Quantum mechanics in the general quantum systems (V): Hamiltonian eigenvalues

We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of eigenvalues of arbitrary Hamiltonian via solving an algebra equation satisfied by a kernal function, which involves the contributions from all order perturbations. In order to verify the validity of our expressions and reveal the power of our approach, we calculate the ground state energy of a quartic anharmonic oscillator and have obtained good enough results comparing with the known one.Comment: 18 pages, No figure. This is the fifth manuscript. Previous manuscripts see arXiv:quant-ph/0611216, arXiv:quant-ph/0611217, arXiv:quant-ph/0601051 and arXiv:quant-ph/061206

On the nature of the $\pi_2(1880)

The strong decays of the $\pi_2(1880)$ as the $2 ^1D_2$ quark-antiquark state are investigated in the $^3P_0$ model and the flux-tube model, respectively. The results are similar in the two models. It is found that the decay patterns of the conventional $2 ^1D_2$ meson and the $2^{-+}$ light hybrid are very different, and the experimental evidence for the $\pi_2(1880)$ is consistent with it being the conventional $2 ^1D_2$ meson rather than the $2^{-+}$ light hybrid. The possibility of the $\pi_2(1880)$ being a mixture of the conventional $q\bar{q}$ and the hybrid is discussed.Comment: 11 pages, 3 figures, version accepted for publication in Phys. Rev.

Study of the elastocaloric effect and mechanical behavior for the NiTi shape memory alloys

The NiTi shape memory alloy exhibited excellent superelastic property and elastocaloric effect. Large temperature changes of 30 K upon loading and -19 K upon unloading were obtained at room temperature, which were higher than those of the other NiTi-based materials and among the highest values reported in the elastocaloric materials. The asymmetry of the measured temperature changes between loading and unloading process was ascribed to the friction dissipation. The large temperature changes originated from the large entropy change during the stress-induced martensite transformation (MT) and the reverse MT. A large coefficient-of-performance of the material (COPmater) of 11.7 was obtained, which decreased with increasing the applied strain. These results are very attractive in the present solid-state cooling which is potential to replace the vapor compression refrigeration technologies

Short-term load forecasting using optimized LSTM networks based on EMD

Short-term load forecasting is one of the crucial sections in smart grid. Precise forecasting enables system operators to make reliable unit commitment and power dispatching decisions. With the advent of big data, a number of artificial intelligence techniques such as back propagation, support vector machine have been used to predict the load of the next day. Nevertheless, due to the noise of raw data and the randomness of power load, forecasting errors of existing approaches are relatively large. In this study, a short-term load forecasting method is proposed on the basis of empirical mode decomposition and long short-term memory networks, the parameters of which are optimized by a particle swarm optimization algorithm. Essentially, empirical mode decomposition can decompose the original time series of historical data into relatively stationary components and long short-term memory network is able to emphasize as well as model the timing of data, the joint use of which is expected to effectively apply the characteristics of data itself, so as to improve the predictive accuracy. The effectiveness of this research is exemplified on a realistic data set, the experimental results of which show that the proposed method has higher forecasting accuracy and applicability, as compared with existing methods.Comment: 16 pages,11 figure

Almost Optimal Channel Access in Multi-Hop Networks With Unknown Channel Variables

We consider distributed channel access in multi-hop cognitive radio networks. Previous works on opportunistic channel access using multi-armed bandits (MAB) mainly focus on single-hop networks that assume complete conflicts among all secondary users. In the multi-hop multi-channel network settings studied here, there is more general competition among different communication pairs. We formulate the problem as a linearly combinatorial MAB problem that involves a maximum weighted independent set (MWIS) problem with unknown weights which need to learn. Existing methods for MAB where each of $N$ nodes chooses from $M$ channels have exponential time and space complexity $O(M^N)$, and poor theoretical guarantee on throughput performance. We propose a distributed channel access algorithm that can achieve $1/\rho$ of the optimum averaged throughput where each node has communication complexity $O(r^2+D)$ and space complexity $O(m)$ in the learning process, and time complexity $O(D m^{\rho^r})$ in strategy decision process for an arbitrary wireless network. Here $\rho=1+\epsilon$ is the approximation ratio to MWIS for a local $r$-hop network with $m<N$ nodes,and $D$ is the number of mini-rounds inside each round of strategy decision. For randomly located networks with an average degree $d$, the time complexity is $O(d^{\rho^r})$.Comment: 9 page

