Research ArticleA New Model for Competitive Knowledge Diffusion inOrganization Based on the Statistical Thermodynamics

Ju-Yong Jong ,1,2 Wei-Wei Wu ,1 and Sung-Ryol So1,3

1School of Management, Harbin Institute of Technology, Harbin 150001, China2Department of Energy Science, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea3Institute of Advanced Science, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

Correspondence should be addressed to Wei-Wei Wu; wuweiwei@hit.edu.cn

Received 24 April 2019; Revised 16 July 2019; Accepted 6 August 2019; Published 21 March 2020

Academic Editor: Antonio Scarfone

Copyright © 2020 Ju-Yong Jong et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study, we have constructed a new model for competitive knowledge diffusion in organization based on the statisticalthermodynamics of physics. In order to achieve the purpose of research, we newly define the absorptive capacity coefficient, thecreativity ability coefficient, the depreciation coefficient of knowledge, the ambiguity coefficient of knowledge, and theknowledge affinity coefficient of organizational culture. And various knowledge quantities such as knowledge energy, knowledgetemperature, and diffusion coefficient for the knowledge diffusion equation were defined and simulations were carried out bythe lattice kinetic method. And, based on the new model, we have successfully studied the impact of the characteristics ofmembers, knowledge itself, and organizational culture on the diffusion of competitive knowledge. The results show that thediffusion velocity of knowledge in the organization increases as the knowledge absorbing ability of the members is larger, andthe ambiguity of knowledge has a negative impact on the diffusion of knowledge. The degree of knowledge affinity oforganizational culture is a decisive factor in the diffusion and accumulation of knowledge in the organization, and the culturalcharacteristics of the organization have a much greater influence on the diffusion of competitive knowledge than the personalcharacteristics of members. Therefore, the organization manager needs to pay more attention to building a better organizationalculture than improving personal characteristics. Our research is helpful in analyzing the factors affecting competitive knowledgediffusion and constructing an effective knowledge management system.

1. Introduction

In the current era of knowledge-economy, knowledge is seenas an important intangible asset that can guarantee andsustain competitive advantage [1]. Therefore, knowledge hasbeen recognized as the organization’s lifeblood and has beenidentified as a key element in the organization’s survival intoday’s dynamic and competitive era [2, 3]. Thus, a successfulcompany in the present time can be said to consistently createnew knowledge, spread its knowledge to the whole organiza-tion, and continuously introduce new technologies and prod-ucts to the market [4]. Thus, knowledge management, likeother asset management, has become an important part oforganizational management, andmany economists andman-agement professionals are paying more attention to research

on knowledgemanagement, such as the creation, transforma-tion, and sharing of technical knowledge.

Davenport defines knowledge management as a processof acquiring, storing, sharing, and utilizing knowledge [5],and Nonaka and Takeuchi define knowledge managementas creating newknowledge, spreading it to the entire organiza-tion and making it into a product or service system [6]. Abelland Oxbrow pointed out that important parts of knowledgemanagement are the promotion of innovation and creativitythrough the connection of people and people and knowledgeand people; information is transformed into knowledge [7],and Nonaka suggested that new knowledge comes fromindividuals and the core activity of a knowledge-innovationcompany is to transfer individual knowledge to other peo-ple for making individual knowledge into organizational

HindawiAdvances in Mathematical PhysicsVolume 2020, Article ID 8491516, 12 pageshttps://doi.org/10.1155/2020/8491516

knowledge [4]. Among other processes of knowledge man-agement, knowledge sharing has been identified as the mostvital one, and it is adopted as a survival strategy [8]. If knowl-edge remains only as personal knowledge and cannot betransformed into organizational knowledge, such knowledgeis easily corroded. Knowledge sharing could be defined asknowledge transfer between individuals, groups, teams,departments, and organizations [9]. Especially, sharing tacitknowledge that resides in the minds of people accumulatedover time is very important [10]. Tacit knowledge is highlypersonal and difficult to formalize, articulate, and communi-cate fully, based on experience and job specific, transferredthrough conversation or narrative, and not captured by for-mal education or training [6, 11]. Tacit knowledge could bean important source of sustainable competitive advantagebecause competitors are not easy to imitate.

Although knowledge diffusion is very important foreconomic development, to effectively transfer knowledgeis not an easy task because of the unstructured nature ofthe tacit knowledge and many barriers that hinder the suc-cessful flow of knowledge [12]. So, many studies have beencarried out on the complex influencing factors of theknowledge diffusion process, such as the restricting factorsof knowledge diffusion in organizations [13, 14], the effectfactors of knowledge diffusion [15], and methods to pro-mote knowledge diffusion [16].

