The Experts below are selected from a list of 133878 Experts worldwide ranked by ideXlab platform
Takahiro Yajima - One of the best experts on this subject based on the ideXlab platform.
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Differential Geometric Structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory
Journal of Dynamical Systems and Geometric Theories, 2016Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:AbstractWe considered the differential Geometric Structure of non-equilibrium dynamics in non-linear interactions, such as competition and predation, based on Kosambi-Cartan-Chern (KCC) theory. The stability of a geodesic flow on a Finslerian manifold is characterized by the deviation curvature (the second invariant in the dynamical system). According to KCC theory, the value of the deviation curvature is constant around the equilibrium point. However, in the non-equilibrium region, not only the value but also the sign of the deviation curvature depend on time. Next, we reapplied KCC theory to the dynamics of the deviation curvature and determined the hierarchical Structure of the Geometric stability. The dynamics of the deviation curvature in the nonequilibrium region is accompanied by a complex periodic (node) pattern in the predation (competition) system.
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lotka volterra system and kcc theory differential Geometric Structure of competitions and predations
Nonlinear Analysis-real World Applications, 2013Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:Abstract We consider the differential Geometric Structure of competitions and predations in the sense of the Lotka–Volterra system based on KCC theory. For this, we visualise the relationship between the Jacobi stability and the linear stability as a single diagram. We find the following. (I) Ecological interactions such as competition and predation can be described by the deviation curvature. In this case, the sign of the deviation curvature depends on the type of interaction, which reflects the equilibrium point type. (II) The Geometric quantities in KCC theory can be expressed in terms of the mean and Gaussian curvatures of the potential surface. In this particular case, the deviation curvature can be interpreted as the Willmore energy density of the potential surface. (III) When the equations of the system have nonsymmetric Structure for the species (e.g. a predation system), each species also has nonsymmetric Geometric Structure in the nonequilibrium region, but symmetric Structure around the equilibrium point. These findings suggest that KCC theory is useful to establish the geometrisation of ecological interactions.
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Lotka–Volterra system and KCC theory: Differential Geometric Structure of competitions and predations
Nonlinear Analysis-real World Applications, 2013Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:Abstract We consider the differential Geometric Structure of competitions and predations in the sense of the Lotka–Volterra system based on KCC theory. For this, we visualise the relationship between the Jacobi stability and the linear stability as a single diagram. We find the following. (I) Ecological interactions such as competition and predation can be described by the deviation curvature. In this case, the sign of the deviation curvature depends on the type of interaction, which reflects the equilibrium point type. (II) The Geometric quantities in KCC theory can be expressed in terms of the mean and Gaussian curvatures of the potential surface. In this particular case, the deviation curvature can be interpreted as the Willmore energy density of the potential surface. (III) When the equations of the system have nonsymmetric Structure for the species (e.g. a predation system), each species also has nonsymmetric Geometric Structure in the nonequilibrium region, but symmetric Structure around the equilibrium point. These findings suggest that KCC theory is useful to establish the geometrisation of ecological interactions.
Kazuhito Yamasaki - One of the best experts on this subject based on the ideXlab platform.
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Differential Geometric Structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory
Journal of Dynamical Systems and Geometric Theories, 2016Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:AbstractWe considered the differential Geometric Structure of non-equilibrium dynamics in non-linear interactions, such as competition and predation, based on Kosambi-Cartan-Chern (KCC) theory. The stability of a geodesic flow on a Finslerian manifold is characterized by the deviation curvature (the second invariant in the dynamical system). According to KCC theory, the value of the deviation curvature is constant around the equilibrium point. However, in the non-equilibrium region, not only the value but also the sign of the deviation curvature depend on time. Next, we reapplied KCC theory to the dynamics of the deviation curvature and determined the hierarchical Structure of the Geometric stability. The dynamics of the deviation curvature in the nonequilibrium region is accompanied by a complex periodic (node) pattern in the predation (competition) system.
