The Physics of Strategic Doing: Modeling Trust, Collaboration, and Network Emergence

Written By Ubaldo M. Córdova-Figueroa

Introduction to Strategic Doing: Agile Networks for Complex Challenges

In a world where complexity moves faster than plans on paper, traditional strategic planning falters in the face of wicked problems—those tangled challenges that cut across disciplines, institutions, and conventional boundaries. Strategic Doing is a novel approach developed to fill this gap. Originating from work by Ed Morrison at Purdue University, Strategic Doing is an open-source discipline for designing and guiding complex collaborations by following simple rules. Unlike linear, top-down strategic planning methods of the past, Strategic Doing is agile and iterative, emphasizing guided conversations that align “stakeholders” around shared outcomes, rapidly identify opportunities, and drive tangible action. It was explicitly created to help loosely connected groups form networks that can tackle wicked problems – challenges with no clear solution where collaboration is the only path forward.

At its core, Strategic Doing “emphasizes action over planning,” enabling participants to move quickly from idea to implementation. Instead of producing static plans, small teams engage in cycles of asking four key questions: What could we do? (explore all opportunities with available assets), What should we do? (prioritize and pick a direction), What will we do? (make commitments to act), and What’s our 30/30? (set a 30-day review to learn and adapt). By repeating this cycle, groups leverage personal networks and assets to “link and leverage” their capabilities, expanding the collaboration with each iteration. Early wins and visible progress build trust and mutual accountability, which in turn attract more partners in a virtuous cycle. In essence, Strategic Doing transforms a loose collection of individuals and resources into a goal-oriented collaboration network. As one case study notes, such networks are “not hierarchical entities but are loosely formed networks of local stakeholders… The success of any network is driven by the structure and nature of the social relationships of the people that comprise the network.” In practice, this means nurturing connections and trust so that small clusters of collaborators can self-organize into larger, sustainable networks. Strategic Doing’s focus on simple rules and rapid execution has been shown to deliver results more quickly than traditional plans – a crucial advantage when trying to solve complex community challenges or build innovation ecosystems.

However, while the principles of Strategic Doing are well documented in management terms, we lack a rigorous predictive model for how these collaboration networks form, evolve, and sometimes dissolve. What if we could borrow frameworks from physics – particularly the science of particles, colloids, and phase transitions – to better understand the dynamics of Strategic Doing? In the following sections, I develop a physics-inspired mathematical model that uses analogies from colloidal systems, Brownian motion, and network science to describe how individuals (as “particles”) come together into clusters (collaboration projects) and ultimately form an interconnected innovation network. This model provides insight into the mechanisms behind Strategic Doing’s success, yielding equations and principles that mirror concepts like interparticle forces, diffusion-limited aggregation, and percolation theory. By capturing Strategic Doing’s dynamics in mathematical form, we aim to predict when and how sustainable, agile collaboration networks emerge, how they grow, and under what conditions they might fragment. The hope is that this approach not only advances academic understanding (by framing social collaboration as a complex system with parallels in physics), but also offers practical guidance – for example, helping leaders tune variables like trust, commitment, and interaction frequency to “nudge” their networks toward greater connectivity and resilience.

Why Physics? Drawing Parallels Between Social Networks and Particle Systems

It may seem unconventional to use physics models to describe strategic collaborations, but the analogy is powerful. In essence, a Strategic Doing network behaves like a complex adaptive system of many interacting agents, much like a fluid or colloidal suspension of particles interacting under forces. Individuals and organizations in a network are loosely connected and move within a “landscape” of ideas and opportunities, occasionally bumping into others. If conditions are right (shared goals, trust, mutual benefit), these agents may “stick” together to form a collaborative project. Over time, small projects link up with others, creating larger clusters or an even broader network of partnerships. This process is strikingly analogous to how particles undergo random collisions and sometimes adhere to form larger aggregates. By translating the qualitative principles of Strategic Doing into the language of statistical physics and network science, we can leverage well-established models to gain fresh insights.

Brownian Motion and Random Encounters

In colloidal physics, particles suspended in a fluid move randomly due to Brownian motion, an erratic, diffusive motion resulting from countless tiny collisions with the surrounding molecules of the fluid. These collisions arise because the fluid molecules are themselves in constant thermal motion, propelled by the kinetic energy associated with the system’s temperature. As these fast-moving fluid molecules bombard the larger colloidal particles from all directions in an uneven and fluctuating manner, the resulting net force drives the irregular trajectory characteristic of Brownian motion. Likewise, in an ecosystem of innovators or community members, people often interact in a somewhat random fashion: chance meetings at events, spontaneous conversations, or serendipitous connections via mutual contacts. We can view these as “random walks” of individuals in a social space. Most encounters are fleeting, but occasionally a meaningful connection (analogous to a particle collision) occurs. This sets the stage for cluster formation. Notably, a classic model of cluster growth is diffusion-limited aggregation (DLA), wherein diffusing particles stick together upon contact and gradually build up a cluster. DLA produces ramified, tree-like clusters as particles undergoing random walks (Brownian motion) join an aggregate one by one. Figure 1 shows an example: a copper sulfate DLA cluster grown experimentally, where copper particles diffusing in solution have aggregated into a fractal pattern.

Figure 1: An example of diffusion-limited aggregation. A copper sulfate solution produced this branching copper cluster via random motion and sticking of particles. In Strategic Doing terms, one can think of each branching cluster like a growing collaborative project: individual actors (particles) randomly encounter a nascent initiative (the cluster seed) and, if the alignment is right, they attach, causing the project cluster to grow in a path-dependent, branchy way. Such analogies help illustrate how small actions and chance meetings can lead to large, self-organized structures in social innovation networks.

