Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We propose a new method, called projected density matrix embedding theory (p-DMET), which achieves self-consistency without needing to optimize a correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.Comment: 25 pages, 8 figure

Solvability of a higher-order multi-point boundary value problem at resonance

summary:Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance \displaylines { x^{(n)}(t)=f(t, x(t), x'(t),\cdots , x^{(n-1)}(t)),\quad t\in (0,1),\cr x(0)=\sum _{i=1}^{m}\alpha _{i}x(\xi _{i}),\quad x'(0)=\cdots =x^{(n-2)}(0)=0,\quad x^{(n-1)}(1)=\sum _{j=1}^{l}\beta _{j}x^{(n-1)}(\eta _{j}),\cr } where $f\colon [0, 1]\times \mathbb R^n\rightarrow \mathbb R$ is a Carathéodory function, $0<\xi _{1}<\xi _{2}<\cdots <\xi _{m}<1$, $\alpha _{i}\in \mathbb R$, $i=1,2,\cdots , m$, $m\geq 2$ and $0<\eta _{1}<\cdots <\eta _{l}<1$, $\beta _{j}\in \mathbb R$, $j=1,\cdots , l$, $l\geq 1$. In this paper, two of the boundary value conditions are responsible for resonance

Periodic solution to a multispecies predator-prey competition dynamic system with Beddington-DeAngelis functional response and time delay

summary:In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent)

EXPERIMENTAL EVALUATION AND SIMULATION RESEARCH ON NOVEL VARIABLE REFRIGERANT FLOW SYSTEM

Variable refrigerant flow (VRF) system is a popular building air conditioning system which could provide cooling or heating to individual rooms independently. The system is called “variable refrigerant flow” system due to its capability of regulating the refrigerant flow via the precise control of variable speed compressors and electronic expansion valves in each indoor unit. In this dissertation, an advanced VRF system which could provide space cooling, heating and water heating is experimentally evaluated in cooling and heating season for both heat recovery operation and water heating operation. The VRF system is simulated in EnergyPlus and validated with experimental data. Based on the deviation analysis and literature review, it is found that the existing VRF model could not fully reflect the operation characteristic of VRF systems, leading to a high uncertainty in cooling/heating energy and energy consumption. A new VRF model is thereafter proposed, validated in this research and resulted in a model uncertainty less than 5%. Based on the new model, the seasonal performance of an energy saving control strategy and the concept of chilled water storage are investigated. Meanwhile, to solve the mismatch between the building’s thermal load and cooling/heating capability of the VRF system, a new VRF system with phase change material (PCM) based thermal energy storage (TES) is proposed. The new VRF system utilizes single TES device to support both cooling and heating season operation. The performance of new VRF system with PCM based TES is investigated and compared to that of the baseline VRF system. It is found that the new VRF system with PCM based TES could achieve both energy efficiency and demand response goals in cooling and heating season. Based on the comparison, the effect of operation strategies and grid incentive program are discussed. Finally, the economic analysis of the new VRF system with PCM based TES based on annual performance is carried out

Review of Temperature and Humidity Control Technology for Heat Pump and Air Conditioning Systems

Nowadays, indoor temperature and humidity controls have been more important to provide thermal comfort to occupants. In residential and commercial buildings, split-type air conditioning systems have been widely used for its compactness and installation flexibility. However, the current split-type systems could not effectively control the thermal comfort of the occupants due to its insufficiency in humidity control. In this paper, the existing independent temperature and humidity controllers of the single unit split-type system are reviewed. Then, the study has extended to the variable refrigerant flow (VRF) system, which is a typical multiple-unit split-type system. Several VRF systems that has the humidity control option have been reviewed and their performance is discussed. Based on the literature review, the feasibility of VRF systems with independent temperature and humidity controllers is discussed

Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results