arXiv subjects

Jean-François de Kemmeter

Publications and source records attributed to Jean-François de Kemmeter.

10 recordsLinked to original sources

arXiv2026

Sandpile Models on complex networks

We investigate the sandpile model on complex networks by developing a branching-process framework that explicitly incorporates dissipation during avalanche propagation. Unlike classical branching descriptions, which assume conservative transport and locally tree-like independence, the present approach introduces grain-loss effects directly into the offspring distribution, yielding generalized generating functions for dissipative avalanche dynamics. In the dissipative regime, avalanche-size distributions acquire exponential cutoffs while preserving topology-dependent scaling behavior. Numerical simulations confirm the theoretical predictions on sparse random networks and reveal systematic deviations in highly structured topologies. In particular, by using Holme-Kim clustered scale-free networks, we show that increasing clustering continuously lowers the avalanche exponent and enhances the probability of large cascades, demonstrating that short cycles generate strong correlations that invalidate the classical independent-branch approx imation. Surprisingly, trees also exhibit substantial deviations from power-law because low edge density and the abundance of leaves constrain avalanche propagation. These results show that dissipation, clustering, and sparse connectivity fundamentally reshape avalanche size distribution of the sandpile model on networks and establish quantitative limits for branching-process descriptions of avalanche dynamics.

cond-mat.stat-mech↗

arXiv2026

Dynamical universality class for competing short- and long-range interactions

Understanding the dynamical universality classes of systems with long-range interactions remains a key challenge in statistical physics. In this Letter, we analytically and numerically investigate the non-equilibrium critical dynamics of the one-dimensional spin-$1/2$ Nagle-Kardar model, which is characterized by the competition between short- and long-range interactions and the presence of a tricritical point. We focus on the slowing-down of the magnetization $m$ at criticality under Glauber dynamics. Starting from the corresponding master equation, we perform a coarse-graining procedure to obtain a Fokker-Planck equation for the macroscopic variables. Then, the asymptotic decay of the magnetization is derived using central manifold theory. We find that $m$ decays as $t^{-1/2}$ along the critical line and as $t^{-1/4}$ precisely at the tricritical point. This finding confirms that the dynamical critical exponent is $z=2$ as for mean-field models, proving that the macroscopic critical dynamics of the Nagle-Kardar model falls within the dynamical universality class of purely relaxational, non-conserved order parameters (model A). While Kardar proved that the equilibrium Curie-Weiss theory extends to Ising models where nearest-neighbor interactions are included, we here show that such result is valid also for critical dynamics. Our work provides the semi-analytical solution for the critical dynamics of a model with mixed-range interactions, assigning its universality class.

cond-mat.stat-mech↗

arXiv2026

Macroscopic Fokker-Planck equation from microscopic Glauber dynamics for the Nagle-Kardar model

In the companion Letter we have highlighted the dynamical universality class of the Nagle-Kardar model, where a mean-field interaction is added to the one-dimensional nearest-neighbor Ising model. Starting from the microscopic Glauber dynamics, this paper provides a complete derivation of the Fokker-Planck equation that describes the time evolution of the macroscopic variables (magnetization and defect density) appearing in the model's Hamiltonian. The study of the Langevin equation, associated with the Fokker-Planck equation, allowed us to prove that the model belongs to the universal class of systems with diffusive dynamics and non-conserved order parameter (model A). To this goal, we used several features of the model at equilibrium, including the phase diagram and the fluctuations of macroscopic variables, which are here discussed for completeness. The derivation of the Fokker-Planck equation requires the solution of some combinatorial problems that appear in the counting of configurations at an intermediate level between the microscopic Glauber dynamics and the macroscopic Fokker-Planck one. Finally, we apply both the Glauber and the Langevin dynamics to the study of the average first passage time between local equilibrium states. We confirm that this time obeys an exponential Arrhenius law in terms of system's size, offering a direct link between microscopic energy landscapes and macroscopic relaxation mechanisms.

cond-mat.stat-mech↗

arXiv2024

Emergence of power-law distributions in self-segregation reaction-diffusion processes

Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give rise to power-law distributions, where emergent patterns and structures become visible across vastly different scales. Recent observations reveal power-law distributions in the spatial organization of, e.g., tree clusters and forest patch sizes. Crucially, these patterns do not follow a spatially periodic order but rather a statistical one. Unlike the spatially periodic patterns elucidated by the Turing mechanism, the statistical order of these particular vegetation patterns suggests an incomplete understanding of the underlying mechanisms. Here, we present a novel self-segregation mechanism, driving the emergence of power-law scalings in pattern-forming systems. The model incorporates an Allee-logistic reaction term, responsible for the local growth, and a nonlinear diffusion process accounting for positive interactions and limited resources. According to a self-organized criticality (SOC) principle, after an initial decrease, the system mass reaches an analytically predictable threshold, beyond which it self-segregates into distinct clusters, due to local positive interactions that promote cooperation. Numerical investigations show that the distribution of cluster sizes obeys a power-law with an exponential cutoff.