The random, path-dependent growth seen in DLA is a useful analogy for Strategic Doing. Early steps in a collaboration can have outsized, path-dependent effects: for instance, which individuals connect first or which idea they choose to pursue can shape the structure of the emerging project (much as the branching pattern in a DLA cluster depends on the sequence of particle arrivals). This underscores a key principle of Strategic Doing: start with small, doable projects and iterate, because one cannot fully predict what emergent structure will form – yet with simple rules and repeated interactions, order can emerge from randomness. The usefulness of the physics analogy is that it gives us conceptual and mathematical tools to describe this emergence. Where Strategic Doing practitioners speak of “linking and leveraging assets” or “finding opportunity spaces”, we can model analogous processes like particle bonding and potential energy landscapes guiding those bonds. The result is not a rigid formula for success, but a flexible framework to explore what-if scenarios and critical thresholds (e.g. how much trust or how many connections are needed to get a self-sustaining network).

Interparticle Forces = Trust and Alignment

In physical systems, particles interact via forces that can be attractive (pulling them together) or repulsive (pushing them apart). These forces are often described by potential energy functions – for example, an electrically charged or polar particle might attract others of opposite charge, or steric hindrance might create short-range repulsion. In a collaboration context, we can think of trust, shared values, and aligned interests as analogous to attractive forces, whereas lack of trust or conflicting goals act like repulsive forces. When two people highly aligned in mission discover each other, there is an innate attraction – they are more likely to form a bond (collaborate). Trust between partners lowers the “energy barrier” to working together, much as an attractive potential well facilitates particle bonding. Conversely, if two actors have misaligned incentives or a history of distrust, they may avoid linking (repulsion). In effect, we can map social variables to a “potential field”: a pair of agents has a low potential energy (stable bond) if they trust each other and see mutual benefit, or a high potential energy (unstable) if they do not. Prior research in social network dynamics has even formalized such notions, assigning attractive forces between nodes with positive relations and repulsive forces for negative relations. In our model, we treat trust as a form of potential energy shaping the landscape of interactions. High trust = deep potential well (strong attraction), high distrust or misalignment = potential barrier (effectively repulsion).

Collision Frequency = Interaction Rates

Another ingredient in physical aggregation is how often particles collide, which is governed by their diffusion rate or external stirring. In Strategic Doing, this corresponds to the frequency of interactions among people – how often do potential collaborators “bump into” each other (in meetings, online forums, etc.)? We can liken networking events, workshops, or platform connections to increasing the diffusion coefficient of particles: more movement and mixing leads to more collisions. If the “collision rate” is too low (few interactions), the formation of collaborations will be slow or stagnate because people simply don’t encounter each other’s ideas. If it’s high, there are many opportunities for bonding. Thus, interaction frequency in our model acts like a tunable parameter (akin to temperature or diffusion speed) that accelerates or decelerates the formation of clusters. Strategic Doing workshops intentionally create frequent, structured interactions in short cycles (the 30/30 cadence). This effectively raises the collision rate so that promising connections are more likely to form.

Smoluchowski’s Aggregation Model for Cluster Growth

One of the fundamental frameworks from colloid physics we draw upon is the Smoluchowski coagulation equation, developed by Marian Smoluchowski in 1916 to describe how particles clump together over time. This model considers clusters of various sizes and how they merge when particles collide and stick. It has been widely applied to phenomena like aerosols coalescing, droplets aggregating, even the formation of asteroid clusters. Essentially, it assumes any two clusters of size $i$ and $j$ can merge to form a cluster of size $i+j$ with a certain rate kernel $K(i,j)$, which encapsulates how likely that collision and sticking is. The Smoluchowski equation then tracks the time evolution of $N_k(t)$, the number of clusters containing $k$ members at time $t$. A simple form (for irreversible aggregation with no fragmentation) is:

$$\frac{dN_k}{dt} \;=\; \frac{1}{2}\sum_{i+j=k} K(i,j)\,N_i\,N_j \;-\; N_k \sum_{j\ge 1} K(k,j)\,N_j.$$

This equation says: the number of clusters of size $k$ increases when smaller clusters $i$ and $j$ merge ($i+j=k$) and decreases when a $k$-cluster collides with any other cluster to form a larger one. How does this translate to Strategic Doing? We can interpret $N_k$ as the number of collaborative groups (projects) that consist of $k$ members. Initially, at time $t=0$, each individual is essentially a cluster of size 1 (so $N_1$ equals the number of people, and $N_{k>1}=0$). As people begin to connect and form teams or projects, we’ll see $N_2, N_3, …$ grow while $N_1$ drops (fewer unconnected individuals). The collision kernel $K(i,j)$ in this context would depend on how likely two groups are to discover a potential linkage and successfully combine. In a homogeneous random mixing scenario, $K(i,j)$ might be roughly constant or proportional to $ij$ (mass-action like kinetics). But here, we might build in the idea that larger groups or well-connected people have higher visibility – akin to preferential attachment, where those with more links attract even more. For instance, if one cluster has developed a reputation (high trust capital), others are more likely to join it, increasing its size further – a rich-get-richer effect analogous to preferential attachment in network growth. We can encode this by making $K(i,j)$ larger for bigger $i,j$; indeed, one generalized network coagulation model uses $K \propto i^\alpha j^\beta$ to model processes like firm mergers with preferential bias to size.

By solving or simulating the Smoluchowski equations under various parameters, we could predict the evolving cluster size distribution of a collaboration network. For example, if trust and alignment are high (strong attraction) and interaction frequency is high (lots of collisions), the model would show rapid growth of larger clusters (multi-partner projects) over time. If trust is low or interactions infrequent, the model might predict many small clusters persisting (everyone stuck in siloed pairs or trios). Additionally, Smoluchowski’s framework can be extended to include fragmentation (clusters breaking apart) by adding extra terms, or to a finite population context. This might be relevant if, say, a project fails and its members go back to being “single” agents (cluster of one) or join other groups. In a Strategic Doing sense, fragmentation could represent collaborations that dissolve due to waning commitment or external shocks. Incorporating fragmentation parameters (e.g. a probability per unit time that a link breaks or a cluster splits) would let us examine network stability and churn.

