The Martini coarse-grained (CG) force field enables efficient simulations of biomolecular systems but cannot reliably maintain folded protein structures. To stabilize proteins during simulation, Martini is typically combined with structure-based force fields such as elastic network models (ENMs) or Go̅ models. While these approaches preserve global folds and capture protein flexibility, their ability to reproduce conformational dynamics remains unclear. Here, we evaluate Martini 3 combined with ENMs or Go̅ models on three folded proteins and show that both approaches struggle to sample the conformational space observed in atomistic simulations, even when uniform interaction strengths or equilibrium bond distances are adjusted. This limitation arises from the assumption of a uniform interaction network, in which all Go̅-bonds are assigned the same ϵ value, and therefore have the same potential depth. To overcome this, we present a fully automated, perturbation-based optimization approach for Go̅ networks, PoGo̅, that iteratively refines a nonuniform Go̅ network against a precomputed atomistic free-energy landscape in essential conformational space. Moreover, we demonstrate that our approach can also be used to optimize ENMs. In both cases, convergence is rapid and yields CG ensembles in close agreement with reference atomistic simulations. As a cross-validation, the optimization also improves the root-mean-square fluctuation profile.

In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The generality of the formulation enables a systematic search for ecological mechanisms that may lead to self-organized patterns. We identify two distinct mechanisms generating Turing instabilities across a broad class of models. The first mechanism arises from intensified competition in the areas between vegetated patches due to the cumulative pressure from their surroundings, and is well-documented in the literature. The second mechanism is novel and occurs when local growth outpaces competitive susceptibility near the uniform equilibrium. The analytical findings are complemented by numerical simulations of two benchmark models, both exhibiting a supercritical Turing bifurcation that leads to the formation of stable and robust vegetation patterns.

Swarm coverage by unmanned underwater vehicles (UUVs) is essential for inspection, environmental monitoring, and search operations, but remains challenging in three-dimensional domains under limited sensing and communication. Pheromone-based stigmergic coordination provides a low-bandwidth alternative to explicit communication, yet conventional single-field models are susceptible to depth-dependent sensing inconsistencies and multi-source signal interference. This paper introduces a dual-trail stigmergic coordination framework in which a virtual pheromone field encodes short-term motion cues while an auxiliary coverage trail records the accumulated exploration effort. UUV motion is guided by the combined gradients of these two fields, enabling more consistent behavior across depth layers and mitigating ambiguities caused by overlapping pheromone sources. At the macroscopic level, swarm evolution is modeled by a coupled system of partial differential equations (PDEs) describing vehicle density, pheromone concentration, and coverage trail. A Lyapunov functional is constructed to derive sufficient conditions under which perturbations around the uniform coverage equilibrium decay exponentially. Numerical simulations in three-dimensional underwater domains demonstrate that the proposed framework reduces coverage holes, limits redundant overlap, and improves robustness with respect to a single-pheromone baseline and a potential-field-based controller. These results indicate that dual-field stigmergic control is a promising and scalable approach for UUV coverage in constrained underwater environments.

Cyanobacterial blooms (CBs) pose significant global challenges due to their harmful toxins and socio-economic impacts, with nutrient availability playing a key role in their growth, as described by ecological stoichiometry (ES). However, real-world ecosystems exhibit spatial heterogeneity, limiting the applicability of simpler, spatially uniform models. To address this, we develop a spatially explicit partial differential equation model based on ES to study cyanobacteria in the epilimnion of freshwater systems. We establish the well-posedness of the model and perform a stability analysis, showing that it admits two linearly stable steady states, leading to either extinction or a spatially uniform positive equilibrium where cyanobacterial biomass stabilizes at its carrying capacity. Further, we discuss the possibility of long-term spatially nonuniform solution with small diffusion and space-dependent parameters. We use the finite elements method (FEM) to numerically solve our system on a real lake domain derived from Geographic Information System (GIS) data and realistic wind conditions extrapolated from ERA5-Land. Additionally, we use a cyanobacteria estimation (CE) obtained from Sentinel-2 to set initial conditions, and we achieve strong model validation metrics. Our numerical results highlight the importance of lake shape and size in bloom monitoring, while global sensitivity analysis using Sobol Indices identifies light attenuation and intensity as primary drivers of bloom variation, with water movement influencing early bloom stages and nutrient input becoming critical over time. This model supports continuous water-quality monitoring, informing agricultural, recreational, economic, and public health strategies for mitigating CBs.