Many researchers have discussed in detail the factors thataffect the diffusion of knowledge in the organization, such asknowledge characteristics, knowledge source characteristics,and knowledge receiver characteristics, context characteris-tics, tacit characteristics of knowledge transferred, causalambiguity, uncertainty of knowledge action, lack of absorp-tive capacity, organizational environmental disorder, anddifficulty of communication among knowledge agents[1, 13–17]. Knowledge diffusion in networks has been stud-ied widely. Cowan et al. have demonstrated that spatialclustering generates higher long-term knowledge growthrates by a completely random network characterized witha low path length and low cliquishness, and modeled knowl-edge growth in an innovating industry [18]. Morone andTaylor presented a general model for a knowledge diffusionrule based on a face-to-face network and suggested somemechanisms that dominate knowledge diffusion known as“social learning” [19]. Kiss et al. applied individual-basedmodels from mathematical epidemiology to the diffusion ofa contact network representing knowledge and the resultsshowed that knowledge diffusion had better quality fits witha directed weight network [20].

Recently, attempts have been made to apply physical the-ories to knowledge management. Dragulescu and Yakovenkoconsidered wealth distribution in a closed economy byemploying a kinetic exchange model from the point of viewof gaseous kinetic theory for the first time [21], and Chakra-borti and Chakraborti studied the saving propensity affectingwealth distribution in market economy based on Boltzmanntransport equation [22]. Zhang et al. processed knowledgeflow in a similar way to the theoretical model of electric field[23], and Jun and Xi concluded that the knowledge flow pro-cess is essentially an interaction of strength and resistance by

adopting the concepts of knowledge potential, resistance, andfield strength [24]. Lucas and Moll discussed a balanced eco-nomic growth path using the Boltzmann-type equationmodel [25]. In both natural and social phenomena, the math-ematical modeling is very useful to explain their nature and itis important to establish accurate management strategies byanalyzing and forecasting socioeconomic phenomena.

From the results of many articles on knowledge manage-ment, we can know that the characteristics of organizationalmembers, organizational culture, and knowledge have animportant influence on organizational knowledge accumula-tion in organizational knowledge management. However,previous studies have not studied the effects of these factorscomprehensively and quantitatively. So, we are going toinvestigate the effects of these factors comprehensively inthe process of dynamic change. And the knowledge we aimat in this paper means competitive knowledge. In otherwords, the diffusion of knowledge that can create economicvalue in an organization was discussed. Not all knowledgeleads to economic value. Knowledge that anyone can easilyunderstand and easily acquire from anywhere is knowledgethat cannot create economic value. In other words, it is acompetitive knowledge that requires many skills and know-how difficult to imitate and that can directly bring economicvalue. The goal of knowledge management is to improve thecompetitiveness of organization and ultimately to derive eco-nomic value. In this paper, we have introduced member per-formance index, organizational culture index, and knowledgecomplexity index, which can represent the change of thesefactors, and developed a new equation-based knowledge dif-fusion model by employing physical theory (diffusion andkinetics theory) and methods for the multiparticle systemand analyzed the competitive knowledge diffusion character-istics in an organization.

2. The Model of Competitive KnowledgeDiffusion Based on theStatistical Thermodynamics

In this section, the factors affecting the diffusion of the com-petitive knowledge are analyzed in various aspects, and newcharacteristic quantity and indices are introduced. And thetheoretical study was carried out to construct a new modelusing the thermodynamics and the lattice Boltzmannmethodof physics.

2.1. Analysis of Factors Affecting Competitive KnowledgeTransfer. Knowledge is the insights, understandings, andpractical know-how that people possess and it is the funda-mental resource that allows people function intelligently.And people live in social organization and use knowledge.Therefore, knowledge transfer in an organization will havea close relationship with the characteristics of the organiza-tion members, the relationship between the members, andthe characteristics of the organization.

2.1.1. Personal Characteristics of Organization Members.People are the sources of knowledge. The ability of humansto think creatively and uniquely, coupled with experiences

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and talents, makes humans sources of knowledge. Therefore,knowledge sharing in the organization is closely related to thecharacteristics of an organization members that possessingsuch knowledge. The effects of personal characteristics onknowledge sharing in organizations have been studied exten-sively [26–28]. In this study, we distinguished the knowledge-absorbing ability and the innovation ability as the character-istics of the members for knowledge transfer research.Absorption capacity is associated with many other propertiessuch as knowledge level, existing experience, self-efficacy,activity ability, hobbies, and psychology of the member.It refers to the ability to identify, learn, and digest knowl-edge by assessing external knowledge that can generateorganizational benefits. Therefore, we introduce the variableak and try to distinguish the degree of absorption of themembers through.

Innovation ability is the ability to combine and utilizeacquiring knowledge and existing knowledge to create newcompetitive knowledge necessary to create profit for theorganization. Innovation ability is related to knowledge utili-zation ability, organizational commitment, organizationalcultural characteristics, integrity, belief, and will. We intro-duce the variable ik and try to assess the degree of innovationcapacity of the member. These personal characteristic coeffi-cients are large when absorption capacity and innovationability are high.

