Pressure Dependence of Wall Relaxation in Polarized 3^3He Gaseous Cells

We have observed a linear pressure dependence of longitudinal relaxation time ($T_1$) at 4.2 K and 295 K in gaseous $^3$He cells made of either bare pyrex glass or Cs/Rb-coated pyrex due to paramagnetic sites in the cell wall. The paramagnetic wall relaxation is previously thought to be independent of $^3$He pressure. We develop a model to interpret the observed wall relaxation by taking into account the diffusion process, and our model gives a good description of the data

SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions arising in the applications such as the Euclidean norm, the maximum eigenvalue function and the least squares functions with $\ell_1$-regularization or elastic net regularization used in statistics and compressed sensing. We show that, under commonly used strict feasibility conditions, the optimal value and an optimal solution of SOS-convex semi-algebraic programs can be found by solving a single semi-definite programming problem (SDP). We achieve the results by using tools from semi-algebraic geometry, convex-concave minimax theorem and a recently established Jensen inequality type result for SOS-convex polynomials. As an application, we outline how the derived results can be applied to show that robust SOS-convex optimization problems under restricted spectrahedron data uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP relaxation result for restricted ellipsoidal data uncertainty and answers the open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a robust solution from the semi-definite programming relaxation in this broader setting

Can the Bump be Observed in the Early Afterglow of GRBS with X-Ray Line Emission Features?

Extremely powerful emission lines are observed in the X-ray afterglow of several GRBs. The energy contained in the illuminating continuum which is responsible for the line production exceeds 10$^{51}$ erg, much higher than that of the collimated GRBs. It constrains the models which explain the production of X-ray emission lines. In this paper, We argue that this energy can come from a continuous postburst outflow. Focusing on a central engine of highly magnetized millisecond pulsar or magnetar we find that afterglow can be affected by the illuminating continuum, and therefore a distinct achromatic bump may be observed in the early afterglow lightcurves. With the luminosity of the continuous outflow which produces the line emission, we define the upper limit of the time when the bump feature appears. We argue that the reason why the achromatic bumps have not been detected so far is that the bumps should appear at the time too early to be observed.Comment: 13 pags, 2 tables, appear in v603 n1 pt1 ApJ March 1, 2004 issu

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

The official published version can found at the link below.Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.This work was funded by Royal Society of the U.K.; Foundation for the Author of National Excellent Doctoral Dissertation of China. Grant Number: 2007E4; Heilongjiang Outstanding Youth Science Fund of China. Grant Number: JC200809; Fok Ying Tung Education Foundation. Grant Number: 111064; International Science and Technology Cooperation Project of China. Grant Number: 2009DFA32050; University of Science and Technology of China Graduate Innovative Foundation

China's building stock estimation and energy intensity analysis

Reliable and objective data regarding building stock is essential for predicting and analyzing energy demand and carbon emission. However, China's building stock data is lacking. This study proposes a set of China building floor space estimation method (CBFSM) based on the improved building stock turnover model. Then it measures China's building stocks by vintage and type from 2000 to 2015, as well as building energy intensity (national level and provincial level) and energy-efficient buildings. Results showed that total building stocks increased significantly, rising from 35.2 billion m2 in 2000 to 63.6 billion m2 in 2015, with the average growth rate 4.0%. The deviations were well below 10% by comparing with China Population Census, which validated the reliability of CBFSM and the results. As for energy intensity, urban dwellings and rural dwellings showed relatively stable and increasing trend respectively. The commercial building energy intensity saw a downward trend during “12th Five Year Plan” period. This indicated the effectiveness of building energy efficiency work for commercial buildings since 2005.38.6 billion m2 residential dwellings and 5.7 billion m2 commercial buildings still need to be retrofitted in future. CBFSM can overcome shortages in previous studies. It can also provide Chinese government with technical support and data evidence to promote the building energy efficiency work

Understanding the Frequency Distribution of Mechanically Stable Disk Packings

Relative frequencies of mechanically stable (MS) packings of frictionless bidisperse disks are studied numerically in small systems. The packings are created by successively compressing or decompressing a system of soft purely repulsive disks, followed by energy minimization, until only infinitesimal particle overlaps remain. For systems of up to 14 particles most of the MS packings were generated. We find that the packings are not equally probable as has been assumed in recent thermodynamic descriptions of granular systems. Instead, the frequency distribution, averaged over each packing-fraction interval $\Delta \phi$, grows exponentially with increasing $\phi$. Moreover, within each packing-fraction interval MS packings occur with frequencies $f_k$ that differ by many orders of magnitude. Also, key features of the frequency distribution do not change when we significantly alter the packing-generation algorithm--for example frequent packings remain frequent and rare ones remain rare. These results indicate that the frequency distribution of MS packings is strongly influenced by geometrical properties of the multidimensional configuration space. By adding thermal fluctuations to a set of the MS packings, we were able to examine a number of local features of configuration space near each packing including the time required for a given packing to break to a distinct one, which enabled us to estimate the energy barriers that separate one packing from another. We found a positive correlation between the packing frequencies and the heights of the lowest energy barriers $\epsilon_0$. We also examined displacement fluctuations away from the MS packings to correlate the size and shape of the local basins near each packing to the packing frequencies.Comment: 21 pages, 20 figures, 1 tabl