Percolation Theory and Network Connectivity

As collaborative links form, there is an analogy to percolation theory, which studies how connectivity emerges in a network as more nodes or edges are added. In percolation models, we often ask: is there a critical threshold at which a giant connected component spans the system? Below that threshold, you have only isolated clusters; above it, a large fraction of nodes become interconnected in one network. This is essentially a phase transition from a fragmented state to a connected state. In the context of Strategic Doing, one can imagine that if enough people and projects become interlinked (through shared members or goals), an “innovation ecosystem”suddenly coalesces – analogous to a spanning cluster in percolation. Percolation theory tells us that this transition often happens abruptly at a certain critical link probability or density. Translating that, our model might predict that beyond a certain level of average trust or interaction frequency, the network will “tip” from scattered collaborations to a large, self-sustaining network where nearly everyone is connected through some path (directly or indirectly). Figure 2 conceptually illustrates this idea: initially, you have many small groups working in isolation (left side). As connections increase (e.g. via Strategic Doing workshops forging links between groups), clusters merge. If the process continues, you reach a point where a single giant cluster (network) forms that connects most participants (right side). This is akin to pouring water on a porous material – at first only wetting patches, but once enough water is added (beyond critical percolation threshold), a continuous path of fluid spans from top to bottom.

Figure 2: Schematic of a network “phase transition” in a collaboration network. Small circles represent individuals or assets, and lines represent collaborative links (trust-based connections). Left: At low connectivity (few links), only small clusters exist – analogous to isolated project teams. Right: Once the rate of link formation passes a threshold, clusters coalesce into a large, intersecting network (giant component). In physics, this is described by percolation theory as a critical transition where “the network of small, disconnected clusters merge into significantly larger connected… spanning clusters.” In Strategic Doing, this tipping point might correspond to achieving a level of trust, alignment, and interaction where the community behaves as one big agile ecosystem rather than disconnected efforts.

What determines the critical point in our model? Several factors likely interplay: the number of participants, the propensity to form links (which grows with trust/alignment), and the “collision” frequency. Using tools from network percolation theory, we could derive an equation for the probability that any given actor becomes part of the giant connected component as a function of parameters like average degree (links per actor) or link formation probability. For example, in a simple random graph model (Erdős–Rényi type), the giant component emerges when the average degree $z$ exceeds 1. In our analogy, average degree might increase over time as more collaborations form. The model could reveal a time or condition when $z=1$ is crossed – implying a systemic shift from fragmented to connected. This is important for practitioners: it suggests there is a build-up phase where many small wins gradually increase network connectivity, and at some point a robust network “clicks” into place. Recognizing this, leaders can foster conditions to reach that critical mass of connections (for instance, intentionally connecting disparate project clusters or investing in trust-building across silos to raise the likelihood of cross-cluster links).

Mathematical Formulation of the Model

Having laid out the conceptual parallels, we now present a more formal mathematical model that synthesizes these ideas. Our model combines elements of stochastic particle motion, cluster aggregation equations, and dynamic network graphs:

1. Agent-Based Stochastic Dynamics (Langevin Equation)

Consider $N$ individual agents (people or organizations) in an abstract interaction space. This space could be literal (geographic or virtual meetings) or conceptual (a space of ideas or strategic opportunities). We denote an agent’s position by $\mathbf{x}_i(t)$ in this space. Agents execute a random walk (Brownian motion) representing exploratory behavior – trying new contacts, visiting events, etc. We incorporate attractive forces due to trust and alignment via a potential $U(\mathbf{x}_1,…,\mathbf{x}_N)$, which in general can be written as a sum of pairwise potentials: $U = \sum_{i<j} U_{ij}(\mathbf{x}_i,\mathbf{x}_j)$. If agent $i$ and $j$ have a high alignment or trust, $U_{ij}$ will have a minimum (like a well) when $i$ and $j$ are “close” (interacting/cooperating), indicating an attractive force drawing them together. Mismatches yield either a shallow well or even an effective barrier (no attraction). The equations of motion for each agent can be written in Langevin form:

$$ m \frac{d^2 \mathbf{x}_i}{dt^2} + \gamma \frac{d \mathbf{x}_i}{dt} = -\nabla_i U + \sqrt{2D}\eta_i(t).$$

Here $m$ is a notional “mass” (which we can set to 0 for simplicity, treating the overdamped limit of motion), $\gamma$ is a damping constant, and the right side has two terms: $-\nabla_i U$ is the deterministic force on agent $i$ from the trust/alignment potential (the gradient of $U$), and $\eta_i(t)$ is a random force (Gaussian white noise) with strength related to a diffusion coefficient $D$ (which corresponds to the agent’s level of exploratory movement or interaction frequency). In plain terms, this equation says each agent wanders randomly but is pulled towards others with whom they have attractive potential. If two agents have a strong potential well between them (high mutual trust/interest), their random trajectories are biased towards finding each other and sticking together (like gravity drawing particles together). On the other hand, absent any attraction, $\nabla_i U \approx 0$ and the agent just diffuses randomly.

The corresponding Fokker-Planck equation describes how the probability density $P(\mathbf{x}_1,…,\mathbf{x}_N, t)$ of all agents’ positions evolves. In practice, that high-dimensional distribution is intractable, so we often simplify to either one-agent distribution (mean-field) or pair distributions. For illustration, consider a one-dimensional “alignment axis” $x$ for a single agent with a potential $V(x)$ representing attraction to a cluster center – perhaps $V(x)$ is lowest at the location representing a particular collaborative project’s focus. The Fokker-Planck equation for that agent’s position $x$ would be:

$$\frac{\partial P(x,t)}{\partial t} = D\frac{\partial^2 P}{\partial x^2} + \frac{\partial}{\partial x}\!\Big(\frac{1}{\gamma}\frac{dV}{dx} P\Big),$$

where the second term encodes drift of the agent toward the potential minimum (i.e. toward alignment with the cluster), and the first term is diffusive wandering. In multiple dimensions or many agents, it gets more complex, but qualitatively this captures probabilistic motion with attraction. For our model’s purposes, the main takeaway is that agents have a higher probability of coming together (colliding) if there is an attractive potential (trust/alignment) between them, and we can model the statistics of those encounters using such stochastic equations. We can also include thermal noise or randomness in decision-making – reflecting that even with alignment, collaboration might not occur unless circumstances allow (just as particles need to collide with sufficient energy to overcome any barriers).

