arXiv subjects

Satori Tsuzuki

Publications and source records attributed to Satori Tsuzuki.

At least 19 recordsLinked to original sources

arXiv2026

Finite-resolution exhaustive traversal of thermodynamic state spaces has divergent thermodynamic length

Mapping an entire multidimensional thermodynamic control region is fundamentally different from driving a system between prescribed endpoints. We formulate such mapping as a finite-resolution coverage problem: a rectifiable protocol must come within thermodynamic distance $\varepsilon$ of every point in a regular $d$-dimensional state-space window. A covering argument shows that the required thermodynamic length grows at least as $\varepsilon^{(1-d)}$. Hilbert- and Peano-type finite traversals attain the same exponent, demonstrating that it is fixed by the codimension of a curve rather than by a particular scanning construction. When the coverage metric is a physical friction tensor, or is uniformly dominated by one, this geometric law implies a slow-driving resource constraint: at fixed duration, the quadratic excess-work cost grows at least as $\varepsilon^{(2(1-d))}$, whereas at fixed excess-work budget the required duration grows with the same power. We derive microscopic friction metrics for a detailed-balance three-state Markov jump process and an overdamped harmonic trap. Raster scans of the trap illustrate how refinement costs can appear either as excess work or as acquisition time, depending on the allocation of time along the protocol. Finite experimental or numerical resolution cuts off the continuum divergence, while singular thermodynamic response can additionally modify the prefactor according to a directional-integrability criterion. Morton/Z-order traversal preserves the universal exponent but increases locality-dependent amplitudes. These results establish finite-resolution state-space coverage as a resource problem distinct from endpoint-to-endpoint thermodynamic control.

cond-mat.stat-mech↗

arXiv2026

Curvature-weighted spectra anticipate dissipation peaks in decaying three-dimensional turbulence

We investigate the robustness of a curvature-weighted spectral precursor to dissipation in freely decaying three-dimensional incompressible turbulence. Building on our recent work in \emph{Physical Review Fluids} on the Taylor--Green vortex, we analyze direct numerical simulations using the shell-summed curl-of-vorticity spectrum, denoted here by $\mathcal{C}_{4}(k,t)$ and equivalent to a $k^4$-weighted energy spectrum in the modal incompressible sense. Extending the study across multiple initial conditions -- multi-mode ABC flows, a randomized low-wavenumber ABC field, the Taylor--Green vortex, and the Kida--Pelz flow -- we find a consistent temporal ordering: the characteristic time associated with the advance and saturation of the peak wavenumber of $\mathcal{C}_{4}(k,t)$ precedes the dissipation-peak time, which in turn precedes the characteristic time associated with the peak scale of the nonlinear energy-flux spectrum. We further probe Reynolds-number and scale-separation effects using Taylor--Green simulations at additional viscosities: the precursor ordering persists when adequate scale separation and resolution are maintained, but can change in the low-$R_λ$/limited-scale-separation regime. Throughout, we use explicit inspection of curvature-weighted spectra to distinguish physical peak evolution from cutoff-proximate artifacts. These results support robustness over the deterministic decaying-flow initial conditions examined here and clarify the practical role of Reynolds number, scale separation, and resolution when using curvature-weighted spectral diagnostics in decaying turbulence.

physics.flu-dyn↗

arXiv2026

Extreme-value statistics of curl-of-vorticity precursor peaks in perturbed Taylor-Green vortex turbulence

