arXiv subjects

Johan L. A. Dubbeldam

Publications and source records attributed to Johan L. A. Dubbeldam.

10 recordsLinked to original sources

arXiv2026

Metastability for the Curie-Weiss-Potts model with unbounded random interactions

We analyse the metastable behaviour of the disordered Curie--Weiss--Potts (DCWP) model subject to a Glauber dynamics. The model is a randomly disordered version of the mean-field $q$-spin Potts model (CWP), where the interaction coefficients between spins are general independent random variables. These random variables are chosen to have fixed mean (for simplicity taken to be $1$) and well defined cumulant generating function, with a fixed distribution not depending on the number of particles. The system evolves as a discrete-time Markov chain with single spin flip Metropolis dynamics at finite inverse temperature $β$. We provide a comparison of the metastable behaviour of the CWP and DCWP models, when $N \to \infty$. First, we establish the metastability of the CWP model and, using this result, prove metastability for the DCWP model (with high probability). We then determine the ratio between the metastable transition time for the DCWP model and the corresponding time for the CWP model. Specifically, we derive the asymptotic tail behavior and moments of this ratio. Our proof combines the potential-theoretic approach to metastability with concentration of measure techniques, the latter adapted to our specific context.

math.PR↗

arXiv2026

Gardner volumes and self-organization in a minimal model of complex ecosystems

We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in discrete time extinction and revival events. The dynamics are generated by a random elliptic community matrix with tunable correlation strength. We show that, independent of the correlation strength, solutions of the system are confined to subsets of the phase space that can be cast as time-varying Gardner volumes from the theory of learning in neural networks. These volumes decrease with the diversity (i.e. the fraction of extant species) and become exponentially small in the long-time limit. Using standard results from random matrix theory, the changing diversity is then linked to a sequence of contractions and expansions in the spectrum of the community matrix over time, resulting in a sequence of May-type stability problems determining whether the total population evolves toward complete extinction or unbounded growth. In the case of unbounded growth, we show the model allows for a particularly simple nonlinear extension in which the solutions instead evolve towards a new attractor.

nlin.AO↗

arXiv2025

Controllability in a class of cancer therapy models with co-evolving resistance

Adaptive therapy is a recent paradigm in cancer treatment aiming at indefinite, safe containment of the disease when cure is judged unattainable. In modeling this approach, inherent limitations arise due to the structure of the vector fields and the bounds imposed by toxic side-effects of the drug. In this work we analyze these limitations in a minimal class of models describing a cancer population with a slowly co-evolving drug resistance trait. Chemotherapeutic treatment is introduced as any bounded time-varying input, forcing the cells to adapt to a changing environment. We leverage the affine structure and low dimension of the system to explicitly construct controllable subsets of the state space enclosing sets of equilibria. We show that these controllable sets entirely determine the asymptotic behavior of all trajectories that cannot lead to a cure.

math.DS↗

arXiv2024

A resetting particle embedded in a viscoelastic bath

We examine the behavior of a colloidal particle immersed in a viscoelastic bath undergoing stochastic resetting at a rate $r$. Microscopic probes suspended in viscoelastic environment do not follow the classical theory of Brownian motion. This is primarily because the memory from successive collisions between the medium particles and the probes does not necessarily decay instantly as opposed to the classical Langevin equation. To treat such a system one needs to incorporate the memory effects to the Langevin equation. The resulting equation formulated by Kubo, known as the Generalized Langevin equation (GLE), has been instrumental to describe the transport of particles in inhomogeneous or viscoelastic environments. The purpose of this work, henceforth, is to study the behavior of such a colloidal particle governed by the GLE under resetting dynamics. To this end, we extend the renewal formalism to compute the general expression for the position variance and the correlation function of the resetting particle driven by the environmental memory. These generic results are then illustrated for the prototypical example of the Jeffreys viscoelastic fluid model. In particular, we identify various timescales and intermittent plateaus in the transient phase before the system relaxes to the steady state; and further discuss the effect of resetting pertaining to these behaviors. Our results are supported by numerical simulations showing an excellent agreement.

cond-mat.stat-mech↗

arXiv2021

Emergent order in a continuous state adaptive network model of living systems

Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions that lead to such emergent phenomena. To find these conditions, we use the framework of complex networks to characterize the state of agents and their mutual influence. We formulate a continuous state adaptive network model, from which we obtain the phase boundaries between swarming and disordered phases and characterize the order of the phase transition.

physics.bio-ph↗

arXiv2021

Interspecific competition shapes the structural stability of mutualistic networks

Mutualistic networks have attracted increasing attention in the ecological literature in the last decades as they play a key role in the maintenance of biodiversity. Here, we develop an analytical framework to study the structural stability of these networks including both mutualistic and competitive interactions. Analytical and numerical analyses show that the structure of the competitive network fundamentally alters the necessary conditions for species coexistence in communities. Using 50 real mutualistic networks, we show that when the relative importance of shared partners is incorporated via weighted competition, the feasibility area in the parameter space is highly correlated with May's stability criteria and can be predicted by a functional relationship between the number of species, the network connectance and the average interaction strength in the community. Our work reopens a decade-long debate about the complexity-stability relationship in ecological communities, and highlights the role of the relative structures of different interaction types.

physics.soc-ph↗

arXiv2018

Power-Imbalance Allocation Control of Power Systems-Secondary Frequency Control

The traditional secondary frequency control of power systems restores nominal frequency by steering Area Control Errors (ACEs) to zero. Existing methods are a form of integral control with the characteristic that large control gain coefficients introduce an overshoot and small ones result in a slow convergence to a steady state. In order to deal with the large frequency deviation problem, which is the main concern of the power system integrated with a large number of renewable energy, a faster convergence is critical. In this paper, we propose a secondary frequency control method named Power-Imbalance Allocation Control (PIAC) to restore the nominal frequency with a minimized control cost,in which a coordinator estimates the power imbalance and dispatches the control inputs to the controllers after solving an economic power dispatch problem. The power imbalance estimation converges exponentially in PIAC, both overshoots and large frequency deviations are avoided. In addition, when PIAC is implemented in a multi-area controlled network, the controllers of an area are independent of the disturbance of the neighbor areas, which allows an asynchronous control in the multi-area network. A Lyapunov stability analysis shows that PIAC is locally asymptotically stable and simulation results illustrates that it effectively eliminates the drawback of the traditional integral control based methods.

math.OC↗

arXiv2014

Driven translocation of a polymer: role of pore friction and crowding

Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the "crowding" of monomers on the {\it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $α$ in the translocation time - vs. - chain length scaling law, $τ\propto N^α$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $α$ values which were found in experiments and computer simulations.

cond-mat.soft↗

arXiv2010

Fractional Brownian motion approach to polymer translocation: the governing equation of motion

We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time $t$ after the process has begun, and (ii) a sub-diffusive increase of the distribution variance $Δ(t)$ with elapsed time, $Δ(t) \propto t^α$. The latter quantity measures the mean-squared number $s$ of polymer segments which have passed through the pore, $Δ(t) = <[s(t)-s(t=0)]^2>$, and is known to grow with an anomalous diffusion exponent $α< 1$. Our main assumption - a Gaussian distribution of the translocation velocity $v(t)$ - and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation which we performed in $3D$. We also numerically confirm the predictions made in ref.\cite{Kantor_3}, that the exponent $α$ changes from $0.91$ to $0.55$, to $0.91$, for short, intermediate and long time regimes, respectively.

cond-mat.soft↗

arXiv2009

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.

cond-mat.soft↗