We consider the release and subsequent gravity-driven spreading of a dense finite volume of fluid in an anisotropic porous medium bounded by an impermeable substrate. When the permeability in the vertical direction is much smaller than in the horizontal direction, as is the case in many real geological reservoirs, this restricts the spread of the current to a very thin layer near the impermeable base. Using a combination of asymptotic analysis and finite difference computations of Darcy flow, we show that there exist two distinct flow regimes. At early times, the bulk of the current descends slowly and uniformly, injecting fluid into thin finger-like regions near the base. At much later times, the current transitions to the classical gravity-driven solution and continues to spread with a self-similar shape. One interesting consequence is that the swept volume of the current grows differently depending on the anisotropy of the medium. This has important consequences for managing contaminant spills, where it is important to minimize the contacted volume of the aquifer, or during geological CO2 sequestration where a larger contacted volume results in more CO2 being stored.
{"title":"Anisotropy distorts the spreading of a fixed volume porous gravity current","authors":"Graham P. Benham","doi":"10.1098/rspa.2023.0271","DOIUrl":"https://doi.org/10.1098/rspa.2023.0271","url":null,"abstract":"We consider the release and subsequent gravity-driven spreading of a dense finite volume of fluid in an anisotropic porous medium bounded by an impermeable substrate. When the permeability in the vertical direction is much smaller than in the horizontal direction, as is the case in many real geological reservoirs, this restricts the spread of the current to a very thin layer near the impermeable base. Using a combination of asymptotic analysis and finite difference computations of Darcy flow, we show that there exist two distinct flow regimes. At early times, the bulk of the current descends slowly and uniformly, injecting fluid into thin finger-like regions near the base. At much later times, the current transitions to the classical gravity-driven solution and continues to spread with a self-similar shape. One interesting consequence is that the swept volume of the current grows differently depending on the anisotropy of the medium. This has important consequences for managing contaminant spills, where it is important to minimize the contacted volume of the aquifer, or during geological <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">CO</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math> sequestration where a larger contacted volume results in more <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">CO</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math> being stored.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.
{"title":"Plane and axisymmetric problems of an interfacial crack in a power-law graded material","authors":"Y. A. Antipov","doi":"10.1098/rspa.2023.0630","DOIUrl":"https://doi.org/10.1098/rspa.2023.0630","url":null,"abstract":"Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"41 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
James Mason, Clément Erignoux, Robert L. Jack, Maria Bruna
We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume exclusion results in nonlinear mobility dependent on spatial density. Such models of active matter can support motility-induced phase separation, which occurs despite the absence of attractive interactions. We study the onset of phase separation with linear stability analysis and numerical simulations.
{"title":"Exact hydrodynamics and onset of phase separation for an active exclusion process","authors":"James Mason, Clément Erignoux, Robert L. Jack, Maria Bruna","doi":"10.1098/rspa.2023.0524","DOIUrl":"https://doi.org/10.1098/rspa.2023.0524","url":null,"abstract":"We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume exclusion results in nonlinear mobility dependent on spatial density. Such models of active matter can support motility-induced phase separation, which occurs despite the absence of attractive interactions. We study the onset of phase separation with linear stability analysis and numerical simulations.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135216464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.
{"title":"Two-layer gravity currents of generalized Newtonian fluids","authors":"Ian Christy, Edward M. Hinton","doi":"10.1098/rspa.2023.0429","DOIUrl":"https://doi.org/10.1098/rspa.2023.0429","url":null,"abstract":"We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"67 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we consider the potential of cometary impacts to deliver complex organic molecules and the prebiotic building blocks required for life to rocky exoplanets. Numerical experiments have demonstrated that for these molecules to survive, impacts at very low velocities are required. This work shows that for comets scattered from beyond the snow-line into the habitable zone, the minimum impact velocity is always lower for planets orbiting Solar-type stars than M-dwarfs. Using both an analytical model and numerical N-body simulations, we show that the lowest velocity impacts occur onto planets in tightly packed planetary systems around high-mass (i.e. Solar-mass) stars, enabling the intact delivery of complex organic molecules. Impacts onto planets around low-mass stars are found to be very sensitive to the planetary architecture, with the survival of complex prebiotic molecules potentially impossible in loosely packed systems. Rocky planets around M-dwarfs also suffer significantly more high velocity impacts, potentially posing unique challenges for life on these planets. In the scenario that cometary delivery is important for the origins of life, this study predicts the presence of biosignatures will be correlated with (i) decreasing planetary mass (i.e. escape velocity), (ii) increasing stellar-mass and (iii) decreasing planetary separation (i.e. exoplanets in tightly-packed systems).