2.1.2. Relational Characteristics among OrganizationalMembers. When analyzing knowledge transfer among peo-ple, functional, geographical, and organizational level differ-ence between them has a significant impact on knowledgetransfer [29]. The competitive knowledge in organizationsis often associated with know-how and tacit knowledge. Tacitknowledge could be an important source of sustainable com-petitive advantage because competitors are not easy to imi-tate. So, we have chosen physical distance as one of theimportant factors in the diffusion of knowledge. The transferof competitive knowledge is better as the physical distancebetween members is closer, especially because tacit knowl-edge is communicated only through face-to-face contactbetween people, and knowledge providers more easily trans-fer knowledge to physically closer recipients. On the otherhand, if the levels of culture and value are similar amongthe interacting members, it has a good influence on knowl-edge transfer. So, cultural distances will also influence knowl-edge diffusion among members. The difference in knowledgelevel also affects transmission. Knowledge difference is aparameter that shows how much the supplier and receiverhave common knowledge, and knowledge transfer becomeseasier as knowledge difference gets closer. From these consid-erations, we are introducing the concepts of physical dis-tance, knowledge distance, and cultural distance and tryingto use them in the new models. Physical distance means thedifficulty of communication, time requirements, and face-to-face costs. A study of the effects of physical distancerevealed that patent citations occur frequently in certainregions [30]. Research by Galbraith and Lester et al. showedthat the greater the distance between the parties, the slowerand less technological transfer takes place [31, 32]. Knowl-

edge distance is the degree to which the source and recipientpossess similar knowledge. It has been found that, for organi-zational learning to take place, the knowledge distance or“gap” between two parties cannot be too great [33]. Culturaldistance is a concept that shows how much the knowledgeholders and receivers share the same organizational cultureand value system. Many studies on knowledge sharing haveshown that the difference between labor value and organiza-tional culture can have a significant impact on knowledgetransfer [34]. As a result of analyzing the results of previousstudies, it can be seen that knowledge sharing among agentswill proceed better as the difference between physical dis-tance, knowledge distance, and culture distance is smaller.

2.1.3. Organizational Cultural Characteristics. Many knowl-edge management literatures argue that organizationalculture can have a significant impact on organizationalknowledge sharing activities [35–37]. Organizational cultureis defined as the beliefs and behaviors shared by the membersof an organization regarding what constitutes an appropriateway to think and act in the organization [38]. Although,aligning knowledge management approaches to fit organiza-tional culture have been suggested as good, it is better to cre-ate and manage an organizational culture that supportsknowledge sharing and management activity. The reason isthat organizational culture can be changed to create appro-priate knowledge-related behaviors and value. The successof knowledge management can be achieved by modifyingthe culture of the organization in ways that encourage andsupport the desired knowledge attitudes and behaviors.Organizations that do not care about how knowledge is man-aged will not operate optimally. Knowledge is a resource thatis submerged in human minds, so knowledge and sharing ofknowledge require the will of people with knowledge.

Therefore, the organizations should establish an organi-zational culture that promotes knowledge sharing so that allmembers are aware of the importance of knowledge sharingand actively participate in this work. And the organizationshould provide appropriate motivation and rewards formembers’ knowledge sharing, and encourage organizationallearning, lively debate, and discussion in the organization.So, we have introduced the knowledge sharing culture coeffi-cient ok of the organization to assess the degree of knowledgesharing culture in an organization.

2.1.4. Characteristics of Competitive Knowledge. The charac-teristics of knowledge have an important influence on knowl-edge transfer. The competitive knowledge is not easilytransferred. The knowledge transfer process usually involvesthe process of being moved, interpreted, and absorbed. Theambiguity of knowledge in this process affects the knowledgetransfer. Ambiguity is an intrinsic property of knowledge,including tacitness and complexity. Tacit knowledge isgained by internal individual processes such as experience,reflection, internalization, or individual talents. So, it cannotbe managed and taught in the same manner as explicitknowledge. Tacit knowledge is hard to communicate and isdeeply rooted in action, involvement, and commitmentwithin a specific context. In other words, transfer of tacit

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knowledge requires much time and effort. The complexity ofknowledge also influences knowledge transfer. If knowledgetransfer expertise is high and complex training or functionis required, transferring such knowledge also requires muchtime and effort. Therefore, the influence of the knowledgecharacteristics in the knowledge diffusion process was ana-lyzed by using the ambiguity factor uk of knowledge.

On the other hand, rapid acceleration of technologicalinnovation, economic structural changes, and fierce competi-tion in the market economy accelerate the updating ofknowledge. There is no absolute invariable knowledge. Thenew knowledge is being created and spreading at a very fastpace and the knowledge that we have believed to be true oftenchanges. So, knowledge depreciation theory appeared [39].The value of certain knowledge decreases over time. In otherwords, some of the accumulated knowledge of an organiza-tion turns into unnecessary knowledge as it becomes lesscompetitive or useless over time. This decline is the depre-ciation of knowledge. Considering the depreciation charac-teristics, we introduced the depreciation coefficient dk.Knowledge depreciation coefficient dk is the value loss ofknowledge over time; the larger the value, the faster theknowledge needs to be updated.

