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Thermodynamics of Attractive and Repulsive Fermi Gases in Two Dimensions
Weiran Li
Physics , 2014,
Abstract: We study the attractive and repulsive two-component Fermi gas with spin imbalance in two dimensions. Using a generalized $T$-matrix approximation, we examine the thermodynamic properties of both attractive and repulsive contact interacting Fermi gases. The interaction strength, which is characterized by the bound state energy $E_b=\hbar^2/m a_{2d}^2$ in vacuum, can be adjusted through a Feshbach resonance. We calculate the interaction energy, compressibility and spin susceptibility of the two branches of the Fermi gas. For the repulsive branch, we also find a critical strength of interaction $a_{2d}^{(c)}$ above which this metastable thermodynamic state becomes unstable. This critical value depends on the temperature and the spin imbalance (the "magnetization") of the system.
Simulation Analysis of DC-DC Circuit Based on Simulink in Intelligent Vehicle Terminal  [PDF]
Weiran Li, Guoping Yang
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104682
Abstract:
With the popularization of intelligent transportation systems, intelligent vehicle terminal has emerged. As the most important part of the Intelligent Transportation System (ITS), the smart vehicle-mounted terminal integrates technologies such as the Internet of Things, satellite navigation technology, and even artificial intelligence, and is now widely used in various modes of transportation. The output voltage of automotive vehicle power supplies is generally 12 V, 24 V, 36 V, while the operating voltage of embedded chips inside vehicle-mounted terminals such as automobiles or buses generally needs to be depressurized before they can work normally. Therefore, this paper will analyze four basic DC chopper circuits, analyze its working principle, and build a DC-DC circuit model according to Matlab/Simulink software and finally analyze the waveform of the simulation output.
Variational study of polarons in Bose-Einstein condensates
Weiran Li,S. Das Sarma
Physics , 2014, DOI: 10.1103/PhysRevA.90.013618
Abstract: We use a class of variational wave functions to study the properties of an impurity in a Bose-Einstein condensate, i.e. the "Bose polaron". The impurity interacts with the condensate through a contact interaction, which can be tuned by a Feshbach resonance. We find a stable attractive polaron branch that evolves continuously across the resonance to a tight-binding diatomic molecule deep in the positive scattering length side. A repulsive polaron branch with finite lifetime is also observed and it becomes unstable as the interaction strength increases. The effective mass of the attractive polaron also changes smoothly across the resonance connecting the two well-understood limits deep on both sides.
Bose Gases Near Unitarity
Weiran Li,Tin-Lun Ho
Physics , 2012, DOI: 10.1103/PhysRevLett.108.195301
Abstract: We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e. the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length $a_s<0$), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length $a_{s}^{\ast}<0$. For $a_s
A convergent method for linear half-space kinetic equations
Qin Li,Jianfeng Lu,Weiran Sun
Physics , 2014,
Abstract: We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations.
Half-space Kinetic Equations with General Boundary Conditions
Qin Li,Jianfeng Lu,Weiran Sun
Physics , 2015,
Abstract: We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.
Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics
Qin Li,Jianfeng Lu,Weiran Sun
Mathematics , 2014, DOI: 10.1016/j.jcp.2015.03.014
Abstract: In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case.
Partitioned Sampling of Public Opinions Based on Their Social Evolution
Weiran Huang,Liang Li,Wei Chen
Computer Science , 2015,
Abstract: Public opinion polling is typically done by random sampling from the entire population, treating the opinions of individuals as independent. In the real world, individuals' opinions are often correlated, especially among friends in a social network, due to the effect of both homophily and social influence. In this paper, we propose a partitioned sampling method, utilizing the correlations between individuals' opinions to improve the sampling quality. In particular, we propose an adaptation of an opinion evolution model in social networks, and formulate an optimization problem based on this model as finding the optimal partition for the partitioned sampling method to minimize the expected sample variance of the estimated result. For the opinion evolution model, we develop an efficient and exact computation of opinion correlations between every pair of nodes in the social network. For the optimization task, we show that when the population size is large enough, the complete partition which contains only one sample in each component is always better, and utilize the correlation computation result obtained earlier to reduce finding optimal complete partition to a well-studied Max-r-Cut problem. We adopt the semidefinite programming algorithm for Max-r-Cut to solve our optimization problem, and further develop a greedy heuristic algorithm to improve the efficiency. We use both synthetic and real-world datasets to demonstrate that our partitioned sampling method results in significant improvement in sampling quality.
A Temperature Window for the Synthesis of Single-Walled Carbon Nanotubes by Catalytic Chemical Vapor Deposition of CH4over Mo2-Fe10/MgO Catalyst
Yu Ouyang,Daoyong Li,Weiran Cao,Shaohua Shi
Nanoscale Research Letters , 2009,
Abstract: A temperature window for the synthesis of single-walled carbon nanotubes by catalytic chemical vapor deposition of CH4over Mo2-Fe10/MgO catalyst has been studied by Raman spectroscopy. The results showed that when the temperature is lower than 750 °C, there were few SWCNTs formed, and when the temperature is higher than 950 °C, mass amorphous carbons were formed in the SWCNTs bundles due to the self-decomposition of CH4. The temperature window of SWCNTs efficient growth is between 800 and 950 °C, and the optimum growth temperature is about 900 °C. These results were supported by transmission electron microscope images of samples formed under different temperatures. The temperature window is important for large-scale production of SWCNTs by catalytic chemical vapor deposition method.
Alternative Route to Strong Interaction: Narrow Feshbach Resonance
Tin-Lun Ho,Xiaoling Cui,Weiran Li
Physics , 2011, DOI: 10.1103/PhysRevLett.108.250401
Abstract: We show that a narrow resonance produces strong interaction effects far beyond its width on the side of the resonance where the bound state has not been formed. This is due to a resonance structure of its phase shift, which shifts the phase of a large number of scattering states by $\pi$ before the bound state emerges. As a result, the magnitude of the interaction energy when approaching the resonance on the "upper" and "lower" branch from different side of the resonance is highly asymmetric, unlike their counter part in wide resonances. Measurements of these effects are experimentally feasible.
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