Pub Date : 2026-05-01Epub Date: 2026-01-22DOI: 10.1016/j.physd.2026.135116
Fernando F․ Grinstein, Vincent P․ Chiravalle, Robert K. Greene
We focus on coarse graining simulations based on the primary conservation equations, effectively codesigned physics and algorithms, and low-Mach-number corrected (LMC) hydrodynamics. Simulation methods involve LANL’s x-Radiation-Adaptive-Grid-Eulerian Large-Eddy Simulation, Besnard-Harlow-Rauenzahn (BHR) Reynolds-Averaged Navier-Stokes (RANS) approach, and Dynamic BHR – a paradigm bridging RANS and LES.
A relevant question addressed relates to whether 3D RANS and RANS/LES hybrids – the industry standards for aerospace and automotive research, are presently relevant for practical variable-density applications involving shocked and accelerated interface instabilities. Recent simulations of the GaTECH inclined mixing-layer shock-tube and NIF ICF-capsule experiments are used to demonstrate issues, challenges, and potential for 3D coarse grained LMC simulation strategies for robustly simulating complex transitional and coupled hydrodynamics-multiphysics with coarser resolution. Present LES readiness to provide accurate predictions at scale is demonstrated – whereas 3D RANS and RANS/LES bridging do not appear impactful in this context.
{"title":"Recent progress on coarse graining simulations","authors":"Fernando F․ Grinstein, Vincent P․ Chiravalle, Robert K. Greene","doi":"10.1016/j.physd.2026.135116","DOIUrl":"10.1016/j.physd.2026.135116","url":null,"abstract":"<div><div>We focus on coarse graining simulations based on the primary conservation equations, effectively codesigned physics and algorithms, and low-Mach-number corrected (LMC) hydrodynamics. Simulation methods involve LANL’s x-Radiation-Adaptive-Grid-Eulerian Large-Eddy Simulation, Besnard-Harlow-Rauenzahn (BHR) Reynolds-Averaged Navier-Stokes (RANS) approach, and Dynamic BHR – a paradigm bridging RANS and LES.</div><div><em>A relevant question addressed relates to whether 3D RANS and RANS/LES hybrids – the industry standards for aerospace and automotive research, are presently relevant for practical variable-density applications involving shocked and accelerated interface instabilities</em>. Recent simulations of the GaTECH inclined mixing-layer shock-tube and NIF ICF-capsule experiments are used to demonstrate issues, challenges, and potential for 3D coarse grained LMC simulation strategies for robustly simulating complex transitional and coupled hydrodynamics-multiphysics with coarser resolution. <em>Present LES readiness to provide accurate predictions at scale is demonstrated – whereas 3D RANS and RANS/LES bridging do not appear impactful in this context.</em></div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135116"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-29DOI: 10.1016/j.physd.2026.135124
Gaetano Fiore , Paolo Tomassini
We propose and detail a multi-step analytical procedure, based on an improved fully relativistic plane model for Laser Wake Field Acceleration, to tailor the initial density of a cold diluted plasma to the laser pulse profile, so as to control the spacetime localization and features of wave-breakings of the plasma wave and maximize the early stage acceleration of small bunches of electrons self-injected by the first wave-breaking at the density down-ramp. We find an excellent agreement with the results of 1D Particle In Cell simulations obtained with the same input data.