2.2. A Competitive Knowledge Diffusion Model by ThermalDiffusion Equation of Physics. A universal agent-based modelof knowledge diffusion is a model that describes systematicphenomena from the behavior of each agent in the system,and mathematical modeling based on the agent is generallywell known as system dynamics. Many studies on knowledgediffusion are based on agent-based modeling, which cancause many problems in computational cost and accuracywhen applied to massive multiagent systems involvingnumerous agents [19, 40, 41]. The economy is a promisingtarget for statistical mechanics applications because it is alarge statistical system with millions of participating agents.If we formulate a mathematical model for the probabilitydistribution of agent behavior based on statistical theory inphysics, it can be much more advantageous to describesystematic phenomena by a simpler equation set.

Boltzmann kinematics is a physical theory suitable formultiparticle systems developed to overcome the deficienciesof Newtonian dynamics, which must solve a large number ofdifferential equations. So, we tried to construct a knowledgediffusion equation using the Boltzmann kinetic-based ther-mal diffusion equation. Starting from the concept of thisphysical field, the knowledge field can be defined as a systemconsisting of different levels of knowledge for each point(agent) in space. Like all other fields, knowledge field can beseen as a function of time and space, but space in the knowl-edge field should be treated as a specific space different fromspace given only by physical distance.

Therefore, we constructed the coordinates of the specialspace for the knowledge field reflecting the abovementionedmember relation characteristics. For this purpose, we haveassumed the independence between the physical distance,the cultural distance, and the knowledge distance introducedabove, and then constructed the x, y, and z axes based on thatindependence. Origin of coordinate (O) can be determined

from averaging the value by analyzing the physical location,cultural characteristics, and the degree of knowledge owner-ship of all agents in the organization. So, the position vectorof all members in the knowledge field can be expressedas r = rx ⋅ i + ry ⋅ j + rz ⋅ k, and the distance between twoagents can also be defined as r1 − r2.

Next, we considered the knowledge field as a kind ofphysical field and introduced some variables similar to thephysics theory.

First, we introduce the energy of competitive knowledge(Ek) as a quantity that can characterize the level of competi-tiveness that is produced by having knowledge. However,there is one important property to consider. Not all knowl-edge leads to economic value. Knowledge that anyone canknow and easily acquire from anywhere is knowledge thatcannot create economic value. In other words, knowledgebased on talents that few people know or cannot be imitatedcan produce economic value. From this, we focus on the abil-ity to create economic value of knowledge in defining knowl-edge energies. In other words, we can establish the logic thatthe size of the competitive knowledge energy is changeddepending on how much agent has the ability to create eco-nomic value. These knowledge energies change in the twoagents when they collide, but the overall knowledge energiesare preserved. In other words, it can be seen that the knowl-edge energies reduced by passing a certain amount ofknowledge to other agents are transmitted to the other.The important thing here is that the preservation of knowl-edge energy does not mean that knowledge is preserved. Itmeans the preservation of competitiveness by knowledge.Based on this logic, this conservation is similar to theenergy conservation law of the gas motion theory, and thedistribution of the knowledge energy in the steady state fol-lows the Maxwell-Boltzmann equilibrium distribution of thegas motion theory.

f Ekð Þ = A exp −Ek

Tk

� �, ð1Þ

where f is the knowledge energy distribution function andA isconstant. Tk is the average knowledge energy of the systemand can be defined as the knowledge temperature. In otherwords, if knowledge temperature is high, such knowledgecan be considered to have relatively high competitiveness.

Next, we introduce a specific knowledge energy quantityCk, which is defined as a quantity similar to the specific heatin the statistical thermodynamics from the knowledgetemperature.

CK = ΔEK

ΔTK

� �, ð2Þ

where Ck is related to the degree of absorption capacity ak inthe personal characteristics of the members mentioned aboveand specifically has an inverse relationship.

In general, many phenomena in various scientific disci-plines are mathematically expressed using well-known par-tial differential equations. The diffusion equation has been

4 Advances in Mathematical Physics

developed to describe behavior due to randommovements ofparticles in physics and has been extended to various areassuch as information science, life sciences, social sciences,and material sciences.