Precursor peaks in the wavenumber $k_{\mathrm{peak}}(t)$ maximizing the curl-of-vorticity spectrum have been observed to precede the dissipation peak in decaying turbulence. Because small perturbations in the initial condition can shift peak times, the associated lead time should be characterized statistically. We perform a pseudospectral DNS ensemble of $N_s=1000$ perturbed Taylor--Green vortex realizations at $N=256^3$ and $ν=10^{-3}$. For each run we extract $k_{\mathrm{peak}}(t)$, several definitions of the precursor time $t_k$, the dissipation-peak time $t_\varepsilon$, and run-wise extrema including $K_{\max}=\max_t k_{\mathrm{peak}}(t)$ and $M_{\max}=\max_t\max_k \mathcal{C}(k,t)$, where $\mathcal{C}(k,t)$ is the isotropic curl-of-vorticity spectrum. The distribution of $Δt_{\varepsilon,k}=t_\varepsilon-t_k$ shows that the precursor typically leads, while rare lagging realizations occur and are strongly conditioned on $K_{\max}$. Using peaks-over-threshold extreme-value theory, we fit generalized Pareto models to the right tails of $X=-Δt_{\varepsilon,k}$ and $M_{\max}$; the negative shape estimates are consistent with effective bounded tails under the present finite-resolution sampling protocol and provide protocol-dependent endpoint estimates. Finally, $M_{\max}$ correlates strongly with $\varepsilon_{\max}$ and ensemble cross-correlations reveal a reproducible phase offset, consistent with an empirical association between high-curvature activity and dissipation bursts.

physics.flu-dyn↗

arXiv2026

Retained-spin micropolar hydrodynamics from the Boltzmann--Curtiss equation

We derive a retained-spin micropolar hydrodynamic closure from the Boltzmann--Curtiss equation using a generalized Chapman--Enskog construction in which the local mean spin is retained as a quasi-slow variable. Starting from the one-particle kinetic balance identities and the corresponding exact coarse-grained finite-size balances for mass, linear momentum, and intrinsic angular momentum, we keep the collisional-transfer contribution to the antisymmetric stress explicit in the spin balance, decompose the first-order source into irreducible scalar, axial, and symmetric-traceless sectors, and show explicitly how the standard micropolar constitutive structure with coefficients $(η,ξ,η_r,α,β,γ)$ emerges. This decomposition makes clear that the one-particle kinetic stress contributes only to the symmetric stress, whereas the rotational viscosity belongs to a collisional-transfer channel. For perfectly rough elastic hard spheres, we further obtain explicit dilute-gas estimates for the rotational viscosity $η_r$ from homogeneous spin relaxation and for the transverse spin-diffusion combination $β+γ$ from a transport-relaxation calculation. Targeted event-driven molecular-dynamics simulations are used as a posteriori checks: expanded homogeneous-spin density and roughness sweeps support the predicted $n^2$ and $K/(K+1)$ trends for $η_r$, while finite-$k$ transverse runs provide a qualitative diagnostic of the retained-spin response. The result is a self-contained derivation and coefficient-level estimate of retained-spin micropolar hydrodynamics that clarifies which parts of the closure are exact balance-law statements, which are first-order generalized Chapman--Enskog results, and which remain controlled rough-sphere estimates.

cond-mat.soft↗

arXiv2026

Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures

High-curvature observables in incompressible flows, including $k^4$-weighted spectra, can arise from explicit internal rotation, elimination of a fast spin variable, or polynomial higher-gradient closure. Building on a retained-spin micropolar closure derived separately from the Boltzmann--Curtiss equation, we show that these mechanisms are dynamically distinguishable in transverse linear response. In a fast-spin regime the retained-spin theory reduces to a one-field model with a rational $k$-dependent kernel whose low-$k$ expansion generates $k^4$ and $k^6$ terms, while preserving the large-$k$ roll-off of the eliminated degree of freedom. We compare four closures: incompressible Navier--Stokes, a polynomial Burnett-type surrogate, the explicit-spin micropolar theory, and the eliminated-spin rational-kernel theory. The explicit-spin theory has two poles, the eliminated-spin theory retains only the slow pole, and finite polynomial truncations fail qualitatively: a strict $k^4$ truncation becomes over-damped, while a matched $k^6$ truncation develops near-critical amplification and finite-$k$ instability. Many-particle event-driven simulations of perfectly rough spheres show that these observables are measurable and, in targeted campaigns, discriminating at the microscopic level: fixed-$k$ and multi-$k$ harmonic forcing resolve a finite spin-to-vorticity phase lag that strongly favors retained-spin dynamics over instantaneous adiabatic elimination, while the stronger-drive multi-$k$ vorticity response rejects a pure $k^2$ closure and favors the rational eliminated-spin kernel over a polynomial surrogate. Transverse response thus provides a practical diagnostic for separating retained rotational microphysics, eliminated-spin effective dynamics, and ordinary polynomial higher-gradient closures.

