Nonlinear Sciences
- [1] arXiv:2405.19344 [pdf, ps, html, other]
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Title: On the modelling of short and intermediate water wavesComments: 8 pages, 1 figureJournal-ref: Applied Mathematics Letters 142 (2023) 108653Subjects: Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph)
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.
- [2] arXiv:2405.19365 [pdf, ps, html, other]
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Title: Hydrodynamic modulation instability triggered by a two-wave systemSubjects: Pattern Formation and Solitons (nlin.PS)
The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. Following the linear stability analysis of weakly nonlinear waves, the classical MI dynamics, can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system is usually required to initiate the wave focusing process. Breather solutions of the nonlinear Schrödinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with minor distinctions.
- [3] arXiv:2405.19370 [pdf, ps, html, other]
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Title: Interaction and adiabatic evolution of orthodromic and antidromic impulses in the axoplasmic fluidSubjects: Pattern Formation and Solitons (nlin.PS)
Unlike expected from the Hodgkin-Huxley model predictions, in which there is annihilation once orthodromic and antidromic impulses collide, the Heimburg-Jackson model demonstrates that both impulses penetrate each other as it has been shown experimentally. These impulses can be depicted as low amplitude nonlinear excitations in a weakly dissipative soliton model described by the damped NLSE. In view of the above, the Karpman-Solov'ev-Maslov perturbation theory turns out to be ideal to study the interaction and adiabatic evolution of orthodromic and antidromic impulses once axoplasmic fluid is present.
- [4] arXiv:2405.19436 [pdf, ps, other]
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Title: Traffic Modeling and Forecast based on Stochastic Cell-Automata and Distributed Fiber-Optic Sensing -- A Numerical ExperimentComments: 11 pages, 7 figuresSubjects: Cellular Automata and Lattice Gases (nlin.CG); Statistical Mechanics (cond-mat.stat-mech); Physics and Society (physics.soc-ph)
This paper demonstrates accurate traffic modeling and forecast using stochastic cell-automata (CA) and distributed fiber-optic sensing (DFOS). Traffic congestion is a dominant issue in highways. To reduce congestion, real-time traffic control by short-term forecast is necessary. For achieving this, data assimilation using a stochastic CA model and DFOS is promising. Data assimilation with a CA enables us to model real-time traffic flow with simple processes even when rare or sudden events occur, which is challenging for usual machine learning-based methods. DFOS overcomes issues of conventional point sensors that have dead zones of observation. By estimating optimal model parameters that reproduce observed traffic flow in the simulation, future traffic flow is forecasted from the simulation. We propose an optimal model parameter estimation method using mean velocity as an extracted feature and the particle filter. In addition, an estimation methodology for the microscopic traffic situation is developed to set the initial condition of simulation for forecast in accordance with observation. The proposed methods are verified by simulation-based traffic flow. The simulation adopts the stochastic Nishinari-Fukui-Schadschneider model. The optimal model parameters are successfully derived from posterior probability distributions (PPDs) estimated from DFOS data. In contrast, those estimated from point sensors fail. The PPDs of model parameters also indicate that each parameter has different sensitivities to traffic flow. A traffic forecast up to 60 minutes later is carried out. Using optimal model parameters estimated from DFOS, the forecast error of mean velocity is approximately $\pm$10 km/h (percentage error is 18%). The error attains half of it when conventional point sensors are used. We conclude that DFOS is a powerful technique for traffic modeling and short-term forecast.
- [5] arXiv:2405.19478 [pdf, ps, html, other]
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Title: New sector morphologies emerge from anisotropic colony growthComments: 11 pages, 7 figuresSubjects: Pattern Formation and Solitons (nlin.PS); Biological Physics (physics.bio-ph); Populations and Evolution (q-bio.PE)
Competition during range expansions is of great interest from both practical and theoretical view points. Experimentally, range expansions are often studied in homogeneous Petri dishes, which lack spatial anisotropy that might be present in realistic populations. Here, we analyze a model of anisotropic growth, based on coupled Kardar-Parisi-Zhang and Fisher-Kolmogorov-Petrovsky-Piskunov equations that describe surface growth and lateral competition. Compared to a previous study of isotropic growth, anisotropy relaxes a constraint between parameters of the model. We completely characterize spatial patterns and invasion velocities in this generalized model. In particular, we find that strong anisotropy results in a distinct morphology of spatial invasion with a kink in the displaced strain ahead of the boundary between the strains. This morphology of the out-competed strain is similar to a shock wave and serves as a signature of anisotropic growth.