From the introduction of Ek, Tk, and Ck, we have beenable to study the diffusion problem of knowledge based onstatistical thermodynamics. Using the defined coordinatesystem and variables and the heat diffusion equation of ther-modynamics, the competitive knowledge diffusion equationcan be constructed as follows.

ck rð Þ ∂Tk rð Þ∂t

= ∂∂r kk

∂Tk rð Þ∂r

� �: ð3Þ

In this equation, the left side shows the change of theknowledge temperature with time and the right side showsthe knowledge temperature change according to the agentposition. In other words, this equation mathematicallyexplains that the knowledge energy is shifted from the highto the low knowledge temperature by various factors. In theequation, kk is defined as the knowledge conduction coeffi-cient as a quantity that characterizes knowledge diffusion.kk is closely related to the cultural characteristics of theorganization and degree of ambiguity of knowledge amongfactors influencing the transfer of knowledge. Equation (3)considers only the exchange of knowledge between agentswithout knowledge generation or disappearance. Therefore,the creation of knowledge and the depreciation of knowl-edge discussed above must be considered in this diffusionequation. In previous R&D collaboration network studyon knowledge diffusion performance [42, 43], knowledgeaccumulation by creation and depreciation was studied asfollows.

ki,t+1 = 1 − δð Þki,t + αikγi,t , ð4Þ

where ki,t and ki,t+1 are the knowledge accumulationamounts at time t and t + 1, and δ is the knowledge depre-ciation rate. αi can be interpreted as an innovation ability,and γ is constant. Due to learning, the larger the coefficientγ is, the more rapidly productivity increases. From Equa-tion (4), we can express the source term of the knowledgediffusion equation as follows:

S = ik rð ÞTk rð Þλ − dk rð ÞTk rð Þ: ð5Þ

And we should also consider the knowledge affinity char-acteristics that indicate the degree of knowledge culture ofthe organization. As mentioned above, knowledge-friendlycultures value knowledge, create appropriate incentives forcreating new knowledge, and improve members’ creativityand encourage knowledge sharing. Therefore, knowledgeaffinity factors will affect knowledge sharing and creation.Specific knowledge energy capacity is related to knowledgeabsorption capacity. So, we finally constructed the knowledgediffusion equation as follows.

1ak rð Þ

∂Tk rð Þ∂t

= ∂∂r okukkk

∂Tk rð Þ∂r

� �+ okik rð ÞTk rð Þλ

− dk rð ÞTk rð Þ,ð6Þ

where ak, ik, and dk are coefficients that represent the absorp-tive capacity, innovation ability of the members, and knowl-edge depreciation, and uk and ok are ambiguity coefficient ofcompetitive knowledge and knowledge affinity coefficient oforganizational culture discussed above, respectively. λ is thelearning curve factor of the agent. Equation (6) allows us tobuild a new competitive knowledge diffusion model thattakes into account the personal characteristics, relationshipcharacteristics, and organizational cultural characteristicsdiscussed above.

2.3. Numerical Solving Method of Knowledge DiffusionEquation by Lattice Kinetic Method. Lattice Boltzmannmodel is a relatively new simulation technique for complexfluid systems and has attracted interest from researchers incomputational physics because of its powerful numericalsolving ability. Unlike the traditional computational fluiddynamics methods, which solve the conservation equationsof macroscopic properties (i.e., mass, momentum, andenergy) numerically, lattice Boltzmann method models thefluid consisting of fictive particles, and such particles performconsecutive propagation and collision processes over a dis-crete lattice mesh. Therefore, the lattice Boltzmann methodis based on the idea of lattice gas cellular automata (LGCA)to simulate the fluid motion by a simplified microscopicmodel in discrete time steps using a discrete phase space,i.e., discrete velocity and location. The motion of the particlesis represented by a particle distribution function. The Boltz-mann transport equation can be written as follows [44]:

∂f∂t

+ e ⋅ ∇f =Ω ð7Þ

where f is the distribution function, e is the velocity, andΩ isthe collision operator. It is difficult to solve this equationbecause Ω is a function of f , and in a general case, it is anintegro-differential equation. The starting point of the latticeBoltzmann method (LBM) is the kinetic equation.

∂f i r, tð Þ∂t

+ ei ⋅ ∇f i r, tð Þ =Ω, i = 1, 2, 3,⋯,M, ð8Þ

where f i is the particle distribution function denoting thenumber of particles at the lattice node r at the time t movingin direction i with the velocity ei along the lattice link h = eiΔtconnecting the nearest neighbors, and M is the number ofdirections in a lattice through which the information propa-gates. The term Ωi represents the rate of change of f i due tocollisions and is very complicated [45]. The simplest modelfor Ωi is the Bhatnagar-Gross-Krook (BGK) approximation[44–46].

