Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Regularity of strain distribution in short-fiber/whisker reinforced composites

Based on studies on the strain distribution in short-fiber/whisker reinforced metal matrix composites, a deformation characteristic parameter, lambda is defined as a ratio of root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. Quantitative relation between lambda and microstructure parameters of composites is obtained. By using lambda, the stiffness moduli of composites with arbitrary reinforcer orientation density function and under arbitrary loading condition are derived. The upper-bound and lower-bound of the present prediction are the same as those from the equal-strain theory and equal-stress theory, respectively. The present theory provides a physical explanation and theoretical base for the present commonly-used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for stiffness modulus prediction of practical engineering composites in accuracy and simplicity.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Solid-state qubit measurement with single electron transistors

In this paper we consider the continuous weak measurement of a solid-state qubit by single electron transistors (SET). For single-dot SET, we find that in nonlinear response regime the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically on any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents. For double-dot SET, we discuss its robustness against wider range of temperatures, quantum efficiency, and the relevant open issues unresolved.

Stability shear stress and equilibrium cross-sectional geometry of sheltered tidal channels

This study relates tidal channel cross-sectional area (A) to peak spring discharge (Q) via a physical mechanism, namely the stability shear stress ( tau sub(S)) just necessary to maintain a zero gradient in net along-channel sediment transport. It is assumed that if bed shear stress ( tau ) is greater than tau sub(S), net erosion will occur, increasing A, and reducing tau similar to (Q/A) super(2) back toward tau sub(S). If tau < tau sub(S) there will be net deposition, reducing A and increasing tau toward tau sub(S). A survey of the literature allows estimates of Q and A at 242 sections in 26 separate sheltered tidal systems. Assuming a single value of tau sub(S) characterizes the entire length of a given tidal channel, it is predicted that along-channel geometry will follow the relation Ah sub(R) super(1) super(/) super(6) similar to Q. Along-channel regressions of the form Ah sub(R) super(1) super(/) super(6) similar to Q super( beta ) give a mean observed value for beta of 1.00 plus or minus 0.06, which is consistent with this concept. Results indicate that a lower bound on tau sub(S) (and an upper bound on A) for stable channels is provided by the critical shear stress ( tau sub(C)) just capable of initiating sediment motion. Observed tau sub(S) is found to vary among all systems as a function of spring tidal range (R sub(sp)) according to the relation tau sub(S) approximately 2.3 R sub(sp) super(0.79) tau sub(C). Observed deviations from uniform tau sub(S) along individual channels are associated with along-channel variation in the direction of maximum discharge (i.e., flood-versus ebb-dominance).

Gas permeability and permselectivity of polyimides prepared from phenylenediamines with methyl substitution at the ortho position

Polyimides were prepared from diamines: 2,4,6-trimethyl-1,3-phenylenediamine (3MPDA) and 2,3,4,5-tetramethyl-1,4-phenylenediamine (4MPDA). 1,4-Bis(3,4-dicarboxyphenoxy)benzene dianhydride (HQDPA), 3,3',4,4'-benzophenone tetracarboxylic dianhydride (BTDA), 3,3'-4,4'-diphenylsulphone tetracarboxylic dianhydride (SO(2)PDA), 3,3',4,4'-diphenylsulphide tetracarboxylic dianhydride (SPDA), pyromellitic dianhydride (PMDA), and 2,2'-bis(3,4-dicarboxyphenyl)hexa-fluoroisopropane dianhydride (6FDA) were used as dianhydride. The gas permeabilities of H-2, O-2 and N-2 through the polyimides were measured at temperatures from 30 degrees C to 90 degrees C. The results show that as methyl and trifluoromethyl substitution groups densities increase from 7.73 x 10(-3) molcm(-3) to 13.50 x 10(-3)molcm(-3), the peameability of H-2 increases 10-fold at 60% loss of permselectivity of H-2/N-2 however, the permeability of O-2 increases 20-fold at 20% loss of permselectivity of O-2/N-2. For O-2/N-2 separation, PMDA-3MPDA has similar performance to 6FDA-3MPDA and 6FDA-4MPDA; all have higher permeabilities for O-2 than normal polyimides, and the P(O-2)/alpha(O-2/N-2) trade-off relationships lie on the upper bound line for polymers. (C) 1999 Society of Chemical Industry.

