Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers

In this paper, we consider solving multiple-block separable convex minimization problems using alternating direction method of multipliers (ADMM). Motivated by the fact that the existing convergence theory for ADMM is mostly limited to the two-block case, we analyze in this paper, both theoretically and numerically, a new strategy that first transforms a multi-block problem into an equivalent two-block problem (either in the primal domain or in the dual domain) and then solves it using the standard two-block ADMM. In particular, we derive convergence results for this two-block ADMM approach to solve multi-block separable convex minimization problems, including an improved O(1/\epsilon) iteration complexity result. Moreover, we compare the numerical efficiency of this approach with the standard multi-block ADMM on several separable convex minimization problems which include basis pursuit, robust principal component analysis and latent variable Gaussian graphical model selection. The numerical results show that the multiple-block ADMM, although lacks theoretical convergence guarantees, typically outperforms two-block ADMMs

Renormalization group improved pQCD prediction for Υ(1S)\Upsilon(1S) leptonic decay

The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to $\Upsilon(1S)$ leptonic decay rate $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it et al.} \cite{Beneke:2014qea}. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of $\beta$-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for $\Upsilon(1S)$ leptonic decay, i.e. $\Gamma_{\Upsilon(1S) \to e^+ e^-}|_{\rm PMC} = 1.270^{+0.137}_{-0.187}$ keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.Comment: 11 pages, 4 figures. Numerical results and discussions improved, references updated, to be published in JHE

Quantum Nonlinear Effect in Dissipatively Coupled Optomechanical System

A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and real-Kerr nonlinearities. And unexpectedly, the nonlinearities caused by the dissipative coupling have non-Hermitian Hamiltonian-like properties. It can protect the quantum nature of the dispersive coupling beyond the traditional dissipation of the system. This protection mechanism allows the system to exhibit strong quantum nonlinear effects in the parameter region of the hyperbolic function $J^2 = \Delta_c \Delta_e$. Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects

Hydraulic fracturing propagation mechanism during shale gas reservoir stimulation through horizontal well

Način razlamanja stijenske mase u naslagama naftnih škriljaca jedan je od glavnih čimbenika koji djeluju na učinkovitost hidrauličkog frakturiranja (frakiranja). U ovom su radu provedena fizikalna ispitivanja i numeričko modeliranje u svrhu sustavnog ispitivanja učinka in-situ (podzemnog) naprezanja i kuta bušenja na stvaranje tlaka zbog hidrauličkog frakturiranja, širenje razlamanja i način razlamanja u horizontalnoj bušotini naftnog nalazišta Shengli u Luojia pokrajini, u izvođenju Sinopec Corp. Ukupno je razmatrano šest različitih in-situ kombinacija naprezanja i osam različitih kutova bušenja slojevite stijenske mase tijekom hidrauličkog frakturiranja. Sažetak nastanka i širenja pukotine te završni oblici pukotina nastalih hidrauličkim frakturiranjem u slojevitim stijenskim masama otkrivaju da kod stratificiranih stijena s istim kutom bušenja, što je veći in-situ omjer naprezanja (t.j. niže maksimalno horizontalno osnovno naprezanje pri konstantnim vertikalnim naprezanjem), potreban je niži hidraulički tlak za poticanje i širenje hidrauličkog frakturiranja. Štoviše, ustanovljeno je da je kod stratificirane stijenske mase pri istom omjeru naprezanja, tlak hidrauličkog frakturiranja, u slučaju kad je kut bušenja 30°, veći nego u svim drugim slučajevima. Nadalje, zapaženo je da učinak stratifikacije na hidrauličko frakturiranje postaje slabiji s porastom in-situ omjera naprezanja. Konačno je zaključeno da rezultati ove analize mogu biti važan teorijski pokazatelj u poboljšanju oblikovanja hidrauličkog frakturiranja kako bi se osiguralo učinkovito stimuliranje naslaga naftnih škriljaca.The fracture pattern of rock mass in shale gas reservoirs is one of the main factors affecting the efficiency of hydraulic fracturing. In this paper, physical experiments and numerical modelling were conducted to systematically investigate the effect of the in-situ stress and perforation angle on the hydraulic fracture initiation pressure and location, fracture propagation, and fracture pattern in a horizontal well drilled by Sinopec Corp. in Luojia area of Shengli Oilfield. A total of six different in-situ stress combinations and eight different perforation angles were considered for the stratified rock mass during the hydraulic fracturing. A summary of the fracture initiations and propagation, and the final fracture patterns induced by the hydraulic fracturing in the stratified rock masses reveals that, for the stratified rock masses with the same perforation angle, the larger the in-situ stress ratio (i.e. lower maximum horizontal principal stress when the vertical stress remains constant) is, the lower hydraulic pressure is required for hydraulic fracturing initiation and propagation. Moreover, it is found that, for the stratified rock mass under the same stress ratio, the hydraulic fracturing pressure in the case with a perforation angle of 30° is higher than that in all other cases. Furthermore, it is noted that the effect of the stratification on the hydraulic fracturing becomes weaker with the in-situ stress ratio increasing. It is finally concluded that the results from this study can provide important theoretical guidance for improving the hydraulic fracturing design in order to ensure the effective shale gas reservoir stimulations

Fully integrated InGaAs/InP single-photon detector module with gigahertz sine wave gating

InGaAs/InP single-photon avalanche diodes (SPADs) working in the regime of GHz clock rates are crucial components for the high-speed quantum key distribution (QKD). We have developed for the first time a compact, stable and user-friendly tabletop InGaAs/InP single-photon detector system operating at a 1.25 GHz gate rate that fully integrates functions for controlling and optimizing SPAD performance. We characterize the key parameters of the detector system and test the long-term stability of the system for continuous operation of 75 hours. The detector system can substantially enhance QKD performance and our present work paves the way for practical high-speed QKD applications.Comment: 11 pages, 6 figures. Accepted for publication in Review of Scientific Instrument