Ωi = −1τ

f i r, tð Þ − f 0i r, tð Þ� �, ð9Þ

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where τ is the relaxation time and f i0ðr, tÞ is the equilibrium

distribution function. In the knowledge diffusion Equation(6), the equilibrium distribution function is given by

f 0i r, tð Þ =wiTk r, tð Þ, ð10Þ

where wi are the known weights, and at the same time∑M

i=1wi = 1.Additionally, the knowledge temperature Tk at the lattice

node r and for time t is calculated using the formula asfollows:

Tk r, tð Þ = 〠M

i=1f i r, tð Þ: ð11Þ

The evolution equation for Equation (9) can be writtenby using the distribution function as follows:

f i r + Δr, t + Δtð Þ = f i r, tð Þ + Δtτ

f 0i r, tð Þ − f i r, tð Þ� �+ Δtwiak rð Þ okik rð ÞTk rð Þλ − dk rð ÞTk rð Þ

� �:

ð12Þ

Lattice selection is very important in the lattice kineticmodel for knowledge diffusion. In the knowledge space dis-cussed above, we can see that agent interaction proceedsbetween adjacent spaces. In other words, the exchange ofknowledge between knowledge transferor and recipient isconsidered as progressing knowledge exchange from theagent with the shortest physical distance, cultural distance,and knowledge distance. Therefore, we can use the latticeBoltzmann method for natural scientific problems. We usedtwo-dimensional knowledge space to perform numericalexperiments on knowledge transfer in an organization andto verify the lattice dynamics model for knowledge transfer.

For a D2Q9 model, a particle is restricted to stream in apossible of directions, including the one staying at rest, andthese velocities are referred to as the microscopic velocitiesand denoted by ei, where i = 0,⋯, 8:

ei =0, 0ð Þ, i = 0,1, 0ð Þ, 0, 1ð Þ, −1, 0ð Þ, 0,−1ð Þ, i = 1, 2, 3, 4,1, 1ð Þ, −1, 1ð Þ, −1,−1ð Þ, 1,−1ð Þ, i = 5, 6, 7, 8:

8>><>>:

ð13Þ

For each particle on the lattice, we associate a discreteprobability distribution function f iðr, ei, tÞ or simply f iðr, tÞ,i = 0,⋯, 8, which describes the probability of streaming inone particular direction. And their corresponding weights wiare as follows:

wk =4/9, k = 01/9, k = 1 to 41/36, k = 5 to 8

8>><>>:

ð14Þ

If the agents on the outskirts of the computational domaindo not carry out meaningful knowledge transfer to/from out-side, then theboundary conditions forknowledge temperaturecan be written as Tkjoutside = Tkjoutstrike. Boundary conditionfor the distribution function is set by nonequilibrium extrapo-lation scheme [47].

f kjoutside − f eqk��outside = f kjoutstrike − f eqk

��outstrike: ð15Þ

From these considerations, we have been able to constructa new knowledge diffusion model and analyze knowledge dif-fusion characteristics using Equations (4) and (10) and D2Q9model. Inour research, the initial knowledge temperatureTk isa random variable following the uniformdistributionwith theinterval [0,10]. The absorption capacity parameter ak was dis-cussedbetween0and1. Innovationability variable ik is distrib-uteduniformlyover some interval [0,1] andλ is set to 0.1. If theupper bound of learning curve coefficient is set above thatvalue, the knowledge stock did not converge as time goes on.Knowledge depreciation parameter dk is given a value of0.01. The knowledge transfer coefficient was simulated byvarying between 0 and 1 depending on the degree of organiza-tional sharing culture. In our research, the nodes representagents within the organization and 10000 agents are regularlydistributed on the 100 × 100 grid. The simulation was per-formed using MATLAB 2016a.

3. Simulation Results and Discussion

In this section, we have studied the diffusion and accumula-tion of competitive knowledge in organizations accordingto the changes in the personal absorption characteristics oforganizational members, the characteristics of knowledgeitself, and the degree of knowledge affinity of organizationalculture based on knowledge diffusion equations and the lat-tice kinetic simulation. In order to investigate the effect ofknowledge absorptive characteristics of members on theknowledge sharing, the change of mean knowledge tempera-ture in the organization according to time was investigated bychanging the knowledge absorption coefficient of the agent.Figure 1 shows the change of organizational average knowl-edge temperature vs. time on different absorption coefficientsof the agent.

From Figure 1, it can be seen that as the absorption coef-ficient of the agents increases, the average knowledge temper-ature of the organization increases relatively quickly andreaches saturation temperature. In other words, all the agentsin the organization raise their knowledge level by theinteraction with other agents, but the speed is related tothe absorption ability. Over time, the knowledge diffusionrate decreases and the average knowledge temperature of theorganization becomes saturating state. In other words, if themembers of the organization live together in the same organi-zation for a long time, the level of mutual knowledge becomessimilar through the process of information exchange, so thatthe diffusion of valuable knowledge is gradually reduced. Also,from Figure 1, it can be seen that as the knowledge absorptioncoefficient decreases, the negative effect on knowledge diffu-sion becomes greater. In the present age of the knowledge

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economy, knowledge is being renewed rapidly, and the spreadof the latest technologies in the organization at the right timeis closely linked to value creation. Therefore, in order toquickly share and utilize valuable knowledge in an organiza-tion, members’ ability to absorb knowledge should be high.

