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}
We address symmetry-breaking bifurcations (SBBs) in the ground state (GS) and dipole-mode (DM) solitons of the one-dimensional linearly coupled NLS equations, modelling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of PT -symmetric potentials. The PT -symmetric potential is employed to obtain different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the PT and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of PT -symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the PT symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential’s parameters or the system’s coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with PT potential and related experimental designs.
{"title":"Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials","authors":"Song, Jin, Malomed, Boris A., Yan, Zhenya","doi":"10.1098/rspa.2023.0457","DOIUrl":"https://doi.org/10.1098/rspa.2023.0457","url":null,"abstract":"We address symmetry-breaking bifurcations (SBBs) in the ground state (GS) and dipole-mode (DM) solitons of the one-dimensional linearly coupled NLS equations, modelling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> -symmetric potentials. The <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> -symmetric potential is employed to obtain different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> -symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential’s parameters or the system’s coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> <mml:mi mathvariant=\"script\">T</mml:mi> </mml:mrow> </mml:math> potential and related experimental designs.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"26 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":"135509159","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}
Anomalous diffusion and Lévy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate signals. Mathematicians have recently unveiled mechanisms to generate anomalous diffusion, both stochastically and deterministically. However, there exists to the best of our knowledge no explicit example of a spatially extended system which exhibits anomalous diffusion without being explicitly driven by Lévy noise. We show here that the Landau–Lifshitz–Gilbert equation, a stochastic partial differential equation (SPDE), despite only being driven by Gaussian white noise, exhibits superdiffusive behaviour. The anomalous diffusion is an entirely emergent behaviour and manifests itself in jumps in the location of its travelling front solution. Using a collective coordinate approach, we reduce the SPDE to a set of stochastic differential equations driven by Gaussian white noise. This allows us to identify the mechanism giving rise to the anomalous diffusion as random widening events of the front interface.
{"title":"Lévy flights as an emergent phenomenon in a spatially extended system","authors":"Chunxi Jiao, Georg A. Gottwald","doi":"10.1098/rspa.2023.0349","DOIUrl":"https://doi.org/10.1098/rspa.2023.0349","url":null,"abstract":"Anomalous diffusion and Lévy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate signals. Mathematicians have recently unveiled mechanisms to generate anomalous diffusion, both stochastically and deterministically. However, there exists to the best of our knowledge no explicit example of a spatially extended system which exhibits anomalous diffusion without being explicitly driven by Lévy noise. We show here that the Landau–Lifshitz–Gilbert equation, a stochastic partial differential equation (SPDE), despite only being driven by Gaussian white noise, exhibits superdiffusive behaviour. The anomalous diffusion is an entirely emergent behaviour and manifests itself in jumps in the location of its travelling front solution. Using a collective coordinate approach, we reduce the SPDE to a set of stochastic differential equations driven by Gaussian white noise. This allows us to identify the mechanism giving rise to the anomalous diffusion as random widening events of the front interface.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"86 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":"135654227","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}
Oleksandr Burylko, Matthias Wolfrum, Serhiy Yanchuk, Jürgen Kurths
We study two coupled active rotators with Kuramoto-type coupling and focus our attention to specific transitional regimes where the coupling is neither attractive nor repulsive. We show that certain such situations at the edge of synchronization can be characterized by the existence of a time-reversal symmetry of the system. We identify two different cases with such a time-reversal symmetry. The first case is characterized by a non-reciprocal attractive/repulsive coupling. The second case is a reciprocal coupling exactly at the edge between attraction and repulsion. We give a detailed description of possible different types of dynamics and bifurcations for both cases. In particular, we show how the time-reversible coupling can induce both oscillation death and oscillation birth to the active rotators. Moreover, we analyse the coexistence of conservative and dissipative regions in phase space, which is a typical feature of systems with a time-reversal symmetry. We show also, how perturbations breaking the time-reversal symmetry and destroying the conservative regions can lead to complicated types of dissipative dynamics such as the emergence of long-period cycles showing a bursting-like behaviour.
{"title":"Time-reversible dynamics in a system of two coupled active rotators","authors":"Oleksandr Burylko, Matthias Wolfrum, Serhiy Yanchuk, Jürgen Kurths","doi":"10.1098/rspa.2023.0401","DOIUrl":"https://doi.org/10.1098/rspa.2023.0401","url":null,"abstract":"We study two coupled active rotators with Kuramoto-type coupling and focus our attention to specific transitional regimes where the coupling is neither attractive nor repulsive. We show that certain such situations at the edge of synchronization can be characterized by the existence of a time-reversal symmetry of the system. We identify two different cases with such a time-reversal symmetry. The first case is characterized by a non-reciprocal attractive/repulsive coupling. The second case is a reciprocal coupling exactly at the edge between attraction and repulsion. We give a detailed description of possible different types of dynamics and bifurcations for both cases. In particular, we show how the time-reversible coupling can induce both oscillation death and oscillation birth to the active rotators. Moreover, we analyse the coexistence of conservative and dissipative regions in phase space, which is a typical feature of systems with a time-reversal symmetry. We show also, how perturbations breaking the time-reversal symmetry and destroying the conservative regions can lead to complicated types of dissipative dynamics such as the emergence of long-period cycles showing a bursting-like behaviour.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"52 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":"135655568","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}
Ventrella, Francesco Michele, Pujara, Nimish, Boffetta, Guido, Cencini, Massimo, Thiffeault, Jean-Luc, De Lillo, Filippo
Many species of phytoplankton migrate vertically near the surface of the ocean, in search of either light or nutrients. These motile organisms are affected by ocean surface waves. We derive a set of wave-averaged equations to describe the motion of microswimmers with spheroidal body shapes that includes several additional effects, such as gyrotaxis, settling and wind-driven shear. In addition to the well-known Stokes drift, the microswimmer trajectories depend on their orientation in a way that can lead to trapping at a particular depth; this in turn can affect transport of organisms, and may help explain observed phytoplankton layers in the ocean.
{"title":"Microswimmer trapping in surface waves with shear","authors":"Ventrella, Francesco Michele, Pujara, Nimish, Boffetta, Guido, Cencini, Massimo, Thiffeault, Jean-Luc, De Lillo, Filippo","doi":"10.1098/rspa.2023.0280","DOIUrl":"https://doi.org/10.1098/rspa.2023.0280","url":null,"abstract":"Many species of phytoplankton migrate vertically near the surface of the ocean, in search of either light or nutrients. These motile organisms are affected by ocean surface waves. We derive a set of wave-averaged equations to describe the motion of microswimmers with spheroidal body shapes that includes several additional effects, such as gyrotaxis, settling and wind-driven shear. In addition to the well-known Stokes drift, the microswimmer trajectories depend on their orientation in a way that can lead to trapping at a particular depth; this in turn can affect transport of organisms, and may help explain observed phytoplankton layers in the ocean.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"5 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":"136139695","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}
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