{"title":"An analytical optimization of plasma density profiles for downramp injection in laser wake-field acceleration","authors":"Gaetano Fiore , Paolo Tomassini","doi":"10.1016/j.physd.2026.135124","DOIUrl":"10.1016/j.physd.2026.135124","url":null,"abstract":"<div><div>We propose and detail a multi-step analytical procedure, based on an improved fully relativistic plane model for Laser Wake Field Acceleration, to tailor the initial density of a cold diluted plasma to the laser pulse profile, so as to control the spacetime localization and features of wave-breakings of the plasma wave and maximize the early stage acceleration of small bunches of electrons self-injected by the first wave-breaking at the density down-ramp. We find an excellent agreement with the results of 1D Particle In Cell simulations obtained with the same input data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135124"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-12-25DOI: 10.1016/j.physd.2025.135097
Michał Łepek , Agata Fronczak , Piotr Fronczak
Over the last decade, a combinatorial approach to discrete, finite, and irreversibly aggregating systems has been progressively developed. In this work, we review its achievements up to the present moment, focusing on the practical aspects and discussing its limitations. First, we present the assumptions and combinatorial foundations of the approach, which are based on direct counting of the system states, in contrast to the previous approaches of Smoluchowski and Marcus–Lushnikov. A method to obtain combinatorial expressions for the average number of clusters of a given size and, importantly, the corresponding standard deviation is described by solving the simplest example of a constant kernel. An expression for a complete probability distribution for a number of clusters of a given size is also presented. Then, we extend consideration to a number of kernels (e.g., additive, product, linear-chain, condensation), which were recently solved by explicitly finding the number of ways to create a cluster of a given size. We show that, for a general case, the present framework yields approximate solutions. In this way, theoretical predictions for any given kernel may be obtained with no need to find an explicit solution but using a recursive expression. We exploit this opportunity to present the use of combinatorial expressions to solve kernels related to the real processes of aerosol growth and planetesimal formation. At this point, a comparison to numerical results appears. Finally, issues related to the validity and varying precision of the theoretical predictions are summarized. In the last section, we propose open problems. Appendix contains partial Bell polynomials, generating function method, Lagrange inversion, potential fields of further application, and considerations on the relation of the presented combinatorial solutions to the scaling solutions of the Smoluchowski equation.
{"title":"A mini-review on combinatorial solutions to the Marcus–Lushnikov irreversible aggregation","authors":"Michał Łepek , Agata Fronczak , Piotr Fronczak","doi":"10.1016/j.physd.2025.135097","DOIUrl":"10.1016/j.physd.2025.135097","url":null,"abstract":"<div><div>Over the last decade, a combinatorial approach to discrete, finite, and irreversibly aggregating systems has been progressively developed. In this work, we review its achievements up to the present moment, focusing on the practical aspects and discussing its limitations. First, we present the assumptions and combinatorial foundations of the approach, which are based on direct counting of the system states, in contrast to the previous approaches of Smoluchowski and Marcus–Lushnikov. A method to obtain combinatorial expressions for the average number of clusters of a given size and, importantly, the corresponding standard deviation is described by solving the simplest example of a constant kernel. An expression for a complete probability distribution for a number of clusters of a given size is also presented. Then, we extend consideration to a number of kernels (e.g., additive, product, linear-chain, condensation), which were recently solved by explicitly finding the number of ways to create a cluster of a given size. We show that, for a general case, the present framework yields approximate solutions. In this way, theoretical predictions for any given kernel may be obtained with no need to find an explicit solution but using a recursive expression. We exploit this opportunity to present the use of combinatorial expressions to solve kernels related to the real processes of aerosol growth and planetesimal formation. At this point, a comparison to numerical results appears. Finally, issues related to the validity and varying precision of the theoretical predictions are summarized. In the last section, we propose open problems. Appendix contains partial Bell polynomials, generating function method, Lagrange inversion, potential fields of further application, and considerations on the relation of the presented combinatorial solutions to the scaling solutions of the Smoluchowski equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135097"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-16DOI: 10.1016/j.physd.2026.135118
Oleg Schilling
A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θm, and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θmol. The scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.
{"title":"A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing","authors":"Oleg Schilling","doi":"10.1016/j.physd.2026.135118","DOIUrl":"10.1016/j.physd.2026.135118","url":null,"abstract":"<div><div>A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D <strong>402</strong>, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter <em>θ<sub>m</sub></em>, and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, <em>θ<sub>mol</sub></em>. The scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. <em>The explicit modeling and solution of turbulent transport equations are not required</em>. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135118"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-06DOI: 10.1016/j.physd.2026.135137
Xu Han , Bin Yu , Hong Liu
The mixing mechanism in oblique shock-jet interaction (OS/JI), a canonical configuration for mixing enhancement in scramjet combustors, is investigated using high-resolution large-eddy simulation (LES). This study focuses on elucidating the roles of distinct flow structures in governing the mixing process within OS/JI. Two primary flow structures are identified following the interaction between the jet and the shock wave. First, the jet cross-section deforms into a streamwise vortex, whose qualitative morphology and quantitative circulation closely resemble those observed in two-dimensional shock-bubble interaction (SBI), indicating a baroclinic vorticity-driven formation. Second, a shear layer develops as a result of the velocity difference between the post-shock jet and the ambient air, a phenomenon quantitatively described by a shear velocity model. The contribution of the streamwise vortex to mixing is examined using a reduced mixing model, which, despite its success in accurately predicting the mixing fraction in SBI, is shown to systematically underestimate mixing in OS/JI. This finding highlights the pivotal role of the shear layer in enhancing mixing. The effect of the shear layer is further quantified through a shear-enhanced diffusivity, based on which a shear-enhanced mixing model is formulated by incorporating this additional diffusivity into the reduced mixing model. The proposed model establishes a quantitative relationship between these two flow structures and the evolution of the mixing fraction in OS/JI across various shear-layer intensities. Furthermore, the influence of shear-enhanced diffusion on the mixing process is clarified by the scaling behavior of the characteristic mixing time tcharac. In the molecular diffusion dominated mixing, tcharac scales with circulation as , in agreement with the canonical single-vortex mixing law. However, in the shear-enhanced diffusion dominated regime, this scaling shifts to , thereby demonstrating the significant impact of the shear layer on mixing in OS/JI.