We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a phase transition with increasing interaction strength. In the subcritical regime, the uniform distribution, representing incoherence, is the unique and stable stationary equilibrium. Above the critical interaction threshold, the uniform equilibrium becomes unstable and there is a multiplicity of stationary equilibria that are self-organizing. Under a discounted cost, dynamic equilibria spiral around the uniform distribution before converging to the self-organizing equilibria. With an ergodic cost, however, unexpected periodic equilibria around the uniform distribution emerge. Funding: This work was supported by the National Science Foundation [Grant DMS 2406762].

Coupled phase oscillators with both attractive and repulsive interactions offer a valuable framework for exploring collective dynamics in nonlinear dynamics, serving as an analog to the frustrated Ising model in statistical physics. In this work, we study a ring of phase oscillators with nearest-neighbor and next-nearest-neighbor interactions. The coupling strengths, denoted as J_{1} and J_{2}, dictate the behavior of these interactions. For an infinite number of oscillators, the model allows for a continuum of equilibria. For identical oscillators, linear stability analysis shows the prevalence of multistability. To complement the linear stability analysis, we delve into the basin stabilities of these equilibria. We categorize them based on basin stability into in-phase equilibria with nearly zero phase difference between adjacent oscillators, antiphase equilibria with nearly π phase difference, and heterogeneous equilibria characterized by the phase difference, concentrating on the most unstable modes of the uniform equilibrium. The resulting phase diagram in the J_{1}-J_{2} plane mirrors that of the zero-temperature J_{1}-J_{2} Ising model. For nonidentical phase oscillators, similar qualitative outcomes are observed.

Abstract Vertical Displacement Oscillatory Modes (VDOM), with frequency in the Alfvén range, are natural modes of oscillation of magnetically confined laboratory plasmas with elongated cross-section. These axisymmetric modes arise from the interaction between the plasma current, which is in equilibrium with currents flowing in external coils, and perturbed currents induced on a nearby conducting wall. The restoring force exerted by these perturbed currents on the vertical motion of the plasma column leads to its oscillatory behavior. An analytic model for VDOM was proposed by (Barberis et al 2022 J. Plasma Phys. 88 905880511) based on an idealized ‘straight tokamak’ equilibrium with uniform equilibrium current density. This article introduces the first numerical simulations of VDOM in a realistic JET tokamak configuration, using the extended-MHD code NIMROD and drawing comparisons with Global Alfvén Eigenmodes (GAE). The results show qualitative agreement with analytic predictions regarding mode frequency and radial structure, supporting the identification of VDOM as a fundamental oscillation mode in tokamak plasmas. VDOM and GAE are modeled in a representative JET discharge, where axisymmetric perturbations with toroidal mode number n = 0 driven unstable by fast ions were observed. The two modes are examined separately using a forced oscillator within the NIMROD code, which enables a comparison of their characteristics and helps identify the experimentally observed mode possibly as a GAE.

We consider the no-flux initial-boundary value problem for the growth-expansion model with chemotaxis in nutrient-replete environments in smoothly bounded domains [Formula: see text]. It is shown that if [Formula: see text] or if [Formula: see text] under some structural assumptions on parameter functions therein, for any suitably regular initial data the problem admits a unique global bounded classical solution. For any dimensions [Formula: see text], we also prove that the problem has a unique global classical solution which is bounded under a small assumption on the initial data. Moreover, we obtain that these solutions stabilize to a uniquely determined spatially uniform equilibrium. We also provide exponential rates of convergence of solutions in a special case.

ABSTRACT Even though there is a growing literature on the co-movement between energy and currency markets, this issue is still unclear for the Eurasian Economic Union (EEU) countries. Based on this gap in the literature, the purpose of this study is to analyse the dynamic relationships between energy prices (crude oil and natural gas) and exchange rates for the EEU countries (Armenia, Belarus, Kazakhstan, Kyrgyzstan, and Russia) for the 2015–2022 period by means of cointegration and causality approaches without and with structural shifts. While the cointegration test without structural change does not find uniform steady-state equilibrium, considering structural change in the cointegration model reveals the existence of the long-run relationship between exchange rates and energy prices. The causality analysis uncovers predictive information between energy and currency markets in the EEU countries driven by the oil market; and accounting for smooth structural breaks in causality analysis based on the Fourier Toda-Yamamoto approach reinforces these findings. The empirical findings hence imply a strong co-movement between energy and currency markets in the EEU countries shaped by the oil market.

The dynamics and existence results of generalized Caputo fractional derivatives have been studied by several authors. Uniform stability and equilibrium in fractional-order neural networks with generalized Caputo derivatives in real-valued settings, however, have not been extensively studied. In contrast to earlier studies, we first investigate the uniform stability and equilibrium results for complex-valued neural networks within the framework of a generalized Caputo fractional derivative. We investigate the intermittent behavior of complex-valued neural networks in generalized Caputo fractional-order contexts. Numerical results are supplied to demonstrate the viability and accuracy of the presented results. At the end of the article, a few open questions are posed.