Influence of mean water depth and a subsurface sandbar on the onset and strength of wave breaking

Wave breaking in the open ocean and coastal zones remains an intriguing yet incompletely understood process, with a strong observed association with wave groups. Recent numerical study of the evolution of fully nonlinear, two-dimensional deep water wave groups identified a robust threshold of a diagnostic growth-rate parameter that separated nonlinear wave groups that evolved to breaking from those that evolved with recurrence. This paper investigates whether these deep water wave-breaking results apply more generally, particularly in finite-water-depth conditions. For unforced nonlinear wave groups in intermediate water depths over a flat bottom, it was found that the upper bound of the diagnostic growth-rate threshold parameter established for deep water wave groups is also applicable in intermediate water depths, given by k(0) h greater than or equal to 2, where k(0) is the mean carrier wavenumber and h is the mean depth. For breaking onset over an idealized circular arc sandbar located on an otherwise flat, intermediate-depth (k(0) h greater than or equal to 2) environment, the deep water breaking diagnostic growth rate was found to be applicable provided that the height of the sandbar is less than one-quarter of the ambient mean water depth. Thus, for this range of intermediate-depth conditions, these two classes of bottom topography modify only marginally the diagnostic growth rate found for deep water waves. However, when intermediate-depth wave groups ( k(0) h greater than or equal to 2) shoal over a sandbar whose height exceeds one-half of the ambient water depth, the waves can steepen significantly without breaking. In such cases, the breaking threshold level and the maximum of the diagnostic growth rate increase systematically with the height of the sandbar. Also, the dimensions and position of the sandbar influenced the evolution and breaking threshold of wave groups. For sufficiently high sandbars, the effects of bottom topography can induce additional nonlinearity into the wave field geometry and associated dynamics that modifies the otherwise robust deep water breaking-threshold results.

边坡工程的极限分析上限法

Theory of limit analysis include upper bound theorem and lower bound theorem. To deal with slope stability analysis by limit analysis is to approximate the real solution from upper limit and lower limit. The most used method of limit analysis is upper bound theorem, therefore it is often applied to slope engineering in many cases. Although upper bound approach of limit analysis can keep away from vague constitutive relation and complex stress analyses, it also can obtain rigorous result. Assuming the critical surface is circular slip surface, two kinematically admissible velocity fields for perpendicular slice method and radial slice method can be established according to the limit analysis of upper bound theorem. By means of virtual work rate equation and strength reduction method, the upper-bound solution of limit analysis for homogeneous soil slope can be obtained. A log-spiral rotational failure mechanism for homogeneous slope is discussed from two different conditions which represent the position of shear crack passing the toe and below the toe. In the dissertition, the author also establishes a rotational failure mechanics with combination of different logarithmic spiral arcs. Furthermore, the calculation formula of upper bound solution for inhomogeneous soil slope stability problem can be deduced based on the upper bound approach of rigid elements. Through calculating the external work rate caused by soil nail, anti-slide pile, geotechnological grid and retaining wall, the upper bound solution of safety factor of soil nail structure slope, slip resistance of anti-slide pile, critical height of reinforced soil slope and active earth pressure of retaining wall can be obtained by upper bound limit analysis method. Taking accumulated body slope as subject investigated, with study on the limit analysis method to calculate slope safety factor, the kinematically admissible velocity fields of perpendicular slice method for slope with broken slip surface is proposed. Through calculating not only the energy dissipation rate produced in the broken slip surfaces and the vertical velocity discontinuity, but also the work rate produced by self-weight and external load, the upper bound solution of slope with broken slip surface is deduced. As a case study, the slope stability of the Sanmashan landslide in the area of the Three Gorges reservoir is analyzed. Based on the theory of limit analysis, the upper bound solution for rock slope with planar failure surface is obtained. By means of virtual work-rate equation, energy dissipation caused by dislocation of thin-layer and terrane can be calculated; furthermore, the formulas of safety factor for upper bound approach of limit analysis can be deduced. In the end, a new computational model of stability analysis for anchored rock slope is presented after taking into consideration the supporting effect of rock-bolts, the action of seismic force and fissure water pressure. By using the model, not only the external woke-rate done by self-weight, seismic force, fissure water pressure and anchorage force but also the internal energy dissipation produced in the slip surface and structural planes can be totally calculated. According to the condition of virtual work rate equation in limit state, the formula of safety factor for upper bound limit analysis can be deduced.

