Propagation Phenomena for A Reaction-Advection-Diffusion Competition Model in A Periodic Habitat

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the periodic initial value problem. Then we establish the existence of the rightward spreading speed and its coincidence with the minimal wave speed for spatially periodic rightward traveling waves. We also obtain a set of sufficient conditions for the rightward spreading speed to be linearly determinate. Finally, we apply the obtained results to a prototypical reaction-diffusion model

Acrobot Swing Up with MATLAB

This note presents a solution of the swing-up task of two acrobots using trajectory optimization method. The equations of motion for 2-link and 3-link acrobot are manually derived, and then form the dynamics of the robots. Numerical integration method is used to simulate the behaviour of passive robots, with the goal of showing the correctness of the complicated dynamics of the 3-link acrobot. Direct collocation method is used to optimize the trajectory of state and control of the robots with bounds on both

Vector Higgs bosons and possible suppression of flavorchanging neutral current

We replace the scalar Higgs doublet with a vector Higgs boson doublet to the unified electroweak W-S model and find most of important features of W-S model are kept unchanged only the Higgs boson now become vector bosons. Lorentz invariance has been carefully discussed. The most important challenge is there will be three massless vector Higgs bosons. The remarkable effect is the possible suppression of the flavorchanging neutral current compare to the multi-Higgs model.Comment: Some place in this paper it is mathematically not very rigorous but the idea is interesting and very importan

Quantum capacity of lossy channel with additive classical Gaussian noise : a perturbation approach

For a quantum channel of additive Gaussian noise with loss, in the general case of $n$ copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.Comment: 4 page

Quantum capacity of channel with thermal noise

The quantum capacity of thermal noise channel is studied. The extremal input state is obtained at the postulation that the coherent information is convex or concave at its vicinity. When the input energy tends to infinitive, it is verified by perturbation theory that the coherent information reaches its maximum at the product of identical thermal state input. The quantum capacity is obtained for lower noise channel and it is equal the one shot capacity.Comment: 5 page

Introduction to Extra Dimensions and Thick Braneworlds

In this review, we give a brief introduction on the aspects of some extra dimension models and the five-dimensional thick brane models in extended theories of gravity. First, we briefly introduce the Kaluza-Klein theory, the domain wall model, the large extra dimension model, and the warped extra dimension models. Then some thick brane solutions in extended theories of gravity are reviewed. Finally, localization of bulk matter fields on thick branes is discussed.Comment: v2: 53pages, 8 figures, this paper will be collected with other ones as a book to publish in the World Scientific Press in Singapor

Perfect A/D conversion of entanglement

We investigate how entanglement can be perfectly transfered between continuous variable and qubits system. We find that a two-mode squeezed vacuum state can be converted to the product state of an infinitive number of two-qubit states while keeping the entanglement. The reverse process is also possible. The interaction Hamitonian is a kind of non-linear Jaynes-Cumings Hamiltonian.Comment: 3 pages, 1 figur

Gaussian relative entropy of entanglement

For two gaussian states with given correlation matrices, in order that relative entropy between them is practically calculable, I in this paper describe the ways of transforming the correlation matrix to matrix in the exponential density operator. Gaussian relative entropy of entanglement is proposed as the minimal relative entropy of the gaussian state with respect to separable gaussian state set. I prove that gaussian relative entropy of entanglement achieves when the separable gaussian state is at the border of separable gaussian state set and inseparable gaussian state set. For two mode gaussian states, the calculation of gaussian relative entropy of entanglement is greatly simplified from searching for a matrix with 10 undetermined parameters to 3 variables. The two mode gaussian states are classified as four types, numerical evidence strongly suggests that gaussian relative entropy of entanglement for each type is realized by the separable state within the same type.For symmetric gaussian state it is strictly proved that it is achieved by symmetric gaussian state.Comment: 12 pages, 3 figure

Traveling waves and spreading speeds for time-space periodic monotone systems

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence of time-space periodic traveling waves and spreading speeds. We then apply these abstract results to a two species competition reaction-advection-diffusion model. It turns out that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate. We also obtain a set of sufficient conditions for the spreading speed to be linearly determinate.Comment: arXiv admin note: text overlap with arXiv:1410.459

Preliminary Study on Bit-String Modelling of Opinion Formation in Complex Networks

Opinion formation has been gaining increasing research interests recently, and various models have been proposed. These models, however, have their limitations, among which noticeably include (i) it is generally assumed that adjacent nodes holding similar opinions will further reduce their difference in between, while adjacent nodes holding significantly different opinions would either do nothing, or cut the link in between them; (ii) opinion mutation, which describes "opinion changes not due to neighborhood influences" in real life, is typically random. While such models enjoy their simplicity and nevertheless help reveal lots of useful insights, they lack the capability of describing many complex behaviors which we may easily observe in real life. In this paper, we propose a new bit-string modeling approach. Preliminary study on the new model demonstrates its great potentials in revealing complex behaviors of social opinion evolution and formation.Comment: 5 pages, 1 figures, conference publishe