Noether’s Conservation Laws and Stability in Nonlinear Conservative Interactions

Uechi, Lisa; Uechi, Hiroshi

doi:10.4236/oalib.1102592

Cited by 3 publications

(9 citation statements)

References 49 publications

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“…The Lotka-Volterra types of nonlinear differential equations [37] [38] are primitive nonlinear equations and have been applied to study competitive and predator-pray interactions, mathematical models of disease spreading among species, pest-control, evolving ecosystem networks, population and epidemiology and so forth [39] [40] [41]. The Lotka-Volterra types of nonlinear differential equations are easy to use, but they have intrinsic blunder known as the atto-fox problem, which is prevented in the conserving nonlinear equations [5] [6] [7]. Since the Lynx-hare cycle is an approximate nonlinear conserving phenomena, it has a conserved quantity, Ψ-function which restricts unphysical atto-fox problem.…”

Section: The 2-variable Cnis Restoration From External Perturbationsmentioning

confidence: 99%

“…The 2-variable conserving nonlinear differential Equations (2.6)-(2.9) produce generalized nonlinear equations of Lotka-Volterra, Kolmogorov, and Lyapunov function type nonlinear equations, and so, the conserved Ψ-function is related to stability, control and properties of a nonlinear system. The concept of stability is studied in terms of an addition law of Ψ-function [5] [6] [7]. The Ψ-function could be applied to recovery or restoration phenomena caused on a system, which is important for microbiological and ecological systems.…”

Section: The 3-variable Conserving Nonlinear Interactionsmentioning

confidence: 99%

“…Nonlinear differential equations provide us with a possible account for complex change of populations by adjusting coupling constants, but they do not explain physical principles and reasons why such nonlinear interactions and coupling constants are physically chosen by nature, and in this sense, dynamical change of ecological system is not simply solved by computer simulations and big-data accumulations. Hence, we have proposed nonlinear conserving equations for n-body interactions [5] [6] [7] and applied them to population data of species and microbes in order to understand and extract useful information of what the population growth and survival of species would signify. The population cycles in ecosystems and those found in self-organization of biological systems have similar periodic oscillations, and we found a characteristic dynamical rhythm [6] [7] expressed by conserving nonlinear interactions (CNIs).…”

Section: Introductionmentioning

confidence: 99%

“…Hence, we have proposed nonlinear conserving equations for n-body interactions [5] [6] [7] and applied them to population data of species and microbes in order to understand and extract useful information of what the population growth and survival of species would signify. The population cycles in ecosystems and those found in self-organization of biological systems have similar periodic oscillations, and we found a characteristic dynamical rhythm [6] [7] expressed by conserving nonlinear interactions (CNIs). Useful concepts such as the survival of the fittest and relations to conservation laws manifest in nonlinear interactions are gradually recognized when a rhythm of big data is analyzed by the model of conserving nonlinear differential equations (CNDEs).…”

Section: Introductionmentioning

confidence: 99%

“…Though interactions among species could be expressed by nonlinear differential equations, scientific and physical meanings must be yet investigated. The functional form of nonlinearity is generally discussed in [5] [6] [7], and in the current analysis, the nonlinear polynomial of degree two is applied with the variational method (Noether's theorem) and conservation law to examine dynamics from big-data. There are two types of nonlinear differential equations: nonconserving, dissipative nonlinear equations, and conserving nonlinear equations which have the conserved quantity, CNIs and equations are discussed, and symbiosis, the food-chain and the patterns of interaction, the survival of the fittest of consisting species are discussed as much as possible by comparing conserving nonlinear equations with conventional nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

Uechi¹,

Uechi²,

Uechi³

2021

JAMP

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Section: The 2-variable Cnis Restoration From External Perturbationsmentioning

confidence: 99%

Section: The 3-variable Conserving Nonlinear Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

Uechi¹,

Uechi²,

Uechi³

2021

JAMP

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Hardon-Quark Hybrid Stars Constructed by the Nonlinear σ-ω-ρ Mean-Field Model and MIT-Bag Model