If the organization cannot create new competitive knowl-edge based on acquiring knowledge from the outside, theywill fall into the age of development and such organizationcannot guarantee the long-term competitiveness. Especially,because knowledge is constantly updated and competitorsare constantly evolving, creation of new knowledge is essen-tial. The individual’s creative ability will have a significantimpact on the accumulation of knowledge in the organiza-tion as an intrinsic characteristic of the members. So, westudied the effect of the members’ creative ability on theaccumulation of competitive knowledge in the organization.Figure 2 shows the average knowledge temperature value ofthe agents over time while varying the maximum innovationcoefficient of the agents.

From Figure 2, it can be seen that the average knowledgetemperature in the organization increases as the knowledgeinnovation ability of the members increases. In other words,the higher the knowledge innovation capability of the mem-bers, the greater the knowledge accumulation in the organi-zation. And knowledge accumulation increases with time,but it reaches saturation state. The reason is that after a cer-tain period of time, the balance between the creation ofknowledge and depreciation of knowledge is maintained. Inother words, while new knowledge is created, some knowl-edge in the organization loses its competitiveness anddecreases in value as time goes by. When the maximumknowledge creation coefficient is less than 0.4, the averageknowledge temperature does not increase but ratherdecreases. This result shows that the knowledge creation coef-ficient of the members should be constantly high in order to

secure competitiveness in the organization. The accumulationof knowledge in an organizationmeans the competitiveness ofthe organization. From the results in Figure 2, we can also seethat the higher the creative abilities of the members, thegreater the competitiveness that the organization can possess.

Next, we examined the influence of competitive knowl-edge ambiguity, which is a characteristic of knowledge itself,in the diffusion of knowledge in the organization. Figure 3shows the knowledge temperature distribution contoursat t = 100 on different knowledge ambiguity coefficients.

From Figure 3, it can be seen that the difference betweenthemaximumandminimumvalues of the knowledge temper-ature becomes smaller as the number of knowledge ambigui-ties becomes smaller. The complexity and tacitness ofknowledge increase as the ambiguity factor increases. In otherwords, when the ambiguity decreases, knowledge spreadssmoothly in the organization. Figure 4 shows the knowledgetemperature distribution contours at different knowledgeambiguity coefficients when the knowledge diffusion reachesequilibrium.

Figure 4 shows that although knowledge diffusion hasreached an equilibrium state, knowledge differences amongmembers still exist because of the ambiguity of knowledge,and the difference is large when the ambiguity factor is large.On the other hand, when the ambiguity of knowledge is low(for example, Figure 4(c)), knowledge sharing among mem-bers smoothly progresses, and the ratio of members with highknowledge increases. Therefore, in order to improve theknowledge sharing among the members, the organizationshould try to make the implicit knowledge explicit andensure sufficient learning and practice for the knowledge,which requires complex and highly skilled finesse.

In order to investigate the effect of organizational cul-ture characteristics on the competitive knowledge growthand sharing of the organization, we analyze the change

10

9

8

Aver

age k

now

ledg

e tem

pera

ture

7

6

50 1000 2000

Time

𝛼𝜅 max = 0.2𝛼𝜅 max = 0.4

𝛼𝜅 max = 0.6

𝛼𝜅 max = 0.8𝛼𝜅 max = 1.0

3000 4000 5000

Figure 1: Organization-mean knowledge temperature on different absorption capacity coefficients.

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characteristics of the organization-average knowledge tem-perature vs. time by changing values of the organizationalknowledge affinity coefficient from 0.4 to 1 with 0.2 interval.

We studied the diffusion characteristics of knowledgeaccording to organizational knowledge affinity coefficientdefined above. Figure 5 shows the change in average

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5

Aver

age k

now

ledg

e tem

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ture

i𝜅 max = 0.4i𝜅 max = 0.5i𝜅 max = 0.6

i𝜅 max = 0.7i𝜅 max = 0.8

0 1000 2000Time

3000 4000 5000

Figure 2: Average knowledge temperature on different knowledge innovation coefficients.

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Figure 3: Knowledge temperature distribution contours at t = 100 (a (uk = 1), b (uk = 0:5), c (uk = 0:1)).

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knowledge temperature over time on the different knowledgeaffinity coefficients. As can be seen in Figure 5, the knowledgeaverage knowledge temperature of the organization repre-

sents a very large change characteristic according to theknowledge affinity coefficient of the organizational. Inother words, it shows that knowledge affinity degree of

1820222426283032343638

(a)

23

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31

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25.5

26

26.5

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(c)

Figure 4: Knowledge temperature distribution contours at t = 100 (a (uk = 1), b (uk = 0:5), c (uk = 0:1)).

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10

0 200 400 600 800 1000

0

Aver

age k

now

ledg

e tem

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ture

o𝜅 = 1.0o𝜅 = 0.8

o𝜅 = 0.6o𝜅 = 0.4

Time

Figure 5: Organization-average knowledge temperature vs. time on different organizational knowledge affinity coefficients.