2. Cluster Coagulation Equation (Smoluchowski-type)

On a higher level of description, we track the formation of collaborative clusters over time. We define $N_k(t)$ as before: the number of clusters (teams, projects, working groups) of size $k$ at time $t$. Initially, $N_1(0)=N$ (each person alone) and $N_{k>1}(0)=0$. As agents meet and decide to work together, clusters form and grow. We adapt the Smoluchowski coagulation equations to this social context. The general form in our model including both aggregation and fragmentation could be written as:

$$\displaystyle\frac{dN_{k}}{dt}= \frac{1}{2}\sum_{i+j=k}K(i,j)\,N_{i}N_{j}-N_{k}\sum_{j\ge1}K(k,j)\,N_{j}-F_{k}N_{k}+\sum_{j>k}F_{j}\,\Pi_{j\to k}\,N_{j}.$$

The first two terms (the classic Smoluchowski form) account for coagulation: clusters of size $i$ and $j$ merge to form size $k$ (the positive term) and size $k$ clusters merging with any other cluster to form larger ones (negative term). $K(i,j)$ is the aggregation rate kernel as discussed. The latter terms incorporate fragmentation: a cluster of size $k$ can break apart at rate $F_k$ (losing one or more members), and $\Pi_{j\to k}$ represents the probability that when a size-$j$ cluster fragments, one of the resulting pieces is of size $k$. For simplicity, one might assume clusters only lose one member at a time (akin to evaporation) or break into two parts. If a size $j$ cluster splits into an $k$ and $j-k$ cluster, we could have a term like $-\frac{1}{2}B(k,j-k)N_j$ for breakup and corresponding gain terms for $N_k$ and $N_{j-k}$. In any case, these terms allow the model to capture the dynamic equilibrium that might occur in a long-running collaboration network – new partnerships forming while some existing ones dissolve. In a well-functioning innovation ecosystem, we might actually expect a steady state where cluster formation and dissolution balance out, maintaining a certain distribution of project team sizes over time. Alternatively, with strong enough aggregation (high trust and interaction) and low fragmentation (high commitment), the model might not reach equilibrium but instead tend toward all agents ending up in one giant cluster (everyone connected in one network or one overriding initiative).

Notably, the kernel $K(i,j)$ is where we encode Strategic Doing principles in physics terms. Several considerations for $K(i,j)$ in our context:

  • Alignment/Trust Factor: If two clusters have very complementary goals or high mutual trust across their members, their chance of successfully merging is higher. We can let $K(i,j)$ include a factor $A_{ij}$ representing alignment (e.g. $A_{ij}$ could be the fraction of “asset types” or goals they share, or some measure of compatibility). In a crude binary sense, $A_{ij}=1$ if there is sufficient alignment to collaborate, otherwise $A_{ij}=0$. More smoothly, $A_{ij}$ might be proportional to the overlap in their strategic intent or their level of network tie strength. This is analogous to collision cross-sections in physics being larger when particles have complementary orientations or sticky surfaces.

  • Collision Frequency and Size: If we assume random mixing, the rate two clusters encounter each other is proportional to the product of their sizes (any member of cluster $i$ can meet any member of cluster $j$). This yields a kernel $K(i,j)$ proportional to $i\cdot j$ in a mean-field sense. However, real social mixing is not purely random; it could be assortative (like tends to meet like) or influenced by hubs. Preferential attachment would bias $K$ further in favor of large clusters merging (beyond the linear $ij$ factor). Our model could incorporate an exponent or factor: e.g. $K(i,j)=\beta\, i^{\alpha}\,j^{\alpha}$ for some $\alpha$ reflecting that well-connected groups find each other more (if $\alpha>1$). Alternatively, we might include network topology effects, but that leads to the next part (graph model). For now, one can calibrate $K(i,j)$ from empirical data or simulation: for instance, if we observe that collaborations tend to grow by accreting one member at a time (diffusion-limited cluster growth), we might use a simpler kernel where a cluster of size $j$ gains new single members at a rate proportional to $j$ (the number of “surface” connections it has). This is analogous to DLA where clusters grow mostly on their periphery. In that case, $K(i,j)\approx i+j\quad(\text{for }j=1)$ (assuming one of the clusters is size 1 typically).

  • Commitment (Binding Strength): Even if two clusters meet and are aligned, whether they actually merge depends on members’ commitment – analogous to whether colliding particles stick or bounce off. In physics, this could be a sticking probability or reaction rate less than 1. Here we can let commitment increase the effective $K(i,j)$ (high commitment means when people meet and see an opportunity, they actually go through with forming a project). Low commitment would mean many potential collisions don’t result in lasting clusters (people discuss ideas but never commit to action, so the cluster fails to form). One way to include this is to say $K(i,j)=\sigma\, i\,j$ where $\sigma$ is the probability of a successful “reaction” given a contact. $\sigma$ would be higher when commitment levels are high (perhaps due to a culture of accountability fostered by Strategic Doing’s methods). If commitment varies over time or with cluster size, that could be modeled too (e.g. very large clusters might have lower cohesion and thus higher chance to fragment – an effect we could integrate via the fragmentation rates $F_k$ growing with $k$ beyond some optimal size).

The Smoluchowski equation (with any added terms) is a mean-field, population-level model – it doesn’t track who is connected to whom, only how many groups of each size exist. To add more granularity, we turn to a network (graph) representation.