Uechi¹,

Uechi²

2015

OALib

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Density-dependent relations among saturation properties of symmetric nuclear matter and hyperonic matter, properties of hadron-(strange) quark hybrid stars are discussed by applying the conserving nonlinear σ-ω-ρ hadronic mean-field theory. Nonlinear interactions that will be renormalized as effective coupling constants, effective masses and sources of equations of motion are constructed self-consistently by maintaining thermodynamic consistency to the mean-field approximation. The coupling constants expected from the hadronic mean-field model and SU(6) quark model for the vector coupling constants are compared; the coupling constants exhibit different density-dependent results for effective masses and binding energies of hyperons, properties of hadron and hadron-quark stars. The nonlinear σ-ω-ρ hadronic mean-field approximation with or without vacuum fluctuation corrections and strange quark matter defined by MIT-bag model are employed to examine properties of hadron-(strange) quark hybrid stars. We have found that hadron-(strange) quark hybrid stars become more stable in high density compared to pure hadronic and strange quark stars. 1 matter [23], M max (n, p, e) ∼ 2.50 M ⊙ (the solar mass: M ⊙ ∼ 1.989 × 10 30 kg), are found reasonable and admissible in the nonlinear σ-ω-ρ Hartree approximation [18,19].The maximum masses of neutron stars are expected to be below 2.5 M ⊙ [24], or 2.1 ± 0.2M ⊙ [25], which depends on the hadronic equation of state (EOS) for isospin asymmetric, hyperonic matter in the density range, 2ρ 0 ρ B 5ρ 0 . The hadronic liquid-gas phase transition at the surface of neutron stars and determination of the radius of smeared, gas-phase surface are not directly relevant to properties of hadronic matter and maximum masses of neutron stars. The nonlinear interactions exhibit significant density-dependent effects on incompressibility, K, and symmetry energy, a 4 , in high densities; these Fermi liquid properties monotonically increase about saturation density, but they are piecewise continuously softened at an hyperon onset density. These phenomena of piecewise continuous change of Fermi-liquid properties will be important for the analysis of Landau parameters, heavy-ion collision, high energy and high density experiments. At a hyperon onset density from (n, p, e) to (n, p, H, e), the EOS suddenly becomes softer. This is because the nucleon Fermi energy, E N (k F ) in the phase (n, p, e), will be redistributed to the hyperon Fermi energy, E H (k F ) in the phase (n, p, H, e); consequently, the Fermi energies become relatively small in the phase (n, p, H, e) compared with those of (n, p, e). The redistribution and slow increase of Fermi energies appear whenever hyperons are generated, resulting in a softer equation of state and discontinuous changes of K and a 4 . This is numerically checked as discrete changes of physical quantities, such as effective masses of hadrons, incompressibility, symmetry energy and energy density [18,19].Since the hyperon-onset will confine Fermi-energies of baryons as e...

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The Analysis of Thermomechanical Periodic Motions of a Drinking Bird

Uechi¹,

Uechi²,

Nishimura³

2019

WJET

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A water drinking bird or simply drinking bird (DB) is discussed in terms of a thermomechanical model. A mathematical expression of motion derived from the thermomechanical model of a drinking bird and numerical solutions are explicitly shown, which is helpful in understanding physical meanings and fundamental difference between mechanical and thermomechanical periodic motion. The mathematical and physical differences between mechanical and thermomechanical motions are clearly examined, resulting in time-independent and time-dependent coupling constants of equations of motion and continuous transitions between bifurcation solutions. The thermodynamical and irreversible process of a drinking bird motion could be theoretically examined and practically applied to energy harvesting technologies by way of the current modeling. As an example of irreversible thermodynamics, the thermomechanical model of DB will help understand heat engines manifested from microscopic to macroscopic systems.

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Noether’s Conservation Laws and Stability in Nonlinear Conservative Interactions

Cited by 3 publications

References 49 publications

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

Hardon-Quark Hybrid Stars Constructed by the Nonlinear σ-ω-ρ Mean-Field Model and MIT-Bag Model

The Analysis of Thermomechanical Periodic Motions of a Drinking Bird

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