physics.flu-dyn↗

arXiv2026

Entropy stability analysis of smoothed dissipative particle dynamics

This article presents an entropy stability analysis of smoothed dissipative particle dynamics (SDPD) to review the validity of particle discretization of entropy equations. First, we consider the simplest SDPD system: a simulation of incompressible flows using an explicit time integration scheme, assuming a quasi-static scenario with constant volume, constant number of particles, and infinitesimal time shift. Next, we derive a form of entropy from the discretized entropy equation of SDPD by integrating it with respect to time. We then examine the properties of a two-particle system for a constant temperature gradient. Interestingly, our theoretical analysis suggests that there exist eight different types of entropy stability conditions, which depend on the types of kernel functions. It is found that the Lucy kernel, poly6 kernel, and spiky kernel produce the same types of entropy stability conditions, whereas the spline kernel produces different types of entropy stability conditions. Our results contribute to a deeper understanding of particle discretization.

cond-mat.stat-mech↗

arXiv2025

Band-Limited Equivalence of Convolution Operators and its Application to Filtered Vorticity Dynamics

In this study, we established a general theorem regarding the equivalence of convolution operators restricted to a finite spectral band. We demonstrated that two kernels with identical Fourier transforms over the resolved band act identically on all band-limited functions, even if their kernels differ outside the band. This property is significant in applied mathematics and computational physics, particularly in scenarios where measurements or simulations are spectrally truncated. As an application, we examine the proportionality relation $S(\boldsymbol {r}) \approx ζ\,ω(\boldsymbol{r})$ in filtered vorticity dynamics and clarify why real-space diagnostics can underestimate the spectral proportionality due to unobservable degrees of freedom. Our theoretical findings were supported by numerical illustrations using synthetic data.

math.NA↗

arXiv2025

Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence

Predicting when a three-dimensional turbulent flow reaches its dissipation peak is essential for both theory and adaptive algorithms in simulations and experiments. Using direct numerical simulations (DNSs) of the Taylor--Green vortex (TGV) at resolutions of $256^3$--$1024^3$, we introduce and test a small-scale weighted diagnostic: the spectrum of $|\nabla \times \boldsymbolω|^2$ (with $\boldsymbolω=\nabla \times \mathbf{u}$), which, for incompressible flow, is equivalent to a $k^4$-weighted energy spectrum. We show that the peak wavenumber of this spectrum, $k_{\rm peak}[\,|\nabla \times \boldsymbolω|^2\,]$, advances rapidly to intermediate-small scales and then levels off before the dissipation rate $\varepsilon(t)=\sum_k 2νk^2 E(k)$ reaches its maximum. Across all resolutions, we observe robust temporal ordering $t_k<t_\varepsilon<t_Π$, where $t_k$ marks the onset of the rapid rise of $k_{\rm peak}[\,|\nabla \times \boldsymbolω|^2\,]$, $t_\varepsilon$ is the time of the maximal $\varepsilon(t)$, and $t_Π$ is when the cumulative flux $|Π(K)|$ attains its largest peak scale. This early-warning signal correlates with the morphological transition to filament-dominated structures visible in $Q$-criterion isosurfaces and is consistent with integral-scale trends ($L_{\rm int},λ,η$). The diagnostic is simple to compute from standard DNS data and highlights the incipient formation of high-curvature structures, where viscosity acts most strongly.

physics.flu-dyn↗

arXiv2025

Demonstration of the rotational viscosity transfer across scales in Navier-Stokes turbulence

Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular momentum-conserving Navier--Stokes equations offer a theoretical framework for describing such multiscale fluid dynamics by decomposing total angular momentum into bulk and intrinsic spin components. However, this framework still assumes locally non-solid rotational flows, a condition that remains empirically unverified. This study addresses such unvalidated assumptions intrinsic to the model and extends it within the framework of turbulence hierarchy theory. The theory suggests that under certain conditions, small-scale structures may transfer to larger scales through the rotational viscosity. To verify this, we conducted spectral analyses of freely decaying two-dimensional turbulence initialized with a vortex-concentrated distribution. The results indicate that rotational viscosity exhibits interscale transfer behavior, revealing a new mechanism by which order can propagate from small to large scales in Navier--Stokes turbulence.