3. Graph-Theoretic Network Model

We can represent the evolving collaboration network as a graph $G(t)$ where each node is an individual (or asset) and each edge represents a direct collaboration or relationship (e.g. two people on the same project, or an established working connection). Initially, $G(0)$ might be empty or have only a few pre-existing links. As time progresses under Strategic Doing, edges are added as people link up through projects. We can formalize a simple stochastic network growth model: at each small time step $\Delta t$, each pair of nodes $(i,j)$ has some probability $p_{ij}$ to form a link (if not already connected) or an existing link has some probability $q_{ij}$ to drop (representing dissolution). The probabilities $p_{ij}$ should be functions of the factors we discussed – trust between $i$ and $j$, frequency of interaction, etc. For instance: $p_{ij}= \rho\,T_{ij}\,f\!\bigl(\text{alignment}\bigr)\,\Delta t$, where $T_{ij}$ is a measure of trust or tie strength between $i$ and $j$, and $f(\text{alignment})$ is some increasing function of how aligned their goals are. $\rho$ could be a base rate of interaction attempts (related to how often networking happens). If $i$ and $j$ never meet or communicate, $p_{ij}\approx 0$ despite high alignment; if they interact a lot, $p_{ij}$ increases. This aligns with our collision analogy: $\rho$ sets collision frequency, $T_{ij}$ and alignment set the “reaction likelihood” given a collision.

We can simulate such a network model (this becomes an agent-based Monte Carlo simulation approach). Over many runs, one can measure things like the distribution of cluster sizes (connected components in $G$) over time to validate against the Smoluchowski equations. One can also incorporate preferential attachment by making $p_{ij}$ larger if either $i$ or $j$ already has many connections (degree). This yields networks that might follow power-law degree distributions as seen in real collaborative networks. In fact, a network science study of Japanese firms introduced what is known as the MTT model, a framework that captures how real-world collaboration networks evolve through a combination of random link formation (spontaneous connections), preferential attachment (where well-connected firms attract even more links), and mergers of nodes representing corporate consolidations or partnerships. Remarkably, the structural evolution of this network could be accurately described using a Smoluchowski-type coagulation equation, which tracked changes in the degree distribution over time. This mathematical treatment demonstrated how microscopic interaction rules could explain macroscopic network behavior. We draw on these same principles in our model of Strategic Doing, where collaborators rather than firms form, merge, and grow project clusters governed by similar dynamics of trust, visibility, and alignment.

Encoding Strategic Doing principles: Now let’s ensure we have explicitly mapped the Strategic Doing concepts into the model parameters:

  • Linking and Leveraging Assets: This is represented by cluster aggregation – separate assets or people coming together to form a cluster (project). In equations, any term that causes small clusters to merge into bigger ones (the $K(i,j)N_i N_j$ term in Smoluchowski, or the $p_{ij}$ link formation in the network model) is essentially “linking and leveraging.” The rate at which assets link is accelerated by the structured process of Strategic Doing (short cycles, focus on action). We might incorporate a time-dependent $\rho(t)$ to model this – e.g. during a Strategic Doing workshop or sprint, the interaction rate $\rho$ spikes, leading to rapid link formation. After the session, $\rho$ might settle to a baseline (ongoing but slower network growth).

  • Framing Strategic Opportunities: In Strategic Doing workshops, participants identify an opportunity where they can collaborate (the What Could/Should We Do? leading to an Opportunity Framing). This is akin to nucleating a cluster around a shared goal. In physical terms, framing an opportunity creates a “seed” that lowers the energy barrier for aggregation. We can model this as introducing a potential well or an attractor in the interaction space. For example, suppose a small team frames an opportunity and commits to it – this can create a focal point that attracts other individuals who hear about it. In the agent-based model, that could be a region in state space that now has a stronger attractive pull (since a cluster exists there, exuding a “field” of success or excitement). In network terms, that seed team has connections to spare and is actively reaching out, so their high degree and enthusiasm increase $p_{ij}$ for others $j$ to join with any member $i$ of that team. In the Smoluchowski equation, an opportunity framing could be seen as externally setting a certain number of initial small clusters of size >1 at $t=0$ (if the workshop pre-forms teams), which then grow. Or it might effectively boost the kernel $K$ at early times by focusing attention on particular merge pathways (like giving people a shortlist of project ideas encourages mergers around those ideas rather than randomly).

In summary, the formal system of equations consists of: (i) the Langevin/Fokker-Planck describing agent motion and encounter probabilities under attractive social forces, (ii) the Smoluchowski aggregation-fragmentation equations for cluster size evolution, and (iii) a network model for link dynamics. These are different perspectives on the same underlying process. We can derive one from the other under certain assumptions. For instance, starting from the pairwise link formation model (iii), one can derive a mean-field equation for expected cluster counts, which recovers a form of Smoluchowski equation. Likewise, one can derive the link formation probabilities $p_{ij}$ from integrating the Langevin equations’ hitting probabilities (basically computing how often two random-walking agents with an attractive force will meet per unit time). Doing so rigorously is complex, but qualitatively we can assert: greater trust (deeper potential well) $\rightarrow$ higher meeting and sticking rate $\rightarrow$ higher $K(i,j)$ for those agents; greater interaction frequency (higher $D$ or more mixing) $\rightarrow$ more collisions $\rightarrow$ $K(i,j)$ effectively higher system-wide.

By presenting the model at multiple levels, we ensure we capture both the micro-level (individual behavior and decisions) and macro-level (emergent network structure) dynamics. Next, we discuss what this model teaches us and walk through an example scenario to illustrate its predictive power.