- [6] arXiv:2405.19602 [pdf, ps, html, other]
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Title: Rogue wave patterns associated with Adler--Moser polynomials featuring multiple roots in the nonlinear Schr\"odinger equationSubjects: Exactly Solvable and Integrable Systems (nlin.SI)
In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and their modified patterns. A correlation is established between these rogue wave patterns and the root structures of the Adler--Moser polynomials with multiple roots. At the positions in the $(x,t)$-plane corresponding to single roots of the Adler--Moser polynomials, these high-order rogue wave patterns asymptotically approach first-order rogue waves. At the positions in the $(x,t)$-plane corresponding to multiple roots of the Adler--Moser polynomials, these rogue wave patterns asymptotically tend toward lower-order fundamental rogue waves, dispersed first-order rogue waves, or mixed structures of these rogue waves. These structures are related to the root structures of special Adler--Moser polynomials with new free parameters, such as the Yablonskii--Vorob'ev polynomial hierarchy, among others. Notably, the positions of the fundamental lower-order rogue waves or mixed structures in these rogue wave patterns can be controlled freely under specific conditions.
- [7] arXiv:2405.19887 [pdf, ps, html, other]
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Title: Modulational Instability of the Coupled Nonlinear volatility and option price modelC. Gaafele, Edmond B. Madimabe, K. Ndebele, P. Otlaadisa, B. Mozola, T. Matabana, K. Seamolo, P. PilaneSubjects: Pattern Formation and Solitons (nlin.PS)
We study the Coupled Nonlinear volatility and option price model via both Modulational instability analysis and direct simulations. Since the coupling term for both the volatility and the option price equation is the same, the MI results are dependent on it, and the stability of the volatility exists for the same condition as that of the price. The numerical simulations are done to comfirm the conditions of MI
- [8] arXiv:2405.19929 [pdf, ps, html, other]
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Title: Periodic forces combined with feedback induce quenching in a bistable oscillatorComments: 11 pages, 10 figuresSubjects: Adaptation and Self-Organizing Systems (nlin.AO); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable oscillators under several perturbations have been addressed in the literature, the mechanism of oscillation quenching, a transition from a limit cycle to a fixed point, has not been fully understood. In this study, we analyze quenching using the extended Stuart-Landau oscillator driven by periodic forces. Numerical simulations suggest that the entrainment to the periodic force induces the amplitude change of a limit cycle. By reducing the system with an averaging method, we investigate the bifurcation structures of the periodically-driven oscillator. We find that oscillation quenching occurs by the homoclinic bifurcation when we use a periodic force combined with quadratic feedback. In conclusion, we develop a state-transition method in a bistable oscillator using periodic forces, which would have the potential for practical applications in controlling and annihilating abnormal oscillations. Moreover, we clarify the rich and diverse bifurcation structures behind periodically-driven bistable oscillators, which we believe would contribute to further understanding the complex behaviors in non-autonomous systems.
- [9] arXiv:2405.19952 [pdf, ps, html, other]
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Title: Generalized Bigraded Toda HierarchyComments: 16 pagesSubjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Bigraded Toda hierarchy $L_1^M(n)=L_2^N(n)$ is generalized to $L_1^M(n)=L_2^{N}(n)+\sum_{j\in \mathbb Z}\sum_{i=1}^{m}q^{(i)}_n\Lambda^jr^{(i)}_{n+1}$, which is the analogue of the famous constrained KP hierarchy $L^{k}= (L^{k})_{\geq0}+\sum_{i=1}^{m}q_{i}\partial^{-1}r_i$. It is known that different bosonizations of fermionic KP hierarchy will give rise to different kinds of integrable hierarchies. Starting from the fermionic form of constrained KP hierarchy, bilinear equation of this generalized bigraded Toda hierarchy (GBTH) are derived by using 2--component boson--fermion correspondence. Next based upon this, the Lax structure of GBTH is obtained. Conversely, we also derive bilinear equation of GBTH from the corresponding Lax structure.
- [10] arXiv:2405.20106 [pdf, ps, html, other]
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Title: Stability and dynamics of nonlinear excitations in a two-dimensional droplet-bearing environmentComments: 14 pages, 6 figuresSubjects: Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas)
We unravel stationary states in the form of dark soliton stripes, bubbles, and kinks embedded in a two-dimensional droplet-bearing setting emulated by an extended Gross-Pitaevskii approach. The existence of these configurations is corroborated through an effectively reduced potential picture demonstrating their concrete parametric regions of existence. The excitation spectra of such configurations are analyzed within the Bogoliubov-de-Gennes framework exposing the destabilization of dark soliton stripes and bubbles, while confirming the stability of droplets, and importantly unveiling spectral stability of the kink against transverse excitations. Additionally, a variational approach is constructed providing access to the transverse stability analysis of the dark soliton stripe for arbitrary chemical potentials and widths of the structure. This is subsequently compared with the stability analysis outcome demonstrating very good agreement at small wavenumbers. Dynamical destabilization of dark soliton stripes via the snake instability is showcased, while bubbles are found to feature both a splitting into a gray soliton pair and a transverse instability thereof. These results shed light on unexplored stability and instability properties of nonlinear excitations in environments featuring a competition of mean-field repulsion and beyond-mean-field attraction that can be probed by state-of-the-art experiments.