physics.flu-dyn↗

arXiv2025

Multi-scale physics of cryogenic liquid helium-4: Inverse coarse-graining properties of smoothed particle hydrodynamics

Our recent numerical studies on cryogenic liquid helium-4 highlight key features of multiscale physics that can be captured using the two-fluid model. In this paper, we demonstrated that classical and quantum hydrodynamic two-fluid models are connected via scale transformations: large eddy simulation (LES) filtering links microscopic to macroscopic scales, while inverse scale transformation through SPH connects macro back to microscales. We showed that the spin angular momentum conservation term, introduced as a quantum-like correction, formally corresponds to a subgrid-scale (SGS) model derived from this transformation. Moreover, solving the classical hydrodynamic two-fluid model with SPH appears to reproduce microscopic-scale fluctuations at macroscopic scales. The amplitude of these fluctuations depends on the kernel radius. This effect may arise from truncation errors from kernel smoothing, which can qualitatively resemble such fluctuations. However, this resemblance lacks first-principle justification and should be viewed as a speculative analogy rather than a physically grounded effect. Our theoretical analysis further suggests that the Condiff viscosity model can act as an SGS model, incorporating quantum vortex interactions under point-vortex approximation into the two-fluid framework. These findings provide new insight into the microscopic structure of cryogenic helium-4 within a multiscale context. Notably, the normal fluid can be understood as a mixture of inviscid and viscous fluid particles. While molecular viscosity renders the normal fluid at microscopic scales, its small magnitude contributes little to the large-scale effective viscosity, which includes both molecular and eddy viscosities; therefore, in laminar regimes where eddy viscosity is negligible, the normal fluid may be effectively treated as inviscid at large scales if molecular viscosity is sufficiently small.

physics.flu-dyn↗

arXiv2024

Effects of external gravitational field on highly rarefied gases: Analysis based on stochastic soft-sphere collision models

This study examines the effects of an external gravitational field on highly rarefied gases in the transitional-flow regime near the free-molecular-flow regime. In our theoretical study, we rederive the classical kinetic theory for an ideal gas in terms of the kinetics of the constituent particles to account for the effect of particle acceleration by an external gravitational field. Subsequently, we derive an extended expression for the virial pressure equation as a generic description of the dynamics under an external gravitational field. We employ the soft-sphere model for the following reasons: In highly rarefied gases, short-range and instantaneous collisional interactions are dominant. Thus, by expanding the asymmetric two-body potential in the virial pressure equation and retaining only the contribution of the short-range interaction, we can obtain a soft-sphere model that represents the interaction in the collision direction as a harmonic oscillation. In the absence of dissipation, the softsphere model has been confirmed to reproduce fully elastic collisions. In our collision simulations, we define two parameters. The first parameter represents the collision probability between each pair of approaching particles, and the second represents the ratio of the magnitude of the external potential energy to the total kinetic energy of the particles. The behavior of the system is analyzed by varying the values of these two parameters. Our analysis shows that if the external potential energy is sufficiently small (1 %-5 %) compared with the total kinetic energy, then a pressure difference emerges between the walls. However, the system retains the properties of equilibrium statistical mechanics, as indicated by the Maxwell--Boltzmann (MB) distribution. In conclusion, highly rarefied gases obey the MB distribution even when placed under weak gravitational fields.

physics.gen-ph↗

arXiv2024

A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4

This paper reports a three-dimensional (3D) simulation of a rotating liquid helium-4, using a two-fluid model with spin-angular momentum conservation. Our model was derived from the particle approximation of an inviscid fluid with residual viscosity. Despite the fully classical mechanical picture, the resulting system equations were consistent with those of the conventional two-fluid model. We consider bulk liquid helium-4 to be an inviscid fluid, assuming that the viscous fluid component remains at finite temperatures. As the temperature decreased, the amount of the viscous fluid component decreased, ultimately becoming a fully inviscid fluid at absolute zero. Weak compressibility is assumed to express the volume change because some helium atoms do not render fluid owing to BECs or change states because of local thermal excitation. One can solve the governing equations for an incompressible fluid using explicit SPH (smoothed particle hydrodynamics), simultaneously reproducing density fluctuations and describing the fluid in a many-particle system. We assume the following fluid-particle duality: a hydrodynamic interfacial tension between the inviscid and viscous components or a local interaction force between two types of fluid particles. The former can be induced in the horizontal direction when non-negligible non-uniformity of the particles occurs during forced two-dimensional rotation, and the latter is non-negligible when the former is negligible. We performed a largescale simulation of 3D liquid helium forced to rotate horizontally using 32 GPUs. Compared with the low-resolution calculation using 2.4 million particles, the high-resolution calculation using 19.6 million particles showed spinning vortices close to those of the theoretical solution. We obtained a promising venue to establish a practical simulation method for bulk liquid helium-4.