Evolving Collaboration Networks: Insights and Predictions

The physics-inspired model of Strategic Doing offers several predictive insights about when and how agile collaboration networks emerge, thrive, or collapse. By analyzing the equations and running simulations, we can identify key conditions for a sustainable innovation ecosystem. Here are some of the notable implications:

  • Critical Mass and Rapid Emergence: The model predicts a threshold behavior similar to a phase transition. In the early stages of Strategic Doing, you may have many small clusters (teams of 2–3) working in parallel. As trust builds and more connections are made, the system can reach a tipping point where clusters start to coalesce into larger components. Percolation theory suggests that beyond a certain connectivity (e.g. each person on average collaborating with >1 others), a giant component spanning most participants is likely. Practically, this means that initial Strategic Doing efforts might feel fragmented, but if participants persist in making new connections and inviting others, suddenly a more coherent network will emerge. For example, in a regional innovation network, you might see multiple small projects around entrepreneurship. If a few bridging individuals link these projects (say by co-hosting events or sharing resources), the network can “snap” into a unified cluster where knowledge and talent flow freely across what used to be separate groups. This emergence often appears rapid – an insight for leaders to monitor network metrics (like cluster size or connectivity) and recognize when the system is near critical mass. Interventions like a large group workshop or a shared digital platform can provide the final push to achieve full network percolation.

  • Role of Trust (Potential Energy) in Sustaining Networks: Trust enters our model as an attractive potential well. One clear prediction is that high trust leads to larger and more stable clusters. Mathematically, deeper potential wells mean agents are more strongly bound, analogous to particles requiring more energy to break apart. Thus, collaborations with strong mutual trust (and clear mutual benefit) will last longer (low fragmentation rates $F_k$) and likely grow bigger (since outsiders see a low-risk, high-reward opportunity in joining, effectively raising $K(i,j)$ with those clusters). Conversely, if trust is low or fragile, clusters might form (especially if pushed by external facilitation) but then dissolve quickly – much like a weakly bound molecule that falls apart on slight perturbation. The model thus underscores the importance of trust-building as a strategic variable: investments in relationship-building (social capital) are analogous to deepening the attractive potential wells, which in turn lowers the likelihood of network fragmentation. If trust can be quantified (some studies attempt to measure trust levels in groups), the model could use that as input to predict collaboration half-lives or the probability of long-term network coherence.

  • Commitment and Binding Energy: Similarly, commitment (modeled as binding strength or sticking probability) influences network survival. A prediction here is the existence of a minimum commitment threshold for sustainable collaboration. If participants treat commitments casually (low binding strength), the fragmentation rate will be high – clusters break before yielding outcomes, and the network may regress to isolated individuals. On a graph, this appears as edges that flicker on and off, never solidifying a giant component. However, once commitment crosses a threshold (people reliably follow through on their 30/30 tasks, etc.), clusters become robust enough to accumulate into a giant cluster. In formula terms, if we denote average commitment as $\bar{\sigma}$ in $K(i,j)$, there might be a critical $\bar{\sigma}_c$ needed for the giant component to persist. This aligns with Strategic Doing’s emphasis on making actionable commitments every cycle – it’s essentially ensuring $\sigma$ is high so that the theoretical links become real collaborations.

  • Path-Dependence and Diffusion-Limited Growth: Because our model allows for diffusion-limited aggregation, it suggests that the order in which connections happen can shape the network’s structure. For instance, if a particular cluster captures a lot of early attention (like one project becomes very popular), it can become a dominant hub – subsequent aggregation tends to happen onto that cluster (a hub-and-spoke network forms). Alternatively, if growth is more evenly distributed (several clusters grow in parallel and later connect), the final network may be more decentralized. This implies that early strategic choices or lucky encounters can lock in certain network topologies. It’s a double-edged sword: a highly central hub can boost efficiency (everyone connected through a key facilitator) but is also a single point of failure (if that hub fails or leaves, the network may fragment). The model can highlight such vulnerabilities by showing, for example, that removing the highest-degree node in a preferentially grown network dramatically raises the fragmentation probability. For Strategic Doing practitioners, this insight advocates for intentionally nurturing multiple connection pathways (so the network isn’t solely reliant on one champion). It also emphasizes an experimental mindset early on – small wins can cascade, but one should be mindful of where those cascades are leading structurally.

  • Speed of Network Formation: The interplay of interaction frequency and cluster dynamics in the equations gives an estimate of how fast a fully networked state can form. If we dial up the “collision rate” (more frequent meetings, workshops, communications), the time to reach a giant component decreases. There are diminishing returns, however: beyond some point, throwing more interactions at the system can saturate people’s capacity (there’s a limit to how many ties a person can maintain – akin to a physical saturation when too many collisions cause congestion). Our model might show that an optimal interaction frequency maximizes sustainable links without causing overload or superficial connections. This could guide scheduling of Strategic Doing cycles (maybe a 30-day cycle is chosen because it’s near optimal for giving people time to act and then reconnect – too short and they can’t follow through, too long and momentum fades).

  • Fragmentation and Network Dissolution: Under what conditions might a previously thriving collaboration network break down? The model can simulate scenarios of shock or gradual decay. For example, if trust diminishes (perhaps due to a conflict or external stress) we can simulate the potential wells becoming shallower or turning repulsive. The Smoluchowski model with fragmentation would then show cluster sizes shrinking over time. Similarly, if interaction frequency drops (people stop meeting – think of what happened to many networks during the early pandemic lockdowns except via virtual means), then new link formation $K(i,j)$ plummets, and without fresh links, existing clusters might eventually dissolve due to entropy or member turnover. These “what-if” experiments highlight that networks are not static – continuous effort is needed to maintain the bonds (which aligns with Strategic Doing’s continuous cycles of check-ins and making new commitments). If a community sees their agile network faltering, the model directs attention to likely levers: rebuild trust, increase communication, or reinforce commitment with quick wins to restore the attractive forces and collision rates.

Example Scenario: To make this more concrete, let’s walk through a hypothetical application of the model. Imagine an innovation cluster in a mid-sized city trying to foster an entrepreneurial ecosystem (a real-world context where Strategic Doing is often applied). Initially, there are 50 individual stakeholders (entrepreneurs, faculty, economic development folks), largely unconnected (“monomers” in our model). They hold a Strategic Doing workshop, where in the first session they identify 5 opportunity areas (say, a startup mentorship program, a co-working space, a tech meetup series, etc.). These serve as seeds (nuclei) – small teams form around each idea, so by the end of the workshop we have, say, 5 clusters of size ~5 and some individuals still unclustered. Over the next 6 months, these teams meet regularly (30/30 cycles). According to our model, during this period the network parameters are: trust increasing within each team (strong intra-cluster attraction), commitment is high (teams deliver some quick wins, which further deepen trust – positive feedback in $K$), and interaction frequency among different teams is moderate (they occasionally share progress at community events, introducing some inter-cluster collisions).

