Energy Loss in Pulse Detonation Engine due to Fuel Viscosity

Fluid viscosity is a significant factor resulting in the energy loss in most fluid dynamical systems. To analyze the energy loss in the pulse detonation engine (PDE) due to the viscosity of the fuel, the energy loss in the Burgers model excited by periodic impulses is investigated based on the generalized multisymplectic method in this paper. Firstly, the single detonation energy is simplified as an impulse; thus the complex detonation process is simplified. And then, the symmetry of the Burgers model excited by periodic impulses is studied in the generalized multisymplectic framework and the energy loss expression is obtained. Finally, the energy loss in the Burgers model is investigated numerically. The results in this paper can be used to explain the difference between the theoretical performance and the experimental performance of the PDE partly. In addition, the analytical approach of this paper can be extended to the analysis of the energy loss in other fluid dynamic systems due to the fluid viscosity

R\'{e}nyi Divergence Deep Mutual Learning

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using R\'{e}nyi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is able to consistently improve performance over vanilla DML with limited additional complexity. The convergence properties of the proposed paradigm are analyzed theoretically, and Stochastic Gradient Descent with a constant learning rate is shown to converge with $\mathcal{O}(1)$-bias in the worst case scenario for nonconvex optimization tasks. That is, learning will reach nearby local optima but continue searching within a bounded scope, which may help mitigate overfitting. Finally, our extensive empirical results demonstrate the advantage of combining DML and R\'{e}nyi divergence, which further improves generalized models

Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results

Spatially resolved Spectro-photometry of M81: Age, Metallicity and Reddening Maps

In this paper, we present a multi-color photometric study of the nearby spiral galaxy M81, using images obtained with the Beijing Astronomical Observatory 60/90 cm Schmidt Telescope in 13 intermediate-band filters from 3800 to 10000{\AA}. The observations cover the whole area of M81 with a total integration of 51 hours from February 1995 to February 1997. This provides a multi-color map of M81 in pixels of 1\arcsec.7 \times 1\arcsec.7. Using theoretical stellar population synthesis models, we demonstrate that some BATC colors and color indices can be used to disentangle the age and metallicity effect. We compare in detail the observed properties of M81 with the predictions from population synthesis models and quantify the relative chemical abundance, age and reddening distributions for different components of M81. We find that the metallicity of M81 is about $Z=0.03$ with no significant difference over the whole galaxy. In contrast, an age gradient is found between stellar populations of the central regions and of the bulge and disk regions of M81: the stellar population in its central regions is older than 8 Gyr while the disk stars are considerably younger, $\sim 2$ Gyr. We also give the reddening distribution in M81. Some dust lanes are found in the galaxy bulge region and the reddening in the outer disk is higher than that in the central regions.Comment: Accepted for publication in AJ (May 2000 issue). 27 pages including 6 figures. Uses AASTeX aasms4 styl

Intermediate-band Surface Photometry of the Edge-on Galaxy: NGC 4565

We present a deep, 42.79 hr image of the nearby, edge-on galaxy NGC 4565 in the Beijing-Arizona-Taipei-Connecticut (BATC) 6660A band using the large-format CCD system on the 0.6m Schmidt telescope at the Xinglong Station of the National Astronomical Observatories of China (NAOC). we obtain a final image that is calibrated to an accuracy of 0.02 mag in zero point, and for which we can measure galaxy surface brightness to an accuracy of 0.25 mag at a surface brightness at 27.5 mag arcsec^-2 at 6660A, corresponding to a distance of 22 kpc from the center of the disk. The integrated magnitude of NGC4565 in our filter is m6660=8.99 (R magnitude of 9.1) to a surface brightness of 28 mag arcsec-2. We analyze the faint outer parts of this galaxy using a two-dimensional model comprised of three components: an exponential thin disk, an exponential thick disk, and a power-law halo. A total of 12 parameters are included in our model. We determine the best values of our model parameters via 10,000 random initial values, 3,700 of which converge to final values. The thin disk and thick disk parameters we determine here are consistent with those of previous studies of this galaxy. However, our very deep image permits a better determination of the power law fit to the halo, constraining this power law to be between r^-3.2 and r^-4.0, with a best fit value of r^-3.88. We find the axis ratio of the halo to be 0.44 and its core radius to be 14.4 kpc (for an adopted distance of 14.5 Mpc).Comment: 34 pages, 11 figures, will appear in March 2002 of A

Baichuan 2: Open Large-scale Language Models

Large language models (LLMs) have demonstrated remarkable performance on a variety of natural language tasks based on just a few examples of natural language instructions, reducing the need for extensive feature engineering. However, most powerful LLMs are closed-source or limited in their capability for languages other than English. In this technical report, we present Baichuan 2, a series of large-scale multilingual language models containing 7 billion and 13 billion parameters, trained from scratch, on 2.6 trillion tokens. Baichuan 2 matches or outperforms other open-source models of similar size on public benchmarks like MMLU, CMMLU, GSM8K, and HumanEval. Furthermore, Baichuan 2 excels in vertical domains such as medicine and law. We will release all pre-training model checkpoints to benefit the research community in better understanding the training dynamics of Baichuan 2.Comment: Baichuan 2 technical report. Github: https://github.com/baichuan-inc/Baichuan

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

Comparative Study on the Cooling Characteristics of Different Fill Layout Patterns on a Single Air Inlet Induced Draft Cooling Tower

To enhance the cooling capacity of a single air inlet induced draft cooling tower (SIDCT), the stepped fill layout pattern is proposed in this paper. A three-dimensional numerical model is established and validated by field measurement data. The cooling capacity of towers equipped with uniform fill and stepped fill is compared under various crosswind velocities (0 m/s–12 m/s) and crosswind angles (0°–180°). The results showed that the ventilation rate of the total tower with stepped fill is increased. Under the studied crosswind velocity and angle, the cooling capacity of the stepped fill tower is superior to the uniform fill tower. After using stepped fill, the mean drop of outlet water temperature rises by 0.29 °C, 0.27 °C, 0.17 °C, 0.10 °C, and 0.19 °C, corresponding to crosswind angles from 0° to 180°. The increment of cooling capacity is the maximum under the crosswind angles of 0° and 45° and is the minimum under the crosswind angles of 90° and 135°. The maximum increased value of N is 0.65 under the crosswind velocity of 4 m/s, 0.85 under 8 m/s, and 0.95 under 12 m/s

Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

We prove the existence of a pullback attractor in L2(ℝn) for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions

An Investigation into the Multi-Pass Radial-Mode Micro Abrasive Air Jet Turning of Fused-Silica Rods

With the increased requirement of miniaturization structures on hard and brittle substrates, micro abrasive air jet turning technology has become a promising machining technology for manufacturing miniaturization structures. This paper presents an investigation on multi-pass radial-mode micro abrasive air jet turning of fused silica. The effect of machining parameters on the depth of cut and materials removal rate was analyzed. The waviness and striation formation mechanisms were studied. It was found that increasing the number of passes significantly increases the depth of cut and materials removal rate. When the surface speed is reduced, the depth of cut and materials removal rate significantly increases. The waviness may be attributed to the intersection and overlap of the adjoint jet footprint. The crossed striations have been found, which may lead to the elimination of the striation. A predictive model of the material removal rate was developed using the dimensional analysis method. The model was assessed and shown to be able to give adequate predictions