Directionality-Induced Jamming

• Directionality-induced jamming is a phenomenon where asymmetric couplings in interconnected systems suppress global transport even as individual subsystems remain well-connected.
• It is characterized by the spectral gap closure in the system’s interaction matrix, showing how directed interlayer interactions can fragment dynamic flows.
• These insights enable control strategies across fields such as multiplex networks, wireless communications, and mechanical systems, guiding both jamming and anti-jamming designs.

Directionality-induced jamming refers to the suppression or complete arrest of transport phenomena—such as diffusion, flow, or signal propagation—arising solely from the directional asymmetry or structure of couplings between subsystems, agents, or network layers. Unlike classical jamming, which is typically caused by local bottlenecks, density, or external blockages, directionality-induced jamming is emergent, mathematically rooted in spectral properties, and driven by the orientation or asymmetry of coupling terms even when the individual subsystems remain uncongested or undirected.

1. Conceptual Foundations and Definition

Directionality-induced jamming manifests when asymmetric (often directed) couplings block steady-state transport between otherwise well-connected subsystems. This generic phenomenon occurs in systems spanning multiplex networks, granular media, mobile and wireless sensor networks, mmWave communications, pedestrian dynamics, and mechanical assemblies.

Critical to this definition is the distinction between internal subsystem connectivity (layers, agents, or particles) and inter-subsystem connectivity. Directionality-induced jamming requires that:

• Each subsystem is internally undirected/connected (e.g., both network layers are undirected and connected, or all pedestrian corridors are unobstructed).
• Directed or asymmetric couplings between subsystems prevent or strongly hinder global convergence, flow, or transport.

The suppression is fundamentally linked to the spectral structure of the system's interaction matrix (e.g., supra-Laplacian for networks, Hessian for granular matter, wireless channel matrices) and does not rely on physical barriers or external congestion.

2. Mathematical Modeling in Multiplex Networks

The archetypal setting is diffusion on multiplex networks (Bouchet et al., 26 Oct 2025), representing systems with multiple layers (e.g., modes of urban transport, communication channels, biological pathways) interconnected via directed interlayer links.

State Representation and Dynamics

For a multiplex network of two layers (each with $N$ nodes):

$$\mathbf{x}(t) = (x_1 | x_2)^T,\qquad \frac{d\mathbf{x}}{dt} = -\mathcal{L} \mathbf{x}$$

Here, $\mathcal{L}$ is the supra-Laplacian comprising intra-layer Laplacians ($L_1$, $L_2$) and interlayer connections.

Interlayer Directionality Mechanisms

• Induced Directionality: Asymmetric interlayer diffusion rates, $D_{12} \neq D_{21}$, on otherwise undirected interlayer links. Supra-Laplacian structure:

$$\mathcal{L} = \begin{pmatrix} L_1 & 0 \ 0 & L_2 \end{pmatrix} + D_{12} \begin{pmatrix} I & -I \ 0 & 0 \end{pmatrix} + D_{21} \begin{pmatrix} 0 & 0 \ -I & I \end{pmatrix}$$

• Topological Directionality: Directed interlayer links via diagonal matrices $\Delta_1, \Delta_2$:

$$\mathcal{L} = \begin{pmatrix} L_1 & 0 \ 0 & L_2 \end{pmatrix} + D_X \begin{pmatrix} \Delta_1 & -\Delta_1 \ -\Delta_2 & \Delta_2 \end{pmatrix}$$

Spectral Characterization

The long-term transport is governed by the spectrum of $\mathcal{L}$, notably the smallest nonzero eigenvalue $\Lambda_2$:

• Superdiffusion and Prime Regime: Asymmetry can yield non-monotonic dependence of $\Lambda_2$ on coupling, producing faster-than-layer relaxation (prime regime).
• Jamming Regime: For strong directed coupling ($D_X \to \infty$), $\Lambda_2 \sim 1/D_X$ vanishes—diffusion halts, and the system fragments into disconnected dynamic components.

Perturbative analysis confirms that, even as coupling strengthens, directed interlayer links can restore degeneracies (zero modes) associated with multiple dynamically disjoint sectors.

3. Directionality-Induced Jamming in Physical and Information Systems

Wireless Communications

• RIS-based selective jamming: Reconfigurable Intelligent Surfaces (RIS) enable attackers to induce jamming selectively via environment-adaptive spatial control (Mackensen et al., 21 Feb 2024). Maximizing jamming energy to targets ($\mathcal{T}$) and minimizing to non-targets ($\mathcal{N}$), optimized RIS reflection phases can suppress only specific devices—even at millimeter separation.
• Massive MIMO and mmWave networks: Systems exploiting angular domain sparsity can both detect and suppress jamming via directional information; excluding the jammer’s angular subspace from channel estimation restores high spectral efficiency (Bagherinejad1 et al., 2021).