physics.flu-dyn↗

arXiv2024

Extreme value statistics of nerve transmission delay

Nerve transmission delay is an important topic in neuroscience. Spike signals fired or received at the dendrites of a neuron travel from the axon to the presynaptic cell. The spike signal triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, and regenerates electrical signals by a chemical reaction process through ion channels and transmits it to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme order statistics. By considering the statistical variance in the time constant of the Leaky Integrate-and-Fire model, which is a deterministic time evolution model of spike signals, we enabled randomness in the time interval of spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, which is one of the three types of extreme value statistics. We also confirmed that the histogram of the maximum time interval follows a Fréchet distribution when the time interval of the spike signal follows a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and could, therefore, be used as a new indicator for transmission delay.

q-bio.NC↗

arXiv2024

Effects of topological structure and destination selection strategies on agent dynamics in complex networks

We analyzed agent behavior in complex networks: Barabási-Albert (BA), Erdos-Rényi (ER), and Watts-Strogatz (WS) models under the following rules: agents (a) randomly select a destination among adjacent nodes; (b) exclude the most congested adjacent node as a potential destination and randomly select a destination among the remaining nodes; or (c) select the sparsest adjacent node as a destination. We focused on small complex networks with node degrees ranging from zero to a maximum of approximately 20 to study agent behavior in traffic and transportation networks. We measured the hunting rate, that is, the rate of change of agent amounts in each node per unit of time, and the imbalance of agent distribution among nodes. Our simulation study reveals that the topological structure of a network precisely determines agent distribution when agents perform full random walks; however, their destination selections alter the agent distribution. Notably, rule (c) makes hunting and imbalance rates significantly high compared with random walk cases (a) and (b), irrespective of network types, when the network has a high degree and high activity rate. Compared with the full random walk in (a), (b) increases the hunting rate while decreasing the imbalance rate when activity is low; however, both increase when activity is high. These characteristics exhibit slight periodic undulations over time. Furthermore, our analysis shows that in the BA, ER, and WS network models, the hunting rate decreases and the imbalance rate increases when the system disconnects randomly selected nodes in simulations where agents follow rules (a)-(c) and the network has the ability to disconnect nodes within a certain time of all time steps. Our findings can be applied to various applications related to agent dynamics in complex networks.

physics.soc-ph↗

arXiv2023

Three-dimensional analysis of vortex-lattice formation in rotating Bose-Einstein condensates using smoothed-particle hydrodynamics

Recently, we presented a new numerical scheme for vortex lattice formation in a rotating Bose-Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit time-integrating scheme; our SPH scheme could reproduce the vortex lattices and their formation processes in rotating quasi-two-dimensional (2D) BECs trapped in a 2D harmonic potential. In this study, we have successfully demonstrated a simulation of rotating 3D BECs trapped in a 3D harmonic potential forming "cigar-shaped" condensates. We have found that our scheme can reproduce the following typical behaviors of rotating 3D BECs observed in the literature: (i) the characteristic shape of the lattice formed in the cross-section at the origin and its formation process, (ii) the stable existence of vortex lines along the vertical axis after reaching the steady state, (iii) a "cookie-cutter" shape, with a similar lattice shape observed wherever we cut the condensate in a certain range in the vertical direction, (iv) the bending of vortex lines when approaching the inner edges of the condensate, and (v) the formation of vortex lattices by vortices entering from outside the condensate. Therefore, we further validated our scheme by simulating rotating 3D BECs.