Now, input these conditions into a simulation: each of the 5 clusters grows by recruiting a few new members (some of the initially unclustered folks or newcomers from the community). Small clusters occasionally merge – perhaps the mentorship team and co-working space team realize they can join forces to run a combined startup hub (clusters merge into one larger cluster). The Smoluchowski equation would show the count of clusters dropping from 5 to 4 to 3… with one cluster maybe reaching ~15-20 people. Eventually, we might get 2 large clusters that encompass most participants. At this juncture, consider percolation: maybe these two clusters connect via one key individual who is involved in both. Once that happens, a single giant cluster of ~50 forms – effectively an ecosystem network where everyone is indirectly connected. The model predicted that around month 9, given the rates, a giant component would emerge. Indeed, in our scenario, by month 9-12, the community perceives a tangible network: people from different original teams are collaborating, information is flowing freely, and the effort is self-sustaining (less facilitation needed to drive connections). If we charted cluster size over time, we’d see a steep inflection when these merges happen – reminiscent of a phase transition curve.

Now, suppose a year later, funding dries up for the co-working space and a few leaders move away. Trust suffers slightly (some unmet expectations), and interaction frequency drops (no central co-working hub to meet at daily). The model could be used to anticipate potential fragmentation: e.g., if commitment from remaining members isn’t reinforced, we might see the giant cluster break into two medium clusters (perhaps a tech sector group and a social-impact startups group separate). Recognizing this, facilitators could intervene: organize a renewal Strategic Doing session to re-formulate shared goals (strengthening the potential wells of trust and alignment) and to encourage new links (maybe spin up a new initiative that involves members from both subgroups, preventing the split). In other words, the model not only predicts outcomes but also suggests interventions to maintain network coherence.

Practical Implications for Network Leadership and Innovation Governance

Translating these theoretical insights to practice, several recommendations emerge for those guiding agile collaboration networks (e.g. backbone organizations of innovation ecosystems, community leaders, or Strategic Doing practitioners):

  • Measure and Nurture Trust: Since trust acts like a binding energy in our model, it is a critical lever. Tools like network surveys or social capital audits can gauge the trust and relationship strength within the group. Leaders should prioritize trust-building activities – for example, encourage transparency, small joint wins, and mutual respect – especially in early phases. The model indicates that even a modest increase in overall trust can dramatically increase cluster stability and growth. Trust effectively “lowers the activation energy” for collaboration; investments here have a multiplier effect on all other processes.

  • Facilitate Frequent, Quality Interactions: Strategic Doing already emphasizes regular check-ins (30/30). The model reinforces this: frequent interactions correspond to higher collision rates, meaning more opportunities for partnerships to form. However, quality matters too (alignment during those collisions). So designing events and forums that bring diverse but complementary people together is key – akin to increasing not just the quantity of collisions, but the fraction that are high-energy and head-on (leading to bonding). This might involve curated workshops, cross-sector mixers, or shared digital collaboration spaces. Essentially, be deliberate in stirring the “social mixture” so that random motion becomes productive motion.

  • Identify and Support Network “Seeds”: Just as certain particles can act as nucleation centers for crystals, certain ideas or teams can nucleate a larger collaboration network. When framing strategic opportunities, facilitators should look for ideas that have broad appeal and multiple entry points (so they can readily attract others). The model suggests these seeds create potential wells drawing in more participants. Once identified, support these nascent clusters with resources and visibility; they will serve as the scaffolding of the emergent network. Additionally, encourage these clusters to be open (porous boundaries) so that new members can attach – this is like ensuring the surface of a cluster remains “sticky.” In Strategic Doing terms, avoid cliquishness; keep inviting fresh contributions.

  • Watch for Phase Transition Signals: Network leaders should monitor metrics such as the size of the largest cluster, the fraction of participants engaged in collaborations, or the average degree of the network. A sudden uptick in these could indicate the network is nearing a critical connectivity threshold (the percolation point). That is a moment to reinforce success – celebrate the emerging network identity – and perhaps formalize structures to support the now larger community. Conversely, if growth stalls below the threshold (many small clusters but none connecting), that may signal a need for an intervention (like a “network weaver” connecting clusters, or addressing a trust gap between groups).

  • Use the Model as a Policy Simulator: The equations and agent-based models can be turned into simulation tools. Leaders could simulate scenarios like “What if we doubled the frequency of our meetups?” or “What if trust deteriorates in one subgroup?” to see potential outcomes. While not perfectly predictive (people are not identical particles, of course), the simulation can highlight qualitative trends (e.g. diminishing returns of too many meetings, or the fragility if one hub is removed). This can inform strategy for network governance. For instance, the model might show that beyond a certain cluster size, fragmentation risk increases unless governance structures (norms, roles) are implemented – which could prompt establishing a light coordination team when projects grow past 10 people.

  • Resilience Through Redundancy: The attractive-repulsive force analogy (from the multicultural network example) reminds us that too much homogeneity (all attraction, no repulsion) can lead to one giant cluster that might suppress diversity. On the other hand, too much repulsion (groups not trusting each other at all) leads to fragmentation. A balance is ideal: one can foster multiple clusters that are distinct (different approaches, maintaining diversity) yet still connected by some long-range attraction (shared higher goal or values). In practice, this means pursue a portfolio of projects under a unifying vision. Let teams operate semi-autonomously (to maintain creativity – a bit of “repulsive” force preventing total consensus), but ensure regular cross-pollination and a shared narrative (so that there remains attraction keeping the whole network cohesive). The physics analogy of short-range repulsion and long-range attraction could be intentionally applied by network designers to keep an ecosystem both cohesive and innovative.