{"title":"Can comets deliver prebiotic molecules to rocky exoplanets?","authors":"R. J. Anslow, A. Bonsor, P. B. Rimmer","doi":"10.1098/rspa.2023.0434","DOIUrl":"https://doi.org/10.1098/rspa.2023.0434","url":null,"abstract":"In this work, we consider the potential of cometary impacts to deliver complex organic molecules and the prebiotic building blocks required for life to rocky exoplanets. Numerical experiments have demonstrated that for these molecules to survive, impacts at very low velocities are required. This work shows that for comets scattered from beyond the snow-line into the habitable zone, the minimum impact velocity is always lower for planets orbiting Solar-type stars than M-dwarfs. Using both an analytical model and numerical N-body simulations, we show that the lowest velocity impacts occur onto planets in tightly packed planetary systems around high-mass (i.e. Solar-mass) stars, enabling the intact delivery of complex organic molecules. Impacts onto planets around low-mass stars are found to be very sensitive to the planetary architecture, with the survival of complex prebiotic molecules potentially impossible in loosely packed systems. Rocky planets around M-dwarfs also suffer significantly more high velocity impacts, potentially posing unique challenges for life on these planets. In the scenario that cometary delivery is important for the origins of life, this study predicts the presence of biosignatures will be correlated with (i) decreasing planetary mass (i.e. escape velocity), (ii) increasing stellar-mass and (iii) decreasing planetary separation (i.e. exoplanets in tightly-packed systems).","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"42 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yield criteria for porous material have been widely used to model the decrease of yield strength caused by porosity during ductile failure which deserves long-term efforts in modelling to remedy the current drawbacks. To improve their accuracy, a method of building yield criteria for porous single crystals based on physics-informed neural networks (PINNs) has been developed, and the newly well-trained yield functions are capable of predicting the yield stress of porous single crystals with different porosity, stress states and crystal orientations. The reliability of the yield functions is guaranteed by the precise datasets generated by the crystal plasticity finite-element method. In particular, through embedding the associated flow rule into the training process, the PINN-based yield function not only achieves higher accuracy in comparison with the analytical methods (e.g. variational nonlinear homogenization or limit analysis) but also avoids the improper appearance of grooves that happens in feed-forward neural networks. The proposed framework enjoys an excellent portability as the yield functions can be rebuilt in the similar non-trivial procedure when new influencing factors must be introduced, which makes us believe in its potential to be extended.
{"title":"A data-driven yield criterion for porous ductile single crystals containing spherical voids via physics-informed neural networks","authors":"Liujun Wu, Jiaqi Fu, Haonan Sui, Xiaoying Wang, Bowen Tao, Pengyu Lv, Mohan Chen, Zifeng Yuan, Huiling Duan","doi":"10.1098/rspa.2023.0433","DOIUrl":"https://doi.org/10.1098/rspa.2023.0433","url":null,"abstract":"Yield criteria for porous material have been widely used to model the decrease of yield strength caused by porosity during ductile failure which deserves long-term efforts in modelling to remedy the current drawbacks. To improve their accuracy, a method of building yield criteria for porous single crystals based on physics-informed neural networks (PINNs) has been developed, and the newly well-trained yield functions are capable of predicting the yield stress of porous single crystals with different porosity, stress states and crystal orientations. The reliability of the yield functions is guaranteed by the precise datasets generated by the crystal plasticity finite-element method. In particular, through embedding the associated flow rule into the training process, the PINN-based yield function not only achieves higher accuracy in comparison with the analytical methods (e.g. variational nonlinear homogenization or limit analysis) but also avoids the improper appearance of grooves that happens in feed-forward neural networks. The proposed framework enjoys an excellent portability as the yield functions can be rebuilt in the similar non-trivial procedure when new influencing factors must be introduced, which makes us believe in its potential to be extended.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"280 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136117646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a nonlinear inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated with a linear, isotropic fractional elasticity operator from fractional Dirichlet-to-Neumann data. In our analysis, we make use of a fractional matrix Schrödinger equation via a generalization of the so-called Liouville reduction to the case of fractional elasticity. We conclude that unique recovery is possible if the Lamé parameters agree and are constant in the exterior, and their Poisson ratios agree everywhere. Our study is motivated by the significant recent activity in the field of nonlocal elasticity.