Networked Sensing

• Cooperative anti-jamming via direction estimation: Networks of sensing nodes estimate the direction of the jamming channel (not full CSI) using pilot signals, then null out the jamming subspace (via projections) (Mehrabian et al., 20 Jul 2025). This preserves spatial DoF and suppresses jammers as long as the number of sensors exceeds jammers, with minimal SNR penalties.

Mechanical and Crowd Systems

• Pedestrian flow: Directionality in flow (bidirectional vs. unidirectional) combined with attraction-driven clustering can induce distinctive jamming transitions: abrupt freezing in bidirectional scenarios, extended or localized jams in unidirectional regimes (Kwak et al., 2017).
• Granular media and sheared assemblies: Shear jamming, a form of directionality-induced rigidity, arises when anisotropic stresses form persistent force networks below the isotropic jamming density (Pan et al., 2023, Bertrand et al., 2015). In frictionless spheres, the protocol-induced jamming is a finite-size effect and vanishes for large systems.

4. Analytical Results and Numerical Demonstration

Rigorous analytical results clarify the emergence and mechanisms of directionality-induced jamming:

• Spectral gap closure: As directed coupling increases, the spectral gap $\Lambda_2$ closes asymptotically ($\Lambda_2 \sim 1/D_X$). This marks the loss of global steady-state in diffusion and signals fragmentation into dynamically isolated blocks.
• Eigenvalue trajectories and blocking patterns: Simulations on synthetic and real networks (e.g., transport networks) visualize and confirm the analytical predictions; numerical optimization (e.g., simulated annealing) can tune directed couplings to maximize jamming even under complex topologies.

5. Control, Design, and Optimization Strategies

Directionality offers a versatile lever for system control:

• Optimization for jamming: Directed interlayer weights can be tuned via simulated annealing, maximizing a jamming-specific objective while preserving strong global connectivity, thus driving the system into directionality-induced jamming (Bouchet et al., 26 Oct 2025).
• Beamforming and trajectory selection: Coordinated UAVs control antenna phase, orientation, and flight path to maximize jamming at eavesdroppers while nulling interference at friendly clients, computed in closed form (Fotiadis et al., 24 Aug 2025).
• Null-space methods in wireless: By estimating the direction/subspace of the jamming channel, information systems use projection matrices to suppress interference, with scalability limited by available spatial DoF (Mehrabian et al., 20 Jul 2025).

6. Implications, Applications, and Open Problems

Directionality-induced jamming has broad practical and theoretical relevance:

• Critical systems: Urban infrastructure, cyberphysical networks, and transportation grids—where process flows depend on multichannel interconnectivity—require careful design of interlayer link directionality to prevent fragmentation or to throttle congestion.
• Wireless denial and security: Selective jamming enables sophisticated denial-of-service (DoS) attacks, but also defensive strategies in security contexts. RIS and UAV beamforming technologies exemplify new degrees of freedom for both attackers and defenders.
• Non-equilibrium phase transitions in amorphous matter: Directionality expands the mechanical response landscape, connecting shear thickening, fragility, dilatancy, and yielding transitions to jamming.
• Predictive theory: A major open challenge remains the structural prediction of jamming-capable configurations purely from network or system topology.

7. Summary Table: Key Mechanisms and Mathematical Signatures

Mechanism	Model Parameters	Jamming Signature
Asymmetric interlayer coupling	$D_{12} \neq D_{21}$, undirected intralayer links	Prime regime, superdiffusion
Directed interlinks/topology	Diagonal matrices $\Delta_1, \Delta_2$	$\Lambda_2 \sim 1/D_X$, freezing
RIS-based spatial control	Binary phase configurations $\{c_l\}$	Subwavelength selectivity
Null-space projection (MIMO)	Estimated direction(s) of jamming channel	SINR near no-jammer case
Shear-induced jamming	Shear strain $\gamma$, anisotropic force networks	Onset below isotropic threshold

• Directionality-induced jamming in multiplex networks (Bouchet et al., 26 Oct 2025)
• Spatial-Domain Wireless Jamming with Reconfigurable Intelligent Surfaces (Mackensen et al., 21 Feb 2024)
• Direction-Based Jamming Detection and Suppression in mmWave Massive MIMO Networks (Bagherinejad1 et al., 2021)
• Enhancing Resilience Against Jamming Attacks: A Cooperative Anti-Jamming Method Using Direction Estimation (Mehrabian et al., 20 Jul 2025)
• Coordinated UAV Beamforming and Control for Directional Jamming and Nulling (Fotiadis et al., 24 Aug 2025)
• Protocol dependence of the jamming transition (Bertrand et al., 2015)
• A review on shear jamming (Pan et al., 2023)
• Jamming transitions induced by an attraction in pedestrian flow (Kwak et al., 2017)

Directionality—through induced asymmetry, topological design, or physical orientation—emerges as a fundamental and pervasive determinant in jamming phenomena. Its manipulation offers both practical tools and conceptual challenges for steering collective behavior in complex engineered and natural systems.