{"title":"Shear-enhanced diffusion in oblique shock-jet interaction","authors":"Xu Han , Bin Yu , Hong Liu","doi":"10.1016/j.physd.2026.135137","DOIUrl":"10.1016/j.physd.2026.135137","url":null,"abstract":"<div><div>The mixing mechanism in oblique shock-jet interaction (OS/JI), a canonical configuration for mixing enhancement in scramjet combustors, is investigated using high-resolution large-eddy simulation (LES). This study focuses on elucidating the roles of distinct flow structures in governing the mixing process within OS/JI. Two primary flow structures are identified following the interaction between the jet and the shock wave. First, the jet cross-section deforms into a streamwise vortex, whose qualitative morphology and quantitative circulation closely resemble those observed in two-dimensional shock-bubble interaction (SBI), indicating a baroclinic vorticity-driven formation. Second, a shear layer develops as a result of the velocity difference between the post-shock jet and the ambient air, a phenomenon quantitatively described by a shear velocity model. The contribution of the streamwise vortex to mixing is examined using a reduced mixing model, which, despite its success in accurately predicting the mixing fraction in SBI, is shown to systematically underestimate mixing in OS/JI. This finding highlights the pivotal role of the shear layer in enhancing mixing. The effect of the shear layer is further quantified through a shear-enhanced diffusivity, based on which a shear-enhanced mixing model is formulated by incorporating this additional diffusivity into the reduced mixing model. The proposed model establishes a quantitative relationship between these two flow structures and the evolution of the mixing fraction in OS/JI across various shear-layer intensities. Furthermore, the influence of shear-enhanced diffusion on the mixing process is clarified by the scaling behavior of the characteristic mixing time <em>t<sub>charac</sub></em>. In the molecular diffusion dominated mixing, <em>t<sub>charac</sub></em> scales with circulation <span><math><msub><mstyle><mi>Γ</mi></mstyle><mi>t</mi></msub></math></span> as <span><math><mrow><msub><mi>t</mi><mrow><mi>c</mi><mi>h</mi><mi>a</mi><mi>r</mi><mi>a</mi><mi>c</mi></mrow></msub><mo>∼</mo><msubsup><mstyle><mi>Γ</mi></mstyle><mi>t</mi><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msubsup></mrow></math></span>, in agreement with the canonical single-vortex mixing law. However, in the shear-enhanced diffusion dominated regime, this scaling shifts to <span><math><mrow><msub><mi>t</mi><mrow><mi>c</mi><mi>h</mi><mi>a</mi><mi>r</mi><mi>a</mi><mi>c</mi></mrow></msub><mo>∼</mo><msubsup><mstyle><mi>Γ</mi></mstyle><mi>t</mi><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup></mrow></math></span>, thereby demonstrating the significant impact of the shear layer on mixing in OS/JI.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135137"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-19DOI: 10.1016/j.physd.2026.135121
Wennan Zou, Jian He
The contact structures of fluid are described by the streamline pattern in steady flows, where the key to determine the slip topology the streamline pattern around the isotropic point, called the local streamline pattern (LSP). In this paper, taking homogeneous quadratic velocity fields (HQVFs) as the research object and utilizing the swirl field, which is an axis-vector-valued differential 1-form determined by the velocity direction, to define the topological degree, we establish an analytical framework for three-dimensional nonlinear velocity fields. After obtaining the trivial result of the topological degree of three-dimensional HQVFs, we make use of the characteristic problems of high order tensor to work out all radial streamlines entering/exiting an isotropic point, and adopt the pair number of radial streamlines as the key criterion to classify the LSPs. Some typical HQVFs are illustrated for discussion, and the investigation on linear velocity fields shows their particularity. As a preliminary exploration of the streamline pattern of three-dimensional nonlinear velocity fields, this work demonstrates how difficult it is to generalize the research results of two-dimensional velocity fields and three-dimensional linear velocity fields.