{"title":"Uniqueness in an inverse problem of fractional elasticity","authors":"Giovanni Covi, Maarten de Hoop, Mikko Salo","doi":"10.1098/rspa.2023.0474","DOIUrl":"https://doi.org/10.1098/rspa.2023.0474","url":null,"abstract":"We study a nonlinear inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated with a linear, isotropic fractional elasticity operator from fractional Dirichlet-to-Neumann data. In our analysis, we make use of a fractional matrix Schrödinger equation via a generalization of the so-called Liouville reduction to the case of fractional elasticity. We conclude that unique recovery is possible if the Lamé parameters agree and are constant in the exterior, and their Poisson ratios agree everywhere. Our study is motivated by the significant recent activity in the field of nonlocal elasticity.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135654224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jasper J. Wong, Diana Iruretagoyena, Nilay Shah, Paul S. Fennell
Accurate modelling of the gaseous reduction of porous iron oxide powders or fines is important in industry for (i) reinventing the carbon intensive production of iron and steel and (ii) chemical looping technologies in the sphere of carbon capture and storage. A new three-interface random pore model is derived and applied to the gaseous reduction of hematite ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> ) to iron (Fe). The structural reaction–diffusion model is able to describe three simultaneously reacting oxide layers, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> , magnetite ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:math> ) and wustite ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>O</mml:mtext> </mml:math> ). The geometric nature of the model encodes structural information about the particles (porosity, surface area, pore length and size distribution), measured here by experiment. The model is usefully able to separate structural particle properties from individual rates of reaction and product layer diffusion. The results have been compared and fitted to thermogravimetric experiments between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>800</mml:mn> <mml:mtext>–</mml:mtext> <mml:msup> <mml:mn>1000</mml:mn> <mml:mrow> <mml:mo>∘</mml:mo> </mml:mrow> </mml:msup> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> </mml:math> and three <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi mathvariant="normal">CO</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> gas mixtures. Rate constants for each indvidual reaction have been obtained and fit well to Arrhenius plots. The reduction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mtext>–</mml:mtext> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:math> was controlled by diffusion
{"title":"A three-interface random pore model: the reduction of iron oxide in chemical looping and green steel technologies","authors":"Jasper J. Wong, Diana Iruretagoyena, Nilay Shah, Paul S. Fennell","doi":"10.1098/rspa.2023.0173","DOIUrl":"https://doi.org/10.1098/rspa.2023.0173","url":null,"abstract":"Accurate modelling of the gaseous reduction of porous iron oxide powders or fines is important in industry for (i) reinventing the carbon intensive production of iron and steel and (ii) chemical looping technologies in the sphere of carbon capture and storage. A new three-interface random pore model is derived and applied to the gaseous reduction of hematite ( <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> ) to iron (Fe). The structural reaction–diffusion model is able to describe three simultaneously reacting oxide layers, <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> , magnetite ( <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:math> ) and wustite ( <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>O</mml:mtext> </mml:math> ). The geometric nature of the model encodes structural information about the particles (porosity, surface area, pore length and size distribution), measured here by experiment. The model is usefully able to separate structural particle properties from individual rates of reaction and product layer diffusion. The results have been compared and fitted to thermogravimetric experiments between <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mn>800</mml:mn> <mml:mtext>–</mml:mtext> <mml:msup> <mml:mn>1000</mml:mn> <mml:mrow> <mml:mo>∘</mml:mo> </mml:mrow> </mml:msup> <mml:mrow> <mml:mi mathvariant=\"normal\">C</mml:mi> </mml:mrow> </mml:math> and three <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"normal\">CO</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> gas mixtures. Rate constants for each indvidual reaction have been obtained and fit well to Arrhenius plots. The