physics.comp-ph↗

arXiv2023

Numerical model of the Gross-Pitaevskii equation for rotating Bose-Einstein condensates using smoothed-particle hydrodynamics

This study proposed a new numerical scheme for vortex lattice formation in a rotating Bose-Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit real-time integration scheme. Specifically, the Gross-Pitaevskii (GP) equation was described as a complex representation to obtain a pair of time-dependent equations, which were then solved simultaneously following discretization based on SPH particle approximation. We adopt the 4th-order Runge-Kutta method for time evolution. We performed simulations of a rotating Bose gas trapped in a harmonic potential, showing results that qualitatively agreed with previously reported experiments and simulations. The geometric patterns of formed lattices were successfully reproduced for several cases, for example, the hexagonal lattice observed in the experiments of rotating BECs. Consequently, it was confirmed that the simulation began with the periodic oscillation of the condensate, which attenuated and maintained a stable rotation with slanted elliptical shapes; however, the surface was excited to be unstable and generated ripples, which grew into vortices and then penetrated the inside the condensate, forming a lattice. We confirmed that each branch point of the phase of wavefunctions corresponds to each vortex. These results demonstrate our approach at a certain degree of accuracy. In conclusion, we successfully developed a new SPH scheme for the simulations of vortex lattice formation in rotating BECs.

cond-mat.quant-gas↗

arXiv2022

Theoretical framework bridging classical and quantum mechanics for the dynamics of cryogenic liquid helium-4 using smoothed-particle hydrodynamics

Our recent study suggested that a fully classical mechanical approximation of the two-fluid model of superfluid helium-4 based on smoothed-particle hydrodynamics (SPH) is equivalent to solving a many-body quantum mechanical equation under specific conditions. This study further verifies the existence of this equivalence. First, we derived the SPH form of the motion equation for the superfluid component of the two-fluid model, i.e., the motion equation driven by the chemical potential gradient obtained using the Gibbs-Duhem equation. We then derived the SPH form of the motion equation for condensates based on the Gross-Pitaevskii theory, i.e., the motion equation driven by the chemical potential gradient obtained from the Schrodinger equation of interacting bosons. Following this, we compared the two discretized equations. Consequently, we discovered that a condition maintaining zero internal energy for each fluid particle ensures the equivalence of the equations when the quantum pressure is negligible. Moreover, their equivalence holds even when the quantum pressure is nonnegligible if the quantum pressure gradient force equals the mutual friction force. A zero internal energy indicates the thermodynamic ground state, which includes an elementary excitation state. Therefore, the condition can be sufficiently satisfied when the velocities of fluid particles do not exceed the Landau critical velocity, which is not a stringent condition for simulations with a characteristic velocity of a few cms-1 in a laboratory system. Based on the above, we performed a simulation of rotating liquid helium-4 and succeeded in generating a vortex lattice with quantized circulation, known as a quantum lattice.

physics.flu-dyn↗

arXiv2022

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

The importance of fundamental research on network topologies is widely acknowledged. This study aims to elucidate the effect of congestion avoidance of agents given congestion information on optimizing traffic in a network topology. We investigated stochastic traffic networks in a star topology with a central node connected to isolated secondary nodes with different preferences. Each agent at the central node selects a secondary node by referring to the declining preferences based on the congestion rate of the secondary nodes. We examined two scenarios: 1) Each agent can repeatedly visit the central and secondary nodes. 2) Each agent can access each secondary node only once. For 1), we investigated the uniformity of the agent distribution in a stationary state, and for 2), we measured the travel time for all agents visiting all nodes. When agents repeatedly visit central and other nodes, the uniformity of agent distribution has been found to show three types of nonlinear dependence on the increase in nodes. We found that multivariate statistics describe these characteristic dependences well, suggesting that the balance between the equalization of network usage by avoiding congestion and the covariance caused by mutual referral to congestion information determines the uniformity. We discovered that congestion-avoidance linearizes the travel time, which increases exponentially with the number of nodes, notwithstanding the degree of reference to the congestion information. Consequently, we successfully described the optimization effect of congestion-avoidance on the collective dynamics of agents in star topologies. Our findings are useful in many areas of network science.

physics.soc-ph↗