Limitations and Further Research

While the physics-inspired model provides a rich framework, it’s important to acknowledge its limitations and the need for empirical validation:

  • Oversimplification of Human Behavior: Unlike colloidal particles, humans have agency, emotions, and complex decision-making processes. Our model treats interactions in a probabilistic, average sense – which may overlook individual strategic behavior, power dynamics, or institutional constraints. For example, the model doesn’t explicitly include a scenario where an individual might refuse to collaborate even if trust and alignment are high (maybe due to politics or ego). Nor does it capture the role of strong leadership or vision, which in real life can dramatically alter network trajectories. Future refinements could integrate insights from behavioral science or game theory, perhaps coupling our physics model with an economic utility model for decisions to join or leave collaborations.

  • Parameter Estimation and Data: The model introduces parameters like trust (potential depth), alignment (perhaps quantifiable via surveys or topical interest overlap), interaction frequency, commitment level, etc. Estimating these for a real network is challenging. One might calibrate the model using network analysis data – e.g. measure how the number of collaborations grew over time in a known Strategic Doing case study and fit $K(i,j)$ or $\rho$ to that. This requires data that is often hard to obtain (one would need detailed longitudinal network maps from communities employing Strategic Doing). Empirical validation is still an open question: do the cluster size distributions or connectivity transitions in real cases follow the patterns predicted? Collecting such data and comparing to model output would be a valuable research contribution.

  • Dynamics Not in Equilibrium: Many physics models assume a kind of equilibrium or steady state, but social systems may continuously evolve or undergo one-time shifts. Our model can handle dynamic changes, but it’s sensitive to assumptions (e.g. we assumed certain forms for $K(i,j)$ or fragmentation rates). It might need extension to handle non-stationary conditions – for instance, if an external shock like a pandemic hits (suddenly $\rho$ drops, trust potentially drops, etc.), the model should accommodate time-varying parameters. Similarly, Strategic Doing itself might evolve (the rules might change or new tools added), affecting the “rules of interaction” in ways outside our current model.

  • Network Topology Considerations: We largely discussed clusters by size, but networks can have different topologies even for the same size distribution – e.g. a cluster of 10 could be tightly knit (everyone connected) or loosely knit (a line or tree structure). Our macro model doesn’t distinguish these, but they matter for information flow and resilience. Graph theory offers metrics like clustering coefficient, centralization, modularity, etc. Future work could integrate these to differentiate between a highly centralized giant cluster versus a decentralized one, even if both have 50 nodes. Different structures might correspond to different outcomes (a centralized network might innovate faster under one strong leader, but a decentralized might be more resilient and creative). Tuning the model to favor certain topologies (perhaps via adding a term for triadic closure or group clustering propensity) could make it more realistic.

  • Algorithmic Implementation: To actually use this model, one might create an agent-based simulation or solve the differential equations numerically. This technical implementation is another step. Some complexity (like solving the full Smoluchowski with fragmentation analytically) might be intractable and require approximations or numerical simulations. Fortunately, computational power today allows multi-agent simulations that were not possible before. As a result, one promising direction is to build a Strategic Doing simulator that allows users to input parameters (number of people, estimated trust matrix, etc.) and then generates Monte Carlo outcomes of network evolution. This could be a teaching tool or a planning aid. The work by Goto et al. (2018) demonstrates that even complex network merging processes can be simulated and yield insights (like detecting when a “giant node” appears intermittently). A similar approach could be taken for collaboration networks.

  • Interdisciplinary Calibration: The model spans concepts from physics, sociology, and organizational science. Collaborating with experts in each domain could refine the analogies. For instance, social network theorists might suggest additional factors (like homophily – people tend to connect with similar others – which could be seen as an “entropic” factor or an energy landscape with multiple wells). Likewise, physicists might point out analogies to other systems: e.g. chemical reaction kinetics (two agents react to produce a “product” collaboration, akin to $A+B \to C$ reactions) or epidemic models (ideas spreading through contact, analogous to infection, which could complement our approach). By incorporating such analogies, we can enrich the model (for example, viewing the spread of a collaborative culture as an epidemic on the network, alongside the aggregation process).

Conclusion

This physics-grounded model of Strategic Doing is a theoretical step toward understanding agile networks through a new lens. It provides a language of “particles and forces” to discuss how loosely connected actors self-organize into productive clusters and how those clusters intersect to form an ecosystem. While theoretical, it offers conceptual clarity: we can talk about trust as potential energy, commitment as bond strength, interactions as collisions – making the abstract process of network-building a bit more concrete. Moreover, it hints at universal behaviors (like critical mass thresholds and power-law cluster size distributions) that might underlie many collaborative systems, whether in innovation districts, research consortia, or community development initiatives. By bridging Strategic Doing with colloidal physics and network science, we not only enrich the strategic toolkit with predictive modeling, but we also contribute to the broader idea that social innovation can be studied with the same rigor as natural phenomena. The ultimate goal is that such models, once validated, will help practitioners design better interventions – effectively allowing them to “tune the dials” of their collaboration systems (trust, interaction, commitment) to catalyze sustainable, adaptive networks that can meet the complex challenges of our time.

AI Assistance Statement

This work was developed with the support of ChatGPT’s reasoning models and deep research capabilities, which assisted in synthesizing theoretical frameworks, identifying relevant literature, and refining the structure and clarity of the manuscript.

References

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About the author

Dr. Ubaldo M. Córdova-Figueroa is a chemical engineer, strategist, and academic leader whose work spans scientific research, public-sector reform, and entrepreneurial innovation. He is the Founder and CEO of Acerola Strategies LLC and former Executive Vice President for Academic Affairs and Research at the University of Puerto Rico, where he led digital and academic transformation initiatives. A professor at UPR–Mayagüez and NSF CAREER awardee, he has helped secure over $40 million in R&D investments and is known for advancing inclusive innovation and strategic collaboration in Puerto Rico and beyond.

Ubaldo M. Córdova-Figueroa https://www.ubaldocordova.com
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