{"title":"Slip topology of three-dimensional homogeneous quadratic velocity fields","authors":"Wennan Zou, Jian He","doi":"10.1016/j.physd.2026.135121","DOIUrl":"10.1016/j.physd.2026.135121","url":null,"abstract":"<div><div>The contact structures of fluid are described by the streamline pattern in steady flows, where the key to determine the slip topology the streamline pattern around the isotropic point, called the local streamline pattern (LSP). In this paper, taking homogeneous quadratic velocity fields (HQVFs) as the research object and utilizing the swirl field, which is an axis-vector-valued differential 1-form determined by the velocity direction, to define the topological degree, we establish an analytical framework for three-dimensional nonlinear velocity fields. After obtaining the trivial result of the topological degree of three-dimensional HQVFs, we make use of the characteristic problems of high order tensor to work out all radial streamlines entering/exiting an isotropic point, and adopt the pair number of radial streamlines as the key criterion to classify the LSPs. Some typical HQVFs are illustrated for discussion, and the investigation on linear velocity fields shows their particularity. As a preliminary exploration of the streamline pattern of three-dimensional nonlinear velocity fields, this work demonstrates how difficult it is to generalize the research results of two-dimensional velocity fields and three-dimensional linear velocity fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135121"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-24DOI: 10.1016/j.physd.2026.135122
Han-Lin Liao, Guo-Cheng Wu, Dong Li
Fractional differential equations frequently arise in long-range interaction processes. The center manifold theorem is an essential tool in reduction of dynamical systems. First, this paper provides existence conditions for center manifolds by constructing function spaces and fixed-point mappings. Then, determining the center manifolds becomes a parameter estimation problem. Because the chain rule for fractional derivatives cannot be applied, a neural network method is developed to find approximate center manifolds near the zero equilibrium. The automatic model selection is employed to search for a neural network architecture. Two examples are presented to demonstrate the efficiency of reducing high-dimensional fractional order systems under weak data.
{"title":"Center manifold theorem of fractional differential equations and machine learning under weak data","authors":"Han-Lin Liao, Guo-Cheng Wu, Dong Li","doi":"10.1016/j.physd.2026.135122","DOIUrl":"10.1016/j.physd.2026.135122","url":null,"abstract":"<div><div>Fractional differential equations frequently arise in long-range interaction processes. The center manifold theorem is an essential tool in reduction of dynamical systems. First, this paper provides existence conditions for center manifolds by constructing function spaces and fixed-point mappings. Then, determining the center manifolds becomes a parameter estimation problem. Because the chain rule for fractional derivatives cannot be applied, a neural network method is developed to find approximate center manifolds near the zero equilibrium. The automatic model selection is employed to search for a neural network architecture. Two examples are presented to demonstrate the efficiency of reducing high-dimensional fractional order systems under weak data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135122"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-18DOI: 10.1016/j.physd.2026.135119
Edoardo Peroni , Jing Ping Wang
We construct linear and quadratic Darboux matrices compatible with the reduction group of the Lax operator for each of the seven known non-Abelian derivative nonlinear Schrödinger equations that admit Lax representations. The differential-difference systems derived from these Darboux transformations generalise established non-Abelian integrable models by incorporating non-commutative constants. Specifically, we demonstrate that linear Darboux transformations generate non-Abelian Volterra-type equations, while quadratic transformations yield two-component systems, including non-Abelian versions of the Ablowitz-Ladik, Merola-Ragnisco-Tu, and relativistic Toda equations. Using quasideterminants, we establish necessary conditions for factorising a higher-degree polynomial Darboux matrix with a specific linear Darboux matrix as a factor. This result enables the factorisation of quadratic Darboux matrices into pairs of linear Darboux matrices.
