance, the frequency of knowledge transfer in the knowledge alliance, and the relationship distance between the knowledge sending enterprise and each knowledge receiving enterprise. These three influencing factors are interrelated and exert interdependent effects on knowledge transfer. Second, the knowledge field corresponding to knowledge transfer can be divided into a near-field region and a far-field region based on the knowledge Rayleigh distance. In the near field, the curve representing the knowledge influence amplitude shows more variation, whereas in the far field, the knowledge influence amplitude decreases monotonically with increasing distance. The vicinity of the knowledge Rayleigh distance is the region with the best knowledge transfer behaviour. The knowledge Rayleigh distance of a knowledge alliance is affected by the number of enterprises participating in the alliance and the frequency of knowledge transfer. Third, an increase in either the number of enterprises in the knowledge alliance or the frequency of knowledge transfer will cause the knowledge Rayleigh distance to increase. Additionally, the oscillation of the influence amplitude curve in the near field will increase, and the amplitude of the knowledge influence in the far field will decrease more gradually with distance. Therefore, ensuring a relatively large number of knowledge alliance members and a high knowledge transfer frequency is beneficial for adjusting the appropriate relationship distance to achieve a satisfactory knowledge transfer effect in a knowledge alliance. Fourth, compared with the frequency of knowledge transfer, the number of enterprises in the alliance has a more significant impact on knowledge transfer. Therefore, a reasonable grasp of the influence of the number of alliance members is the key to improving the efficiency of knowledge transfer.
The main insights of this paper are as follows: firstly, the simulation analysis found that the number of knowledge alliance enterprises and the frequency of knowledge transfer have mutual influence, and the impact on knowledge transfer is not independent. Secondly, when the number of enterprises and the frequency of knowledge transfer are large, knowledge alliance needs to maintain a stable and relatively intimate relationship distance. Finally, knowledge transfer in knowledge alliance has the best effect at the knowledge Rayleigh distance point.
The above conclusions have certain significance for guiding the development of alliance strategies for knowledge alliances and efforts to improve the knowledge transfer efficiency in knowledge alliances, as follows:
The main theoretical contributions of this paper are as follows: In the research field of strategic alliances and knowledge transfer [ When studying the partner matching of strategic alliance, most scholars emphasize the matching among members in structure, strategy, and culture [ In the research field of knowledge transfer, many literatures emphasized the relationship management among members of strategic alliances [
This paper uses the metaphor model to study knowledge transfer in knowledge alliance, which has certain theoretical and practical value. However, due to the limitations of the author's ability and time, there are still some shortcomings. On the one hand, this paper studies the interaction among the three influencing factors in the process of knowledge transfer. Other factors may also have an impact on knowledge transfer in knowledge alliance, such as the impact of policy factors and knowledge attributes in the process of knowledge transfer. On the other hand, the simulation method used in this paper is not combined with statistical data. The author will do more in-depth and detailed research in the future.
In addition, the author believes that this paper can provide reference for future research in the following three aspects: For the strategic alliances, knowledge transfer, and complexity science research, the use of metaphorical research methods can provide new research directions. In this paper, based on metaphor analysis, concepts and models in the theory of acoustic wave transfer are introduced into the research field of knowledge transfer, which has important implications to future research. This paper explores the influence of alliance characteristics and capabilities on the matching degree of partner selection in knowledge transfer and analyzes the role of the number of alliance enterprises in this process. It expands the research perspective of knowledge transfer. Based on this paper, researchers can do more in-depth research on the number of alliance enterprises. In this paper, the appropriate relationship distance among alliance members is connected on alliance characteristics and alliance capability dimensions, which expands the research paradigm of a single factor of knowledge transfer in knowledge alliance. In the research field of alliance relationship management, researchers can further consider the complex role of multiple factors.
Because
Thus, according to
The knowledge wave number is an important concept. Based on the knowledge wave number, the authors can obtain many variables related to knowledge wave transfer to characterize the specific knowledge transfer situation, such as the knowledge wave frequency
From formula (
Observing formula (
Coordinate frame for the circular knowledge radiator model.
The velocity potential function in the knowledge field is known to be
From formula (
It is worth noting that the influence on knowledge transfer within the knowledge field is equivalent to the knowledge waves. With a continuous cyclical variation over time, the influence amplitude
Distributions of the influence amplitude in the knowledge field when
Distributions of the influence amplitude in the knowledge field when
Similarly, the next step in exploring the influence of different
Distributions of the influence amplitude in the knowledge field when
Distributions of the influence amplitude in the knowledge field when
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (71774036), an MOE (Ministry of Education of China) Project of Humanities and Social Sciences (18YJC630245), the Social Science Foundation of Heilongjiang Province (17GLH21 and 18GLB023), and the Natural Science Foundation of Heilongjiang Province (QC2018088).