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lotka volterra system and kcc theory differential Geometric Structure of competitions and predations
Nonlinear Analysis-real World Applications, 2013Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:Abstract We consider the differential Geometric Structure of competitions and predations in the sense of the Lotka–Volterra system based on KCC theory. For this, we visualise the relationship between the Jacobi stability and the linear stability as a single diagram. We find the following. (I) Ecological interactions such as competition and predation can be described by the deviation curvature. In this case, the sign of the deviation curvature depends on the type of interaction, which reflects the equilibrium point type. (II) The Geometric quantities in KCC theory can be expressed in terms of the mean and Gaussian curvatures of the potential surface. In this particular case, the deviation curvature can be interpreted as the Willmore energy density of the potential surface. (III) When the equations of the system have nonsymmetric Structure for the species (e.g. a predation system), each species also has nonsymmetric Geometric Structure in the nonequilibrium region, but symmetric Structure around the equilibrium point. These findings suggest that KCC theory is useful to establish the geometrisation of ecological interactions.
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Lotka–Volterra system and KCC theory: Differential Geometric Structure of competitions and predations
Nonlinear Analysis-real World Applications, 2013Co-Authors: Kazuhito Yamasaki, Takahiro YajimaAbstract:Abstract We consider the differential Geometric Structure of competitions and predations in the sense of the Lotka–Volterra system based on KCC theory. For this, we visualise the relationship between the Jacobi stability and the linear stability as a single diagram. We find the following. (I) Ecological interactions such as competition and predation can be described by the deviation curvature. In this case, the sign of the deviation curvature depends on the type of interaction, which reflects the equilibrium point type. (II) The Geometric quantities in KCC theory can be expressed in terms of the mean and Gaussian curvatures of the potential surface. In this particular case, the deviation curvature can be interpreted as the Willmore energy density of the potential surface. (III) When the equations of the system have nonsymmetric Structure for the species (e.g. a predation system), each species also has nonsymmetric Geometric Structure in the nonequilibrium region, but symmetric Structure around the equilibrium point. These findings suggest that KCC theory is useful to establish the geometrisation of ecological interactions.
Jianxiang Tian - One of the best experts on this subject based on the ideXlab platform.
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a Geometric Structure theory for maximally random jammed packings
arXiv: Soft Condensed Matter, 2016Co-Authors: Jianxiang Tian, Yang Jiao, Salvatore TorquatoAbstract:Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density phi, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the Geometric-Structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of twodimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares.
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a Geometric Structure theory for maximally random jammed packings
Scientific Reports, 2015Co-Authors: Jianxiang Tian, Yang Jiao, Salvatore TorquatoAbstract:Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the Geometric-Structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density “random-close packing” polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.
Salvatore Torquato - One of the best experts on this subject based on the ideXlab platform.
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a Geometric Structure theory for maximally random jammed packings
arXiv: Soft Condensed Matter, 2016Co-Authors: Jianxiang Tian, Yang Jiao, Salvatore TorquatoAbstract:Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density phi, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the Geometric-Structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of twodimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares.
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a Geometric Structure theory for maximally random jammed packings
Scientific Reports, 2015Co-Authors: Jianxiang Tian, Yang Jiao, Salvatore TorquatoAbstract:Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the Geometric-Structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density “random-close packing” polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.
Jeroen A Van Bokhoven - One of the best experts on this subject based on the ideXlab platform.
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determination of the electronic and Geometric Structure of cu sites during methane conversion over cu mor with x ray absorption spectroscopy
Microporous and Mesoporous Materials, 2013Co-Authors: Evalyn Mae C Alayon, Maarten Nachtegaal, Evgeny Kleymenov, Jeroen A Van BokhovenAbstract:Abstract The endeavor to activate methane through low temperature partial oxidation to a partially oxidized species on Cu-exchanged zeolites relies on the understanding of the reaction mechanism. This necessitates knowing the electronic and Geometric Structure of the Cu sites under the different reaction steps that participate in the reaction. In situ high energy resolved fluorescence detected X-ray absorption spectroscopy (HERFD XAS) and extended X-ray absorption fine Structure (EXAFS) spectroscopy at the Cu K-edge were explored to monitor the Structure of the Cu atoms in Cu-MOR under the different gas feeds. After activation in oxygen, the XAS spectra showed distinct signatures of Cu2+ character. After cooling down in oxygen, and reaction with methane, the spectral signatures indicated a mixed environment of Cu2+/Cu+ states during methane interaction, where the majority of the Cu sites were reduced. Desorption of the formed intermediate by interaction with water showed a partially reduced character where a small reoxidation was attributed the loss of sorbed species and possibly reoxidation by oxygen in the feed.
