Pub Date : 2024-07-23DOI: 10.1088/1751-8121/ad62c9
Connor Roberts, Emir Sezik and Eloise Lardet
We model an overdamped Brownian particle that is subject to resetting facilitated by a ratchet potential on a spatially periodic domain. This asymmetric potential switches on with a constant rate, but switches off again only upon the particle’s first passage to a resetting point at the minimum of the potential. Repeating this cycle sustains a non-equilibrium steady-state, as well as a directed steady-state current which can be harnessed to perform useful work. We derive exact analytic expressions for the probability densities of the free-diffusion and resetting phases, the associated currents for each phase, and an efficiency parameter that quantifies the return in current for given power input. These expressions allow us to fully characterise the system and obtain experimentally relevant results such as the optimal current and efficiency. Our results are corroborated by simulations, and have implications for experimentally viable finite-time resetting protocols.
{"title":"Ratchet-mediated resetting: current, efficiency, and exact solution","authors":"Connor Roberts, Emir Sezik and Eloise Lardet","doi":"10.1088/1751-8121/ad62c9","DOIUrl":"https://doi.org/10.1088/1751-8121/ad62c9","url":null,"abstract":"We model an overdamped Brownian particle that is subject to resetting facilitated by a ratchet potential on a spatially periodic domain. This asymmetric potential switches on with a constant rate, but switches off again only upon the particle’s first passage to a resetting point at the minimum of the potential. Repeating this cycle sustains a non-equilibrium steady-state, as well as a directed steady-state current which can be harnessed to perform useful work. We derive exact analytic expressions for the probability densities of the free-diffusion and resetting phases, the associated currents for each phase, and an efficiency parameter that quantifies the return in current for given power input. These expressions allow us to fully characterise the system and obtain experimentally relevant results such as the optimal current and efficiency. Our results are corroborated by simulations, and have implications for experimentally viable finite-time resetting protocols.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"55 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.1088/1751-8121/ad61d4
Francisco Navarro-Lérida, Eugen Radu and D H Tchrakian
We study the Skyrmion of the SO(2) gauged O(3) sigma model in dimensions in the presence of a Skyrme–Chern–Simons (SCS) term, and compare its properties with the corresponding properties of the Skyrmion in the presence of the usual Chern–Simons (CS) term. We find that these properties are qualitatively largely similar in both cases, meaning that the SCS density can be employed as an alternative to the CS term also in higher dimensions, most importantly in even dimensions where no CS term is defined, in dimensions. The SCS density employed here is defined in terms of the pair of gauge fields and an auxiliary O(5) Skyrme scalar, which is contracted to an effective O(3) Skyrme scalar. Technically, this study maps the methods to be applied in higher dimensional examples.
{"title":"The effect of Skyrme–Chern–Simons dynamics on gauged Skyrmions in 2+1 dimensions","authors":"Francisco Navarro-Lérida, Eugen Radu and D H Tchrakian","doi":"10.1088/1751-8121/ad61d4","DOIUrl":"https://doi.org/10.1088/1751-8121/ad61d4","url":null,"abstract":"We study the Skyrmion of the SO(2) gauged O(3) sigma model in dimensions in the presence of a Skyrme–Chern–Simons (SCS) term, and compare its properties with the corresponding properties of the Skyrmion in the presence of the usual Chern–Simons (CS) term. We find that these properties are qualitatively largely similar in both cases, meaning that the SCS density can be employed as an alternative to the CS term also in higher dimensions, most importantly in even dimensions where no CS term is defined, in dimensions. The SCS density employed here is defined in terms of the pair of gauge fields and an auxiliary O(5) Skyrme scalar, which is contracted to an effective O(3) Skyrme scalar. Technically, this study maps the methods to be applied in higher dimensional examples.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"8 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.1088/1751-8121/ad6412
Shihabul Haque and Jayanta K Bhattacharjee
We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, θ, obeys the dynamics . The linearized approximation gives a divergent response (at long times) but the nonlinear terms make the response finite. We address the nonlinearity-induced finiteness in two ways by separately treating the short and long time scales. At long times, we use the traditional perturbative techniques to extract two drive dependent behaviours—one, the amplitude of oscillation scales as and, two, the time period of the slow mode varies as . For the early time behaviour, on the other hand, we devise an alternate perturbative expansion where the successive terms get larger with the order of evaluation but have alternating signs. The alternating signs (phase differences) between these terms leads to adestructive interference like effect. A careful consideration of this destructive interference like effect between successive terms leads to a finite response which describes the initial behaviour of the amplitude of the response reasonably correctly. We further note that for larger drive values, the system seems to undergo a first order transitional behaviour with a sudden jump in the largest Lyapunov exponent