New submissions for Friday, 31 May 2024 (showing 10 of 10 entries )
- [11] arXiv:2405.19518 (cross-list from physics.ao-ph) [pdf, ps, html, other]
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Title: Exploring the Potential of Hybrid Machine-Learning/Physics-Based Modeling for Atmospheric/Oceanic Prediction Beyond the Medium RangeSubjects: Atmospheric and Oceanic Physics (physics.ao-ph); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD)
This paper explores the potential of a hybrid modeling approach that combines machine learning (ML) with conventional physics-based modeling for weather prediction beyond the medium range. It extends the work of Arcomano et al. (2022), which tested the approach for short- and medium-range weather prediction, and the work of Arcomano et al. (2023), which investigated its potential for climate modeling. The hybrid model used for the forecast experiments of the paper is based on the low-resolution, simplified parameterization atmospheric general circulation model (AGCM) SPEEDY. In addition to the hybridized prognostic variables of SPEEDY, the current version of the model has three purely ML-based prognostic variables. One of these is 6~h cumulative precipitation, another is the sea surface temperature, while the third is the heat content of the top 300 m deep layer of the ocean. The model has skill in predicting the El Niño cycle and its global teleconnections with precipitation for 3-7 months depending on the season. The model captures equatorial variability of the precipitation associated with Kelvin and Rossby waves and MJO. Predictions of the precipitation in the equatorial region have skill for 15 days in the East Pacific and 11.5 days in the West Pacific. Though the model has low spatial resolution, for these tasks it has prediction skill comparable to what has been published for high-resolution, purely physics-based, conventional operational forecast models.
- [12] arXiv:2405.19607 (cross-list from cond-mat.quant-gas) [pdf, ps, html, other]
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Title: Generic transverse stability of kink structures in atomic and optical nonlinear media with competing attractive and repulsive interactionsComments: 4 pages, 3 figuresSubjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS); Atomic Physics (physics.atom-ph)
We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and three-dimensional extended Gross-Pitaevskii models with quantum fluctuations describing droplet-bearing environments but also to the two-dimensional cubic-quintic nonlinear Schrödinger equation containing higher-order corrections to the nonlinear refractive index. Contrary to the generic dark soliton transverse instability, the kink structures are generically robust under the interplay of low-amplitude attractive and high-amplitude repulsive interactions. A quasi-1D effective potential picture dictates the existence of these defects, while their stability is obtained through linearization analysis and direct dynamics in the presence of external fluctuations showcasing their unprecedented resilience. These generic (across different models) findings should be detectable in current cold atom and optics experiments. They also offer insights towards controlling topological excitations and their usage in topological quantum computers.
- [13] arXiv:2405.19798 (cross-list from math-ph) [pdf, ps, html, other]
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Title: Mixed radix numeration bases: H\"orner's rule, Yang-Baxter equation and Furstenberg's conjectureSubjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Number Theory (math.NT); Probability (math.PR); Exactly Solvable and Integrable Systems (nlin.SI)
Mixed radix bases in numeration is a very old notion but it is rarely studied on its own or in relation with concrete problems related to number theory. Starting from the natural question of the conversion of a basis to another for integers as well as polynomials, we use mixed radix bases to introduce two-dimensional arrays with suitable filling rules. These arrays provide algorithms of conversion which uses only a finite number of euclidean division to convert from one basis to another; it is interesting to note that these algorithms are generalizations of the well-known Hörner's rule of quick evaluation of polynomials. The two-dimensional arrays with local transformations are reminiscent from statistical mechanics models: we show that changes between three numeration basis are related to the set-theoretical Yang-Baxter equation and this is, up to our knowledge, the first time that such a structure is described in number theory. As an illustration, we reinterpret well-known results around Furstenberg's conjecture in terms of Yang-Baxter transformations between mixed radix bases, hence opening the way to alternative approaches.
