In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-...In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R<sup>3</sup> based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “<i>Primordial Principle of Self-Interaction</i>”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.展开更多
This paper investigates a new formation motion problem of a class of first-order multi-agent systems with antagonistic interactions.A distributed formation control algorithm is proposed for each agent to realize the a...This paper investigates a new formation motion problem of a class of first-order multi-agent systems with antagonistic interactions.A distributed formation control algorithm is proposed for each agent to realize the antagonistic formation motion.A sufficient condition is derived to ensure that all of the agents make an antagonistic formation motion in a distributed manner.It is shown that all of the agents can be spontaneously divided into several groups and that agents in the same group collaborate while agents in different groups compete.Finally,a numerical simulation is included to demonstrate our theoretical results.展开更多
The genesis of physical particles is essentially a mystery. Quantum field theory creation operators provide an abstract mechanism by which particles come into existence, but quantum fields do not possess energy densit...The genesis of physical particles is essentially a mystery. Quantum field theory creation operators provide an abstract mechanism by which particles come into existence, but quantum fields do not possess energy density. I reference several recent treatments of this problem and develop ideas based on self-stabilizing field structures with focus on higher order self-induced self-stabilizing field structures. I extend this treatment in this paper to related issues of topological charge.展开更多
Stop-and-go waves are commonly observed in traffic and pedestrian flows.In most microscopic traffic models,they occur through a phase transition and instability of the homogeneous solution after fine tuning of paramet...Stop-and-go waves are commonly observed in traffic and pedestrian flows.In most microscopic traffic models,they occur through a phase transition and instability of the homogeneous solution after fine tuning of parameters.Inertia effects are believed to play an important role in this mechanism.In this article,we present a novel explanation for stop-and-go waves based on stochastic effects in the absence of inertia.The model used is a first order optimal velocity(OV)model including an additive stochastic noise.A power spectral analysis for single-file pedestrian trajectories highlights the existence of Brownian speed residuals.We use the Ornstein-Uhlenbeck process to describe such a correlated noise.The introduction of this specific colored noise in the first order OV model allows describing realistic stop-and-go behavior without requiring instabilities or phase transitions,the homogeneous configurations being systematically stochastically stable.We compare the stochastic model to deterministic unstable OV models and analyze individual speed autocorrelation to describe the nature of the waves in stationary states.We apply the approach to pedestrian single-file motion and compare simulation results to real pedestrian trajectories.The simulation results are quantitatively very similar to the real trajectories.We discuss plausible values for the model parameters and their meaning.展开更多
We assessed the spatial distribution of Copernicia alba Morong. In the study area, a lowland palm savanna floodplain, C. alba is the only overstory species. We hypothesized C. alba would be randomly distributed within...We assessed the spatial distribution of Copernicia alba Morong. In the study area, a lowland palm savanna floodplain, C. alba is the only overstory species. We hypothesized C. alba would be randomly distributed within natural stands. Palms were tallied in six randomly located 0.25 haplots and analyzed using a first-order, Ripley’s K function to assess the distribution of juvenile, adult, and total palm populations. While the total population had either aggregated or random distributions, when analyzing juvenile and adult population separately, we found juveniles were consistently more aggregated than the adults.展开更多
The present study is concerned with construct two new semidynamical systems which are generated by two partial differential equations of Lasota type. In addition, this study discusses the asymptotic properties： Stron...The present study is concerned with construct two new semidynamical systems which are generated by two partial differential equations of Lasota type. In addition, this study discusses the asymptotic properties： Strong stability, exponential stability, periodic points, the density of periodic points, transitivity and chaos in two spaces： Lp space and Lp space.展开更多
Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability f...Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.展开更多
We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-c...We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.展开更多
文摘In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R<sup>3</sup> based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “<i>Primordial Principle of Self-Interaction</i>”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.
基金supported by the National Natural Science Foundation of China(Grant Nos.61203080 and 61473051)the Natural Science Foundation of Chongqing City(Grant No.CSTC 2011BB0081)
文摘This paper investigates a new formation motion problem of a class of first-order multi-agent systems with antagonistic interactions.A distributed formation control algorithm is proposed for each agent to realize the antagonistic formation motion.A sufficient condition is derived to ensure that all of the agents make an antagonistic formation motion in a distributed manner.It is shown that all of the agents can be spontaneously divided into several groups and that agents in the same group collaborate while agents in different groups compete.Finally,a numerical simulation is included to demonstrate our theoretical results.
文摘The genesis of physical particles is essentially a mystery. Quantum field theory creation operators provide an abstract mechanism by which particles come into existence, but quantum fields do not possess energy density. I reference several recent treatments of this problem and develop ideas based on self-stabilizing field structures with focus on higher order self-induced self-stabilizing field structures. I extend this treatment in this paper to related issues of topological charge.
基金Financial support by the German Science Foundation under grant SCHA 636/9-1 is gratefully acknowledged.
文摘Stop-and-go waves are commonly observed in traffic and pedestrian flows.In most microscopic traffic models,they occur through a phase transition and instability of the homogeneous solution after fine tuning of parameters.Inertia effects are believed to play an important role in this mechanism.In this article,we present a novel explanation for stop-and-go waves based on stochastic effects in the absence of inertia.The model used is a first order optimal velocity(OV)model including an additive stochastic noise.A power spectral analysis for single-file pedestrian trajectories highlights the existence of Brownian speed residuals.We use the Ornstein-Uhlenbeck process to describe such a correlated noise.The introduction of this specific colored noise in the first order OV model allows describing realistic stop-and-go behavior without requiring instabilities or phase transitions,the homogeneous configurations being systematically stochastically stable.We compare the stochastic model to deterministic unstable OV models and analyze individual speed autocorrelation to describe the nature of the waves in stationary states.We apply the approach to pedestrian single-file motion and compare simulation results to real pedestrian trajectories.The simulation results are quantitatively very similar to the real trajectories.We discuss plausible values for the model parameters and their meaning.
文摘We assessed the spatial distribution of Copernicia alba Morong. In the study area, a lowland palm savanna floodplain, C. alba is the only overstory species. We hypothesized C. alba would be randomly distributed within natural stands. Palms were tallied in six randomly located 0.25 haplots and analyzed using a first-order, Ripley’s K function to assess the distribution of juvenile, adult, and total palm populations. While the total population had either aggregated or random distributions, when analyzing juvenile and adult population separately, we found juveniles were consistently more aggregated than the adults.
文摘The present study is concerned with construct two new semidynamical systems which are generated by two partial differential equations of Lasota type. In addition, this study discusses the asymptotic properties： Strong stability, exponential stability, periodic points, the density of periodic points, transitivity and chaos in two spaces： Lp space and Lp space.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 10625420）.
文摘Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.
基金We thank Shuai Yin and Baoquan Feng for their helpful discussions. This work was supported by the National Natural Science foundation of PRC （Grants Nos. 10625420 and 11575297） and FRFCUC.
文摘We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.