{"title":"Interference aided finite resonant response in an undamped forced oscillator","authors":"Shihabul Haque and Jayanta K Bhattacharjee","doi":"10.1088/1751-8121/ad6412","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6412","url":null,"abstract":"We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, θ, obeys the dynamics . The linearized approximation gives a divergent response (at long times) but the nonlinear terms make the response finite. We address the nonlinearity-induced finiteness in two ways by separately treating the short and long time scales. At long times, we use the traditional perturbative techniques to extract two drive dependent behaviours—one, the amplitude of oscillation scales as and, two, the time period of the slow mode varies as . For the early time behaviour, on the other hand, we devise an alternate perturbative expansion where the successive terms get larger with the order of evaluation but have alternating signs. The alternating signs (phase differences) between these terms leads to adestructive interference like effect. A careful consideration of this destructive interference like effect between successive terms leads to a finite response which describes the initial behaviour of the amplitude of the response reasonably correctly. We further note that for larger drive values, the system seems to undergo a first order transitional behaviour with a sudden jump in the largest Lyapunov exponent","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.1088/1751-8121/ad62c8
Kohei Motegi and Ryo Ohkawa
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant representations for source functions which appeared in previous literature as well as introducing the elliptic version of the determinants, and obtain identities between determinants. We also show several symmetrization formulas for the rational version.
{"title":"Algebraic formulas and geometric derivation of source identities","authors":"Kohei Motegi and Ryo Ohkawa","doi":"10.1088/1751-8121/ad62c8","DOIUrl":"https://doi.org/10.1088/1751-8121/ad62c8","url":null,"abstract":"Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant representations for source functions which appeared in previous literature as well as introducing the elliptic version of the determinants, and obtain identities between determinants. We also show several symmetrization formulas for the rational version.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"59 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.1088/1751-8121/ad6365
Erickson Tjoa and Finnian Gray
In this work we make the connection between the Unruh–DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW model describes a simplified model of light–matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared (IR) divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.Our work clarifies the connection between obstructions due to Haag’s theorem and IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.
{"title":"The Unruh–DeWitt model and its joint interacting Hilbert space","authors":"Erickson Tjoa and Finnian Gray","doi":"10.1088/1751-8121/ad6365","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6365","url":null,"abstract":"In this work we make the connection between the Unruh–DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW model describes a simplified model of light–matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared (IR) divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.Our work clarifies the connection between obstructions due to Haag’s theorem and IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-22DOI: 10.1088/1751-8121/ad6364
Gabriele Bressanini, Marco G Genoni, M S Kim and Matteo G A Paris
We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cramér–Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.
{"title":"Multi-parameter quantum estimation of single- and two-mode pure Gaussian states","authors":"Gabriele Bressanini, Marco G Genoni, M S Kim and Matteo G A Paris","doi":"10.1088/1751-8121/ad6364","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6364","url":null,"abstract":"We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cramér–Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"77 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141753965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-21DOI: 10.1088/1751-8121/ad4c31
Michael te Vrugt, Julian Jeggle and Raphael Wittkowski
The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e. how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the susceptible-infected-recovered (SIR)-dynamical density functional theory (DDFT) model, a combination of the SIR model from epidemiology with DDFT from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.
{"title":"Passive and active field theories for disease spreading","authors":"Michael te Vrugt, Julian Jeggle and Raphael Wittkowski","doi":"10.1088/1751-8121/ad4c31","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4c31","url":null,"abstract":"The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e. how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the susceptible-infected-recovered (SIR)-dynamical density functional theory (DDFT) model, a combination of the SIR model from epidemiology with DDFT from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"17 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-21DOI: 10.1088/1751-8121/ad5ee1
Andrei Zotov
We consider 1+1 field generalization of the elliptic Calogero–Moser model. It is shown that the Lax connection satisfies the classical non-ultralocal r-matrix structure of Maillet type. Next, we consider 1+1 field analogue of the spin Calogero–Moser model and its multipole (or multispin) extension. Finally, we discuss the field analogue of the classical IRF-Vertex correspondence, which relates utralocal and non-ultralocal r-matrix structures.