- [14] arXiv:2405.20021 (cross-list from physics.flu-dyn) [pdf, ps, html, other]
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Title: Chaotic advection in a steady three-dimensional MHD flowComments: Pre-submission version (preprint). Submitted to Physical Review FluidsSubjects: Fluid Dynamics (physics.flu-dyn); Chaotic Dynamics (nlin.CD); Computational Physics (physics.comp-ph)
We investigate a real 3D stationary flow characterized by chaotic advection generated by a magnetic field created by permanent magnets acting on a weakly conductive fluid subjected to a weak constant current. The model under consideration involves the Stokes equations for viscous incompressible fluid at low Reynolds number in which the density forces correspond to the Lorentz force generated by the magnetic field of the magnets and the electric current through the fluid. An innovative numerical approach based on a mixed finite element method has been developed and implemented for computing the flow velocity fields with the electromagnetic force. This ensures highly accurate numerical results, allowing a detailed analysis of the chaotic behavior of fluid trajectories through the computations of associated Poincaré sections and Lyapunov exponents. Subsequently, an examination of mixing efficiency is conducted, employing computations of contamination and homogeneity rates, as well as mixing time. The obtained results underscore the relevance of the modeling and computational tools employed, as well as the design of the magnetohydrodynamic device used.
- [15] arXiv:2405.20177 (cross-list from math-ph) [pdf, ps, html, other]
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Title: On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetrySubjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA); Exactly Solvable and Integrable Systems (nlin.SI)
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from $\mathfrak{g}$, we use the residual $U(1)$ charge and the block Gauss decomposition of the $R$-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation.
- [16] arXiv:2405.20265 (cross-list from math.AP) [pdf, ps, html, other]
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Title: Pinning and dipole asymptotics of locally deformed striped phasesComments: 30pSubjects: Analysis of PDEs (math.AP); Pattern Formation and Solitons (nlin.PS)
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce algebraically decaying, dipole-type farfield deformations. Phase shifts and leading order terms are determined by effective moments of the spatial inhomogeneity. Farfield decay is proportional to the derivatives of the Green's function of an effective Laplacian. Technically, we use mode filters and conjugacies to an effective Laplacian to establish Fredholm properties of the linearization in Kondratiev spaces. Spatial localization in a contraction argument is gained through the use of an explicit deformation ansatz and a subtle cancellation in Bloch wave space.
Cross submissions for Friday, 31 May 2024 (showing 6 of 6 entries )
- [17] arXiv:2404.16715 (replaced) [pdf, ps, html, other]
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Title: Third order interactions shift the critical coupling in multidimensional Kuramoto modelsComments: 15 pages, 4 figures. New analysis of bi-stability and hysteresisSubjects: Pattern Formation and Solitons (nlin.PS)
The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except $D=2$, where a cancellation occurs. After the transition, three and four body interactions combine to facilitate synchronization. Similar to the 2-dimensional case, bi-stability and hysteresis develop for large enough higher order interactions. We show simulations in $D=3$ and $4$ to illustrate the dynamics.
- [18] arXiv:2307.05407 (replaced) [pdf, ps, other]
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Title: Weyl's law in Liouville quantum gravityComments: Typos fixed; re-organised introduction with expanded literature reviewSubjects: Probability (math.PR); Mathematical Physics (math-ph); Differential Geometry (math.DG); Spectral Theory (math.SP); Chaotic Dynamics (nlin.CD)
Can you hear the shape of Liouville quantum gravity? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the $n$-th eigenvalue grows linearly with $n$, with the proportionality constant given by the Liouville area of the domain and a certain deterministic constant $c_\gamma$ depending on $\gamma \in (0, 2)$. The constant $c_\gamma$, initially a complicated function of Sheffield's quantum cone, can be evaluated explicitly and is strictly greater than the equivalent Riemannian constant.
At the heart of the proof we obtain sharp asymptotics of independent interest for the small-time behaviour of the on-diagonal heat kernel. Interestingly, we show that the scaled heat kernel displays nontrivial pointwise fluctuations. Fortunately, at the level of the heat trace these pointwise fluctuations cancel each other, which leads to the result.
We complement these results with a number of conjectures on the spectral geometry of Liouville quantum gravity, notably suggesting a connection with quantum chaos. - [19] arXiv:2308.06766 (replaced) [pdf, ps, html, other]
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Title: Statistics of local level spacings in single- and many-body quantum chaosComments: Published version. Main text: 7 pages, 1 figure and 3 tables. Supplemental material: 5 pages and 4 figuresJournal-ref: Phys. Rev. Lett. 132, 220401 (2024)Subjects: Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians.