nlin.PS↗

arXiv2024

Multigraph reconstruction via nonlinear random walk

Over the last few years, network science has proved to be useful in modeling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex tasks, such as synchronization or collective motions. In this regard, the interplay between network structure and dynamics has long been recognized as a cornerstone of network science. Among dynamical processes, random walks are undoubtedly among the most studied stochastic processes. While traditionally, the random walkers are assumed to be independent, this assumption breaks down if nodes are endowed with a finite carrying capacity, a feature shared by many real-life systems. Recently, a class of nonlinear diffusion processes accounting for the finite carrying capacities of the nodes was introduced. The stationary nodes densities were shown to be nonlinearly correlated with the nodes degrees, allowing to uncover the network structure by performing a few measurements of the stationary density at the level of a single arbitrary node and by solving an inverse problem. In this work, we extend this class of nonlinear diffusion processes to the case of multigraphs, in which links between nodes carry distinct attributes. Assuming the knowledge of the pattern of interactions associated with one type of links, we show how the degree distribution of the whole multigraph can be reconstructed. The effectiveness of the reconstruction algorithm is demonstrated through simulations on various multigraph topologies.

physics.soc-ph↗

arXiv2023

On $λ$-determinants and tiling problems

We review the connections between the octahedral recurrence, $λ$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $λ$-determinant (and generalizations thereof) of an arbitrary matrix in terms of domino tilings of Aztec diamonds. We also reinterpret the general Robbins-Rumsey formula for the rational function of consecutive minors, given by a summation over pairs of compatible alternating sign matrices, as the partition function for tilings of Aztec diamonds equipped with a general measure.

math-ph↗

arXiv2023

Complex contagion in social systems with distrust

Social systems are characterized by the presence of group interactions and by the existence of both trust and distrust relations. Although there is a wide literature on signed social networks, where positive signs associated to the links indicate trust, friendship, agreement, while negative signs represent distrust, antagonism, and disagreement, very little is known about the effect that signed interactions can have on the spreading of social behaviors when higher-order interactions are taken into account. In this paper we focus on processes of complex contagion, such as the adoption of social norms, where exposure to multiple sources is needed for the contagion to occur. Complex contagion has been recently modeled by higher-order networks, such as simplicial complexes, which allow transmission to happen not only through the links connecting pair of nodes, but also in group interactions, namely over simplices of dimension larger or equal than two. Here, we introduce a model of complex contagion on signed simplicial complexes, and we investigate the role played by trust and distrust on the dynamics of a social contagion process. The presence of higher-order signed structures in our model naturally induces new infection and recovery mechanisms. Through numerical simulations and analytical results in the mean-field approximation, we show how distrust determines the way the system moves from a state where no individuals adopt the social behavior, to a state where a finite fraction of the population actively spreads it. Interestingly, the fraction of spreading individuals displays a non-monotonic dependence on the average number of connections between individuals. We then investigate how social balance affects social contagion, finding that balanced triads either promote or impede contagion based on the relative abundance of fully trusted relations.

physics.soc-ph↗

arXiv2023

Fluctuations and arctic curve in the Aztec diamond

Domino tilings of Aztec diamonds are known to exhibit an arctic phenomenon, namely a separation between frozen regions (in which all the dominoes have the same orientation) and a central disordered region (where dominoes are found without any apparent order). This separation was proved to converge, under a suitable rescaling, to the Airy process whose $1$-point distribution is the Tracy-Widom distribution. In this work, we conjecture, by means of numerical analysis, that the boundary between the frozen and disordered regions, converges, for the same rescaling, to the Airy line ensemble, a generalisation of the Airy process.

cond-mat.stat-mech↗

arXiv2022

Self-segregation in heterogeneous metapopulation landscapes

Complex interactions are at the root of the population dynamics of many natural systems, particularly for being responsible for the allocation of species and individuals across apposite niches of the ecological landscapes. On the other side, the randomness that unavoidably characterises complex systems has increasingly challenged the niche paradigm providing alternative neutral theoretical models. We introduce a network-inspired metapopulation individual-based model (IBM), hereby named self-segregation, where the density of individuals in the hosting patches (local habitats) drives the individuals spatial assembling while still constrained by nodes' saturation. In particular, we prove that the core-periphery structure of the networked landscape triggers the spontaneous emergence of vacant habitat patches, which segregate the population in multistable patterns of isolated (sub)communities separated by empty patches. Furthermore, a quantisation effect in the number of vacant patches is observed once the total system mass varies continuously, emphasising thus a striking feature of the robustness of population stationary distributions. Notably, our model reproduces the patch vacancy found in the fragmented habitat of the Glanville fritillary butterfly Melitaea cinxia, an endemic species of the Aland islands. We argue that such spontaneous breaking of the natural habitat supports the concept of the highly contentious (Grinnellian) niche vacancy and also suggests a new mechanism for the endogeneous habitat fragmentation and consequently the peripatric speciation.

cond-mat.stat-mech↗

arXiv2022

Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($Δ=0$), while keeping the ratio $s/n \,\in [0,1]$ as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the $6$V model with partial DWBC. Our results are confirmed by extensive numerical simulations.

cond-mat.stat-mech↗