我们考虑了椭圆卡洛吉罗-莫泽模型的 1+1 场广义化。结果表明，拉克斯连接满足经典的麦莱型非超局域 r 矩阵结构。接下来，我们考虑了自旋卡洛吉罗-莫泽模型的 1+1 场类似物及其多极（或多频）扩展。最后，我们讨论了经典 IRF 顶点对应的场类比，它关联了宇称和非宇称 r 矩阵结构。
{"title":"Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero–Moser model","authors":"Andrei Zotov","doi":"10.1088/1751-8121/ad5ee1","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5ee1","url":null,"abstract":"We consider 1+1 field generalization of the elliptic Calogero–Moser model. It is shown that the Lax connection satisfies the classical non-ultralocal r-matrix structure of Maillet type. Next, we consider 1+1 field analogue of the spin Calogero–Moser model and its multipole (or multispin) extension. Finally, we discuss the field analogue of the classical IRF-Vertex correspondence, which relates utralocal and non-ultralocal r-matrix structures.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"61 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-21DOI: 10.1088/1751-8121/ad6223
Matthew J Simpson, Nizhum Rahman and Alexander K Y Tam
Reaction–diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many reaction–diffusion models of biological invasion are extensions of the well–known Fisher–Kolmogorov–Petrovskii–Piskunov model that describes the spatiotemporal evolution of a 1D population density, , as a result of linear diffusion with flux , and logistic growth source term, . In 2020 Fadai introduced a new reaction–diffusion model of biological invasion with a nonlinear degenerate diffusive flux, , and the model was formulated as a moving boundary problem on , with and at (Fadai and Simpson 2020 J. Phys. A: Math. Theor. 53 095601). Fadai’s model leads to travelling wave solutions with infinitely steep, well–defined fronts at the moving boundary, and the model has the mathematical advantage of being analytically tractable in certain parameter limits. In this work we consider the stability of the travelling wave solutions presented by Fadai. We provide general insight by first presenting two key extensions of Fadai’s model by considering: (i) generalised nonlinear degenerate diffusion with flux for some constant m > 0; and, (ii) solutions describing both biological invasion with , and biological recession with . After establishing the existence of travelling wave solutions for these two extensions, our main contribution is to consider stability of the travelling wave solutions by introducing a lateral perturbation of the travelling wavefront. Full 2D time–dependent level–set numerical solutions indicate that invasive travelling waves are stable to small amplitude lateral perturbations, whereas receding travelling waves are unstable. These preliminary numerical observations are corroborated through a linear stability analysis that gives more formal insight into short time growth/decay of wavefront perturbation amplitude. Julia–based software, including level–set algorithms, is available on Github to replicate all results in this study.
反应-扩散模型常用于描述生物入侵，在这种情况下，随机运动和增殖的个体种群会导致移动前沿。许多生物入侵的反应-扩散模型都是著名的 Fisher-Kolmogorov-Petrovskii-Piskunov 模型的扩展，该模型描述了一维种群密度（Ⅳ）的时空演化，是通量（Ⅴ）的线性扩散和对数增长源项（Ⅴ）的结果。2020 年，Fadai 引入了一个新的生物入侵反应-扩散模型，该模型具有非线性退化扩散通量 ，并被表述为一个关于 ，与 和 的移动边界问题（Fadai 和 Simpson 2020 J. Phys. A: Math. Theor. 53 095601）。Fadai 的模型导致了在移动边界上具有无限陡峭、定义明确的前沿的行波解，并且该模型具有在某些参数极限下可分析的数学优势。在这项研究中，我们考虑了 Fadai 提出的行波解的稳定性。我们首先提出了法戴模型的两个关键扩展，从而提供了一般性的见解：(i) 对于某个常数 m > 0，具有通量的广义非线性退化扩散；以及，(ii) 描述生物入侵（Ⅳ）和生物衰退（Ⅴ）的解。在确定了这两种扩展的行波解的存在性之后，我们的主要贡献是通过引入行波面的横向扰动来考虑行波解的稳定性。全二维随时间变化的水平集数值解表明，入侵的行波对小振幅横向扰动是稳定的，而后退的行波是不稳定的。这些初步数值观察结果通过线性稳定性分析得到了证实，从而对波面扰动振幅的短时间增长/衰减有了更正式的了解。Github 上提供了基于 Julia 的软件，包括水平集算法，可用于复制本研究的所有结果。