- [20] arXiv:2312.09161 (replaced) [pdf, ps, other]
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Title: Spontaneous cold-to-hot heat transfer in a nonchaotic mediumComments: 28 pages, 11 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
It has long been known that, fundamentally different from a large body of rarefied gas, when a Knudsen gas is immersed in a thermal bath, it may never reach thermal equilibrium. The root cause is nonchaoticity: as the particle-particle collisions are sparse, the particle trajectories tend to be independent of each other. Usually, this counterintuitive phenomenon is studied through kinetic theory and is not considered a thermodynamic problem. In current research, we show that if incorporated in a large-sized compound setup, such an intrinsically nonequilibrium behavior has nontrivial consequences and cannot circumvent thermodynamics: cold-to-hot heat transfer may spontaneously take place, either cyclically (with entropy barriers) or continuously (with an energy barrier). It allows for production of useful work by absorbing heat from a single thermal reservoir without any other effect. As the system obeys the first law of thermodynamics, the refrigeration statement and the heat-engine statement of the second law of thermodynamics cannot be applied. The basic principle of maximum entropy is always adhered to.
- [21] arXiv:2312.13256 (replaced) [pdf, ps, html, other]
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Title: Extended Baxter relations and QQ-systems for quantum affine algebrasComments: 42 pages, v3: more details added, accepted for publication in Communications in Math. PhysSubjects: Quantum Algebra (math.QA); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Representation Theory (math.RT); Exactly Solvable and Integrable Systems (nlin.SI)
Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works arXiv:1308.3444 and arXiv:1606.05301. In the present paper, we conjecture a family of analogous relations labeled by elements of the Weyl group W of g, so that the original relations correspond to the identity element. These relations are closely connected to the W-symmetry of q-characters established in arXiv:2211.09779. We prove these relations for all w in W if g has rank two, and we prove the extended TQ-relations if w is a simple reflection. We also generalize our results and conjectures to the shifted quantum affine algebras.
- [22] arXiv:2312.14826 (replaced) [pdf, ps, html, other]
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Title: Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and sizeComments: 34+5 pages, 5 figures. Simulation data and codes for all figures are electronically available from the University of Leeds Data Repository. DOI: this https URL. In this version: typos corrected, formatting improved for readability, reordering of equations between main manuscript and appendixSubjects: Populations and Evolution (q-bio.PE); Statistical Mechanics (cond-mat.stat-mech); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph)
Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from a cooperative behaviour. Moreover, microbes generally evolve in volatile environments that, together with demographic fluctuations (birth and death events), drastically alter population size and strain survival. Motivated by the need to better understand the evolution of AMR, we study a population of time-varying size consisting of two competing strains, one drug-resistant and one drug-sensitive, subject to demographic and environmental variability. This is modelled by a binary carrying capacity randomly switching between mild and harsh environmental conditions, and driving the fluctuating volume (total amount of nutrients and antimicrobials at fixed concentration), and thus the size of the community (number of resistant and sensitive cells). We assume that AMR is a shared public good when the concentration of resistant cells exceeds a fixed concentration cooperation threshold, above which the sensitive strain has a growth advantage, whereas resistant cells dominate below it. Using computational means, and devising an analytical treatment (built on suitable quenched and annealed averaging procedures), we fully characterise the influence of fluctuations on the eco-evolutionary dynamics of AMR, and notably obtain specific strain fixation and long-lasting coexistence probabilities as a function of the environmental variation rate and cooperation threshold. We find that microbial strains tend to coexistence, but demographic fluctuations eventually lead to the extinction of resistant or sensitive cells for small or large values of the concentration cooperation threshold, respectively. This also holds for dynamic environments, whose specific properties determine the extinction timescale.
- [23] arXiv:2404.04870 (replaced) [pdf, ps, html, other]
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Title: Signal-noise separation using unsupervised reservoir computingSubjects: Machine Learning (cs.LG); Signal Processing (eess.SP); Chaotic Dynamics (nlin.CD)
Removing noise from a signal without knowing the characteristics of the noise is a challenging task. This paper introduces a signal-noise separation method based on time series prediction. We use Reservoir Computing (RC) to extract the maximum portion of "predictable information" from a given signal. Reproducing the deterministic component of the signal using RC, we estimate the noise distribution from the difference between the original signal and reconstructed one. The method is based on a machine learning approach and requires no prior knowledge of either the deterministic signal or the noise distribution. It provides a way to identify additivity/multiplicativity of noise and to estimate the signal-to-noise ratio (SNR) indirectly. The method works successfully for combinations of various signal and noise, including chaotic signal and highly oscillating sinusoidal signal which are corrupted by non-Gaussian additive/ multiplicative noise. The separation performances are robust and notably outstanding for signals with strong noise, even for those with negative SNR.