reduction of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mtext>–</mml:mtext> <mml:msub> <mml:mtext>Fe</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:math> was controlled by diffusion ","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135654226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ring structures are crucial in network neuroscience, enabling the integration of neural information through closed loop circuits within feedback systems. Here, we use numerical bifurcation analysis to explore time delay effects on a ring of delay-coupled Wilson–Cowan masses. Investigating a low-dimensional ‘self-coupled’ version of the aforementioned system, we uncover the bifurcation structure of the synchronization manifold, and unveil a diverse array of dynamic synchronization patterns that emerge as a consequence of Hopf branch crossings and subsequent higher-order bifurcations. Analysis of the full system reveals transverse instabilities in the synchronized state for large regions of parameter space, with the ring network architecture promoting various dynamics depending on the balance between coupling strength and delay time. Under weak coupling, emergent oscillations are generally synchronous or anti-phase synchronous, with transitions between them triggered by a torus bifurcation of a periodic orbit. Regions of synchronous and anti-phase synchronous solutions are delineated by weakly chaotic borders due to the breakdown of the torus. As coupling strength increases, the bifurcation diagram displays more overlapped branching structure, resulting in increasingly complicated, multistable dynamics.
{"title":"Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators","authors":"I. Pinder, M. R. Nelson, J. J. Crofts","doi":"10.1098/rspa.2023.0313","DOIUrl":"https://doi.org/10.1098/rspa.2023.0313","url":null,"abstract":"Ring structures are crucial in network neuroscience, enabling the integration of neural information through closed loop circuits within feedback systems. Here, we use numerical bifurcation analysis to explore time delay effects on a ring of delay-coupled Wilson–Cowan masses. Investigating a low-dimensional ‘self-coupled’ version of the aforementioned system, we uncover the bifurcation structure of the synchronization manifold, and unveil a diverse array of dynamic synchronization patterns that emerge as a consequence of Hopf branch crossings and subsequent higher-order bifurcations. Analysis of the full system reveals transverse instabilities in the synchronized state for large regions of parameter space, with the ring network architecture promoting various dynamics depending on the balance between coupling strength and delay time. Under weak coupling, emergent oscillations are generally synchronous or anti-phase synchronous, with transitions between them triggered by a torus bifurcation of a periodic orbit. Regions of synchronous and anti-phase synchronous solutions are delineated by weakly chaotic borders due to the breakdown of the torus. As coupling strength increases, the bifurcation diagram displays more overlapped branching structure, resulting in increasingly complicated, multistable dynamics.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136054684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum–classical correspondence has been supported for the one-body chaotic systems as well as realistic systems with interactions, as in the Dicke model, a model of multi-two-level atoms and cavity field interactions. To this end, we calculate the OTOC for different variations of the Dicke model in an open quantum system setting. The connection between the superradiant phase transition of the Dicke model and the OTOC is studied. Further, we establish a relation between the OTOC and the second-order coherence function. This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.
{"title":"Quantum chaos in the Dicke model and its variants","authors":"Devvrat Tiwari, Subhashish Banerjee","doi":"10.1098/rspa.2023.0431","DOIUrl":"https://doi.org/10.1098/rspa.2023.0431","url":null,"abstract":"Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum–classical correspondence has been supported for the one-body chaotic systems as well as realistic systems with interactions, as in the Dicke model, a model of multi-two-level atoms and cavity field interactions. To this end, we calculate the OTOC for different variations of the Dicke model in an open quantum system setting. The connection between the superradiant phase transition of the Dicke model and the OTOC is studied. Further, we establish a relation between the OTOC and the second-order coherence function. This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136054677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：