{"title":"Front stability of infinitely steep travelling waves in population biology","authors":"Matthew J Simpson, Nizhum Rahman and Alexander K Y Tam","doi":"10.1088/1751-8121/ad6223","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6223","url":null,"abstract":"Reaction–diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many reaction–diffusion models of biological invasion are extensions of the well–known Fisher–Kolmogorov–Petrovskii–Piskunov model that describes the spatiotemporal evolution of a 1D population density, , as a result of linear diffusion with flux , and logistic growth source term, . In 2020 Fadai introduced a new reaction–diffusion model of biological invasion with a nonlinear degenerate diffusive flux, , and the model was formulated as a moving boundary problem on , with and at (Fadai and Simpson 2020 J. Phys. A: Math. Theor. 53 095601). Fadai’s model leads to travelling wave solutions with infinitely steep, well–defined fronts at the moving boundary, and the model has the mathematical advantage of being analytically tractable in certain parameter limits. In this work we consider the stability of the travelling wave solutions presented by Fadai. We provide general insight by first presenting two key extensions of Fadai’s model by considering: (i) generalised nonlinear degenerate diffusion with flux for some constant m > 0; and, (ii) solutions describing both biological invasion with , and biological recession with . After establishing the existence of travelling wave solutions for these two extensions, our main contribution is to consider stability of the travelling wave solutions by introducing a lateral perturbation of the travelling wavefront. Full 2D time–dependent level–set numerical solutions indicate that invasive travelling waves are stable to small amplitude lateral perturbations, whereas receding travelling waves are unstable. These preliminary numerical observations are corroborated through a linear stability analysis that gives more formal insight into short time growth/decay of wavefront perturbation amplitude. Julia–based software, including level–set algorithms, is available on Github to replicate all results in this study.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"36 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-18DOI: 10.1088/1751-8121/ad5e4d
Viktoria Blavatska, Jaroslav Ilnytskyi and Erkki Lähderanta
Coagulation-flocculation, the physicochemical process widely used for purification a wastewater, is affected both by chemical details of involved polymers and by the statistics of their conformations on a large scale. The latter aspect is covered in this study by employing a coarse-grained modeling approach based on a combination of two paradigms of statistical mechanics. One is the self-avoiding walk (SAW) which generates a range of conformations for a linear polymer of NSAW monomers. Another one is a non-trivial diffusion limited aggregation (DLA) process of NDLA impurities (referred thereafter as ‘particles’) which describes their coagulation occurring with the probability (p = 1 recovers a standard DLA). DLA of diffusive particles is complemented by their irreversible adsorption on the SAW monomers occurring with the probability equal to one, both processes resulting in formation of the DLA-SAW agglomerates. The dynamics of formation of such agglomerates, as well as their fractal dimensions and internal structure are of practical interest. We consider a range of related characteristics, such as: (i) absolute Na and relative na adsorbing efficiencies of SAW; (ii) effective gyration radius of the DLA-SAW agglomerates; and (iii) the fractal dimension of these aggregates. These are studied within a wide range for each parameter from a set .
混凝-絮凝是一种广泛用于净化废水的物理化学过程，它既受相关聚合物化学细节的影响，也受其大规模构象统计的影响。本研究采用基于两种统计力学范式组合的粗粒度建模方法，涵盖了后一个方面。一种是自避让行走（SAW），它能为非甾体抗原单体的线性聚合物生成一系列构象。另一种是 NDLA 杂质（以下称为 "颗粒"）的非三维扩散受限聚集（DLA）过程，该过程描述了它们以概率（p = 1 恢复标准 DLA）发生的凝结。扩散颗粒的 DLA 与它们在 SAW 单体上发生的不可逆吸附（概率等于 1）相辅相成，这两个过程都会形成 DLA-SAW 聚集体。这种团聚体的形成动力学及其分形尺寸和内部结构具有实际意义。我们考虑了一系列相关特征，如(i) SAW 的绝对 Na 吸附效率和相对 Na 吸附效率；(ii) DLA-SAW 团聚体的有效回转半径；以及 (iii) 这些团聚体的分形尺寸。这些都是在一组......参数中每个参数的宽范围内进行研究的。
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