9Advances in Mathematical Physics

organizational culture has a great influence on the diffu-sion and growth of knowledge.

In addition, from the saturation knowledge temperatureon the different organizational knowledge affinity coeffi-cients, we can see that the average saturation knowledgetemperature change magnitude becomes larger when theknowledge affinity coefficient increases, and the knowledgegrowth does not proceed at less than 0.4. This implies thatthe higher the knowledge affinity level of organization, thebetter influence on knowledge growth and accumulation.On the contrary, we can also know that organizational cul-ture that is not interested in knowledge has a negative impacton the growth and accumulation of knowledge, and in a seri-ous case, knowledge accumulation becomes smaller andobsolete due to depreciation and time lapse. On the otherhand, comparing the results in Figures 1, 2, and 5 shows thatthe affinity coefficient of the organizational culture has amuch greater influence on the average knowledge tempera-ture than the influence of the characteristic coefficients ofthe agent.

Figure 6 shows the knowledge temperature distributioncontours at equilibrium in the various knowledge affinitycoefficients of the organizational culture. As shown inFigure 6, when the affinity coefficient is small, the diffusionof valuable knowledge is not progressed well, and relatively

high knowledge temperatures are partially extreme. On thecontrary, when the knowledge affinity coefficient increases,knowledge spreads well and high knowledge temperaturedistribution ratio increases. In other words, the higher theaffinity coefficient of the organization, the better the diffusionof knowledge in the organization, and the valuable and com-petitive knowledge sharing among the agents is facilitated.From these results, we can conclude that the main factoraffecting competitive knowledge diffusion and accumulationwithin an organization is the degree of knowledge affinity oforganizational culture.

Many researchers have emphasized the importance oforganizational culture in knowledge management, and sev-eral studies have shown that people and cultural issues arethe most difficult problems to resolve, but produce the great-est benefits [48]. Ruggles examined 431 organizations in theUnited States and Europe to investigate factors that impedeknowledge sharing and found that organizational culture isthe most important factor, and it is necessary to confirmthe organizational culture to activate knowledge sharing[49]. Our knowledge diffusion research results based on thenew model support the previous research theoretically.

Therefore, it is more effective to create and manage anorganizational culture that supports knowledge sharing andmanagement activities rather than adjusting the knowledge

4.5

5.5

5

6

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9

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(d)

Figure 6: Knowledge temperature distribution contours on different organizational knowledge affinity coefficients (a (ok = 0:4), b (ok = 0:6),c (ok = 0:8), d (ok = 1)).

10 Advances in Mathematical Physics

management approach to fit the organizational culture. Sinceknowledge is a resource in the human mind, so the view-points and attitudes of people on the organization have animportant influence on knowledge and knowledge sharing.It is therefore important to build a knowledge-friendlyculture that values knowledge and encourage a knowledge-sharing culture in which all members recognize the impor-tance of knowledge sharing. Our new model can helpmanagers find good management methodologies by simulat-ing the dynamic characteristics of competitive knowledgeaccumulation and sharing by providing accurate values forthe variables discussed above in a particular organizationbased on empirical analysis and data.

4. Conclusion

In this study, we have constructed a new model for compet-itive knowledge diffusion in organization based on the statis-tical thermodynamics of physics and successfully studieddynamic characteristics of competitive knowledge diffusionand the effect of the characteristics of member, knowledge,and organizational culture on knowledge sharing and dif-fusion in the organization. In order to achieve the purposeof research, we newly define the coefficient of absorptivecapacity, the creativity ability coefficient, the depreciationcoefficient of knowledge, the knowledge ambiguity coefficientof knowledge, and the knowledge affinity coefficient oforganizational culture. And various knowledge quantitiessuch as knowledge energy, knowledge temperature, and dif-fusion coefficient for the knowledge diffusion equation weredefined and simulations were carried out by the latticekinetic method. The main achievements of our researchare as follows.

(1) A new model for studying the dynamic character-istics of competitive knowledge diffusion in organi-zations is constructed based on the statisticalthermodynamics of physics

(2) The diffusion velocity of competitive knowledge inthe organization increases as the knowledge absorb-ing ability of the members is larger. The higher thecreative abilities of the members, the greater themaximum competitiveness that the organizationcan possess

(3) The ambiguity of competitive knowledge has a nega-tive impact on the diffusion of knowledge

(4) The degree of knowledge affinity of organizationalculture is a decisive factor in the diffusion andaccumulation of competitive knowledge in anorganization

Comprehensively, organizational cultural characteristicsare much more influential on the diffusion of competitiveknowledge than the personal characteristics of the members.Therefore, organizational managers need to pay greaterattention to building a superior organizational culture thanimproving personal traits.

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (71472055, 71272175), the NationalSocial Science Foundation of China (16AZD0006), Heilong-jiang Philosophy and Social Science Research Project(19GLB087), and the Fundamental Research Funds for theCentral Universities (HIT.NSRIF.2019033).

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