{"title":"Darboux transformations and related non-Abelian integrable differential-difference systems of the derivative nonlinear Schrödinger type","authors":"Edoardo Peroni , Jing Ping Wang","doi":"10.1016/j.physd.2026.135119","DOIUrl":"10.1016/j.physd.2026.135119","url":null,"abstract":"<div><div>We construct linear and quadratic Darboux matrices compatible with the reduction group of the Lax operator for each of the seven known non-Abelian derivative nonlinear Schrödinger equations that admit Lax representations. The differential-difference systems derived from these Darboux transformations generalise established non-Abelian integrable models by incorporating non-commutative constants. Specifically, we demonstrate that linear Darboux transformations generate non-Abelian Volterra-type equations, while quadratic transformations yield two-component systems, including non-Abelian versions of the Ablowitz-Ladik, Merola-Ragnisco-Tu, and relativistic Toda equations. Using quasideterminants, we establish necessary conditions for factorising a higher-degree polynomial Darboux matrix with a specific linear Darboux matrix as a factor. This result enables the factorisation of quadratic Darboux matrices into pairs of linear Darboux matrices.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135119"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-04DOI: 10.1016/j.physd.2026.135136
Dana L. O.-L. Lavacot , Brandon E. Morgan , Ali Mani
Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (Phys. Rev. Fluids, 2025) is used to develop the k–L–F model, an extension of the k–L model of Dimonte and Tipton (Phys. Fluids, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the k–L–F model along with the k–L and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. The analysis reveals that models incorporating nonlocality (k–L–F and BHR–4) match the high-fidelity simulation data better than purely local models (k–L), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.
{"title":"Development and assessment of models for turbulent Rayleigh-Taylor mixing using the macroscopic forcing method","authors":"Dana L. O.-L. Lavacot , Brandon E. Morgan , Ali Mani","doi":"10.1016/j.physd.2026.135136","DOIUrl":"10.1016/j.physd.2026.135136","url":null,"abstract":"<div><div>Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (<em>Phys. Rev. Fluids</em>, 2025) is used to develop the <em>k</em>–<em>L</em>–<em>F</em> model, an extension of the <em>k</em>–<em>L</em> model of Dimonte and Tipton (<em>Phys. Fluids</em>, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the <em>k</em>–<em>L</em>–<em>F</em> model along with the <em>k</em>–<em>L</em> and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. The analysis reveals that models incorporating nonlocality (<em>k</em>–<em>L</em>–<em>F</em> and BHR–4) match the high-fidelity simulation data better than purely local models (<em>k</em>–<em>L</em>), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135136"},"PeriodicalIF":2.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-05DOI: 10.1016/j.physd.2026.135138
Yubin Huang , Liming Ling , Xiaoen Zhang
We study the Cauchy problem for the focusing coupled nonlinear Schrödinger (CNLS) equation with initial data q0 lying in the weighted Sobolev space and the scattering data having n simple zeros. Based on the corresponding 3 × 3 matrix spectral problem, we deduce the Riemann-Hilbert problem (RHP) for CNLS equation through inverse scattering transform. We remove discrete spectra of initial RHP using Darboux transformations. By applying the nonlinear steepest-descent method for RHP introduced by Deift and Zhou, we compute the long-time asymptotic expansion of the solution q(x, t) to an (optimal) residual error of order where 2 ≤ p < ∞. The leading order term in this expansion is a multi-soliton whose parameters are modulated by soliton-soliton and soliton-radiation interactions. Our work strengthens and extends the earlier work regarding long-time asymptotics for solutions of the nonlinear Schrödinger equation with a delta potential and even initial data by Deift and Park.
研究了聚焦耦合非线性Schrödinger （CNLS）方程的柯西问题，该方程初始数据q0位于加权Sobolev空间，散射数据有n个简单零。基于相应的3 × 3矩阵谱问题，通过逆散射变换推导出CNLS方程的Riemann-Hilbert问题（RHP）。我们利用达布变换去除初始RHP的离散谱。应用Deift和Zhou引入的RHP非线性最陡下降法，我们计算了解q（x, t）到O阶（t−3/4+1/(2p)）的（最优）残差的长时间渐近展开，其中2 ≤ p <； ∞。这个展开式中的第一阶项是多孤子，其参数由孤子-孤子和孤子-辐射相互作用调制。我们的工作加强和扩展了Deift和Park关于具有delta势和甚至初始数据的非线性Schrödinger方程解的长期渐近性的早期工作。
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