An accurate front capturing scheme for tumor growth models with a free boundary limit

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure $p$ and density $\rho$ is $p(\rho)=\frac{m}{m-1} \rho^{m-1}$, and when $m \gg 1$, the cell density $\rho$ may evolve its support due to a pressure-driven geometric motion with sharp interface along the boundary of its support. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations, let alone the capturing of the singular free boundary limit. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as $m\gg 1$. In this paper, we develope a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as $m \rightarrow \infty$, and with proper spacial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties and showcase good performance in various applications

Energy landscape and conical intersection points of the driven Rabi model

We examine the energy surfaces of the driven Rabi model, also known as the biased or generalised Rabi model, as a function of the coupling strength and the driving term. The energy surfaces are plotted numerically from the known analytic solution. The resulting energy landscape consists of an infinite stack of sheets connected by conical intersection points located at the degenerate Juddian points in the eigenspectrum. Trajectories encircling these points are expected to exhibit a nonzero geometric phase.Comment: 6 pages, 4 figures, minor correction

Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics

In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor density $n$ is governed by the Darcy law via the pressure $p(n)=n^{\gamma}$. For finite $\gamma$, we prove some a priori estimates of the tumor growth model, such as boundedness of the nutrient density, and non-negativity and growth estimate of the tumor density. As $\gamma \rightarrow \infty$, the cell density models formally converge to Hele-Shaw flow models, which determine the free boundary dynamics of the tumor tissue in the incompressible limit. We derive several analytical solutions to the Hele-Shaw flow models, which serve as benchmark solutions to the geometric motion of tumor front propagation. Finally, we apply a conservative and positivity preserving numerical scheme to the cell density models, with numerical results verifying the link between cell density models and the free boundary dynamical models

Throughput Optimizing Localized Link Scheduling for Multihop Wireless Networks Under Physical Interference Model

We study throughput-optimum localized link scheduling in wireless networks. The majority of results on link scheduling assume binary interference models that simplify interference constraints in actual wireless communication. While the physical interference model reflects the physical reality more precisely, the problem becomes notoriously harder under the physical interference model. There have been just a few existing results on link scheduling under the physical interference model, and even fewer on more practical distributed or localized scheduling. In this paper, we tackle the challenges of localized link scheduling posed by the complex physical interference constraints. By cooperating the partition and shifting strategies into the pick-and-compare scheme, we present a class of localized scheduling algorithms with provable throughput guarantee subject to physical interference constraints. The algorithm in the linear power setting is the first localized algorithm that achieves at least a constant fraction of the optimal capacity region subject to physical interference constraints. The algorithm in the uniform power setting is the first localized algorithm with a logarithmic approximation ratio to the optimal solution. Our extensive simulation results demonstrate correctness and performance efficiency of our algorithms.Comment: A earlier work "Distributed Link Scheduling for Throughput Maximization under Physical Interference Model" is presented in Proc. IEEE Infocom 201

Molecular dynamics simulations with many-body potentials on multiple GPUs - the implementation, package and performance

Molecular dynamics (MD) is an important research tool extensively applied in materials science. Running MD on a graphics processing unit (GPU) is an attractive new approach for accelerating MD simulations. Currently, GPU implementations of MD usually run in a one-host-process-one-GPU (OHPOG) scheme. This scheme may pose a limitation on the system size that an implementation can handle due to the small device memory relative to the host memory. In this paper, we present a one-host-process-multiple-GPU (OHPMG) implementation of MD with embedded-atom-model or semi-empirical tight-binding many-body potentials. Because more device memory is available in an OHPMG process, the system size that can be handled is increased to a few million or more atoms. In comparison with the CPU implementation, in which Newton's third law is applied to improve the computational efficiency, our OHPMG implementation has achieved a 28.9x~86.0x speedup in double precision, depending on the system size, the cut-off ranges and the number of GPUs. The implementation can also handle a group of small boxes in one run by combining the small boxes into a large box. This approach greatly improves the GPU computing efficiency when a large number of MD simulations for small boxes are needed for statistical purposes.Comment: 48 pages, 10 figure