基于精细结构描述及数值试验的断续节理岩体力学参数智能选取

Evaluating the mechanical properties of rock masses is the base of rock engineering design and construction. It has great influence on the safety and cost of rock project. The recognition is inevitable consequence of new engineering activities in rock, including high-rise building, super bridge, complex underground installations, hydraulic project and etc. During the constructions, lots of engineering accidents happened, which bring great damage to people. According to the investigation, many failures are due to choosing improper mechanical properties. ‘Can’t give the proper properties’ becomes one of big problems for theoretic analysis and numerical simulation. Selecting the properties reasonably and effectively is very significant for the planning, design and construction of rock engineering works. A multiple method based on site investigation, theoretic analysis, model test, numerical test and back analysis by artificial neural network is conducted to determine and optimize the mechanical properties for engineering design. The following outcomes are obtained: (1) Mapping of the rock mass structure Detailed geological investigation is the soul of the fine structure description. Based on statistical window，geological sketch and digital photography，a new method for rock mass fine structure in-situ mapping is developed. It has already been taken into practice and received good comments in Baihetan Hydropower Station. (2) Theoretic analysis of rock mass containing intermittent joints The shear strength mechanisms of joint and rock bridge are analyzed respectively. And the multiple modes of failure on different stress condition are summarized and supplied. Then, through introducing deformation compatibility equation in normal direction, the direct shear strength formulation and compression shear strength formulation for coplanar intermittent joints, as well as compression shear strength formulation for ladderlike intermittent joints are deducted respectively. In order to apply the deducted formulation conveniently in the real projects, a relationship between these formulations and Mohr-Coulomb hypothesis is built up. (3) Model test of rock mass containing intermittent joints Model tests are adopted to study the mechanical mechanism of joints to rock masses. The failure modes of rock mass containing intermittent joints are summarized from the model test. Six typical failure modes are found in the test, and brittle failures are the main failure mode. The evolvement processes of shear stress, shear displacement, normal stress and normal displacement are monitored by using rigid servo test machine. And the deformation and failure character during the loading process is analyzed. According to the model test, the failure modes quite depend on the joint distribution, connectivity and stress states. According to the contrastive analysis of complete stress strain curve, different failure developing stages are found in the intact rock, across jointed rock mass and intermittent jointed rock mass. There are four typical stages in the stress strain curve of intact rock, namely shear contraction stage, linear elastic stage, failure stage and residual strength stage. There are three typical stages in the across jointed rock mass, namely linear elastic stage, transition zone and sliding failure stage. Correspondingly, five typical stages are found in the intermittent jointed rock mass, namely linear elastic stage, sliding of joint, steady growth of post-crack, joint coalescence failure, and residual strength. According to strength analysis, the failure envelopes of intact rock and across jointed rock mass are the upper bound and lower bound separately. The strength of intermittent jointed rock mass can be evaluated by reducing the bandwidth of the failure envelope with geo-mechanics analysis. (4) Numerical test of rock mass Two sets of methods, i.e. the distinct element method (DEC) based on in-situ geology mapping and the realistic failure process analysis (RFPA) based on high-definition digital imaging, are developed and introduced. The operation process and analysis results are demonstrated detailedly from the research on parameters of rock mass based on numerical test in the Jinping First Stage Hydropower Station and Baihetan Hydropower Station. By comparison，the advantages and disadvantages are discussed. Then the applicable fields are figured out respectively. (5) Intelligent evaluation based on artificial neural network (ANN) The characters of both ANN and parameter evaluation of rock mass are discussed and summarized. According to the investigations, ANN has a bright application future in the field of parameter evaluation of rock mass. Intelligent evaluation of mechanical parameters in the Jinping First Stage Hydropower Station is taken as an example to demonstrate the analysis process. The problems in five aspects, i. e. sample selection, network design, initial value selection, learning rate and expected error, are discussed detailedly.

Seasonal and spatial distribution of matrix-bound phosphine and its relationship with the environment in the Changjiang River Estuary, China

Sediment is commonly considered as a source of phosphine, which is a highly toxic and reactive atmospheric trace gas. This study aims to investigate the seasonal and spatial distribution of matrix-bound phosphine (MBP) and its relationship with the environment in the Changjiang River Estuary. A total of 43 surface sediments were collected in four seasons of 2006, and concentrations of MBP and relative environmental factors were analyzed. MBP ranged from 1.93 to 94.86 ng kg(-1) dry weight (dw) with an average concentration of 17.14 ng kg(-1) dw. The concentrations of MBP in the tipper estuary were, higher than those in the lower estuary, which could be attributed to greater pollutant inputs in the upper estuary. The concentrations of MBP also varied with season, with November > August > May > February. Significant correlations existed between MBP and total phosphorus (TP), organic phosphorus (OP), inorganic phosphorus (W), organic carbon (OC), total nitrogen (TN), the grain size, and redox potential (Eh), suggesting that these sedimentary environmental characteristics played an important role in controlling the MBP levels in the sediments. Notably, there were positive linear relationships between the concentrations of soluble reactive phosphorus (SRP), TP, and chlorophyll a (Chl a) in bottom water and MBP in sediments. These relationships might be very complicated and need further exploration. This work is the first comprehensive study of the seasonal and spatial distribution of MBP in sediments and its relationships with environmental factors in a typical estuary, and will lead to deeper understanding of the phosphorus (P) biogeochemical cycle. (C) 2008 Elsevier Ltd. All rights reserved.