We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u, v) is a move whenever (v, u) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n-person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players.

In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method’s effectiveness. The article concludes by discussing the biological implications of these outcomes.

Abstract In this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor’s cross-diffusion, the pattern’s development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition.

Theoretical derivation of hydraulic geometry equations for a gravel bed river channel

Lycopodium (L.) clavatum powder, due to its uniform particle size distribution and low equilibrium moisture content, is often used as a reference material and a calibration benchmark for dust combustion and dust explosion studies. The aim of the study was to determine its fire and explosion parameters, compare them to values obtained in the previous literature findings, and assess the appropriateness of using lycopodium powder as a reference material. The research included the determination of minimum ignition temperatures of dust layer and dust clouds, spontaneous ignition behavior, and explosion characteristics of dust clouds including maximum explosion pressure, maximum rate of explosion pressure rise, and the lower explosion limit of the air/dust mixture. The results reveal that the maximum equipment temperature used with lycopodium dust should not exceed 215 °C for dust thickness up to 5 mm. In order to eliminate the risk of lycopodium dust ignition, the temperature of the equipment surfaces that can come into contact with the dust cloud should not exceed 300 °C. In order to prevent explosions, the concentration of lycopodium dust in air should not be greater than 15 g/m3. Based on the obtained results, it can be seen that lycopodium fire and explosion parameters vary slightly, and its usage as a benchmark is considered legitimate.

Motivated by possible applications in fault-tolerant selfish routing, we introduce the notion of uniform mixed equilibrium in network congestion games with adversarial link failures, where agents need to route traffic from a source to a destination node. Given an integer [Formula: see text], a ρ-uniform mixed strategy is a mixed strategy in which an agent plays exactly ρ edge-disjoint paths with uniform probability; therefore, a ρ-uniform mixed equilibrium is a tuple of ρ-uniform mixed strategies, one for each agent, in which no agent can lower her cost by deviating to another ρ-uniform mixed strategy. For games with weighted agents and affine latency functions, we show the existence of ρ-uniform mixed equilibria and provide a tight characterization of their price of anarchy. For games with unweighted agents, we extend the existential guarantee to any class of latency functions, and restricted to games with affine latencies, we derive a tight characterization of the price of anarchy and the price of stability. Funding: This work was partially supported by the INdAM-GNCS and the Italian MIUR PRIN 2017 Project ALGADIMAR “Algorithms, Games, and Digital Markets.”

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform equilibria, provided the system has an entropic structure with a symmetric mobility matrix. One example of such systems are the equations describing a Physical Vapor Deposition (PVD) process. This stabilization is achieved with respect to both the volume fractions and the thickness of the domain. The feedback control is derived using the backstepping technique, adapted to the context of a time-dependent domain. In particular, the norm of the backward backstepping transform is carefully estimated with respect to time.

In corner areas of structures, high stress values and gradients occur, and lead to stress concentrations. Infinite stress and deformations are determined by a solution of the linear elasticity theory problem in the area with a wedge-shape boundary notch. Infinite solutions of the elasticity problem occur under impact of forced deformations, when a surge of the deformation value reaches beyond the area boundary. Relative values of stress concentrations for corner area zones make no more sense. At finite displacements, high deformation and stress values occur in the corner zones of the area. For a linear statement of the elasticity theory problem, at minor deflections, not only first-order, but also second-order derivatives of the displacements function are significant. To account for finite deformations of such corner zones of the area, correct formulations of elasticity problems are required. Study objective: influence determination of the infinitesimal order of the deformation on the appearance of equilibrium equations of an area with induced (temperature) deformations. This allows for the analysis of the influence of linear, shear deformations, and of the swing on the solution of the elasticity problem with induced deformations.

In this article a kinetic model for the dynamics of myxobacteria colonies on flat surfaces is investigated. The model is based on the kinetic equation for collective bacteria dynamics introduced in arXiv:2001.02711, which is based on the assumption of hard binary collisions of two different types: alignment and reversal, but extended by additional Brownian forcing in the free flight phase of single bacteria. This results in a diffusion term in velocity direction at the level of the kinetic equation, which opposes the concentrating effect of the alignment operator. A global existence and uniqueness result as well as exponential decay to uniform equilibrium is proved in the case where the diffusion is large enough compared to the total bacteria mass. Further, the question wether in a small diffusion regime nonuniform stable equilibria exist is positively answered by performing a formal bifurcation analysis, which revealed the occurrence of a pitchfork bifurcation. These results are illustrated by numerical simulations.