THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS B_(p)^(n) OF C^(n)

By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.

Development and performance evaluation of high temperature resistant strong adsorption rigid blocking agent

As drilling wells continue to move into deep ultra-deep layers,the requirements for temperature resistance of drilling fluid treatments are getting higher and higher.Among them,blocking agent,as one of the key treatment agents,has also become a hot spot of research.In this study,a high temperature resistant strong adsorption rigid blocking agent(QW-1)was prepared using KH570 modified silica,acrylamide(AM)and allyltrimethylammonium chloride(TMAAC).QW-1 has good thermal stability,average particle size of 1.46μm,water contact angle of 10.5.,has a strong hydrophilicity,can be well dispersed in water.The experimental results showed that when 2 wt%QW-1 was added to recipe A(4 wt%bentonite slurry+0.5 wt%DSP-1(filtration loss depressant)),the API filtration loss decreased from 7.8to 6.4 m L.After aging at 240.C,the API loss of filtration was reduced from 21 to 14 m L,which has certain performance of high temperature loss of filtration.At the same time,it is effective in sealing 80-100mesh and 100-120 mesh sand beds as well as 3 and 5μm ceramic sand discs.Under the same conditions,the blocking performance was superior to silica(5μm)and calcium carbonate(2.6μm).In addition,the mechanism of action of QW-1 was further investigated.The results show that QW-1 with amide and quaternary ammonium groups on the molecular chain can be adsorbed onto the surface of clay particles through hydrogen bonding and electrostatic interaction to form a dense blocking layer,thus preventing further intrusion of drilling fluid into the formation.

Interaction Mechanisms between Natural Debris Flow and Rigid Barrier Deflectors:A New Perspective for Rational Design and Optimal Arrangement

Rigid barrier deflectors can effectively prevent overspilling landslides,and can satisfy disaster prevention requirements.However,the mechanisms of interaction between natural granular flow and rigid barrier deflectors require further investigation.To date,few studies have investigated the impact of deflectors on controlling viscous debris flows for geological disaster prevention.To investigate the effect of rigid barrier deflectors on impact mechanisms,a numerical model using the smoothed particle hydrodynamics(SPH)method with the Herschel–Bulkley model is proposed to simulate the interaction between natural viscous flow and single/dual barriers with and without deflectors.This model was validated using laboratory flume test data from the literature.Then,the model was used to investigate the influence of the deflector angle and multi-barrier arrangements.The optimal configuration of multi-barriers was analyzed with consideration to the barrier height and distance between the barriers,because these metrics have a significant impact on the viscous flow pile-up,run-up,and overflow mechanisms.The investigation considered the energy dissipation process,retention efficiency,and dead-zone formation.Compared with bare barriers with similar geometric characteristics and spatial distribution,rigid barriers with deflectors exhibit superior effectiveness in preventing the overflow and overspilling of viscous debris flow.Recommendations for the rational design of deflectors and the optimal arrangement of multi-barriers are provided to mitigate geological disasters.

Condition indices for rigid pavements: A comparative analysis of state DOTs using Michigan PMS data

Pavement infrastructure is vital in providing services and links between various sectors of society. Therefore, thepreservation and maintenance of these roads are critical to attaining a pavement network in good conditionthroughout its service life. Various performance indicators like the international roughness index (IRI), pavementcondition index (PCI), and present serviceability rating (PSR) have been used by the state department of transportation (DOT) and highway agencies for evaluating pavement surface conditions and planning future maintenance strategies. Limited data availability, multiple distresses depending on region, lack of correlation of thesecondition indices to maintenance strategies, and data collection limitations pose a challenge for applying theseindices to local conditions. This paper compares condition indices of different states for rigid pavements. Further,using a specific condition index for local conditions is also highlighted. For this purpose, five states and theircorresponding condition indices were evaluated and compared to the Michigan DOT distress index (DI). Thesestates include Virginia, Minnesota, North Dakota, Louisiana, and Oregon. The corresponding distresses of eachcondition index were converted to make them compatible with the MDOT DI. This study used the MDOT'spavement management system (PMS) database to evaluate each condition index for 433 rigid pavement sections.Each distress index was plotted against MDOT DI and compared using a paired t-test. Results show that thecondition indices of Virginia and Minnesota are comparable to DI in terms of the Spearman correlation value. Thet-test results show that except for Virgina, condition indices from other states statistically differ from DI.Therefore, one can't use those directly for local conditions in Michigan. This paper presents the evaluation anddata requirements for each condition index and its impact on selecting a maintenance treatment.

Field Load Test Based SHM System Safety Standard Determination for Rigid Frame Bridge

The deteriorated continuous rigid frame bridge is strengthened by external prestressing. Static loading tests wereconducted before and after the bridge rehabilitation to verify the effectiveness of the rehabilitation process. Thestiffness of the repaired bridge is improved, and the maximum deflection of the load test is reduced from 37.9 to27.6 mm. A bridge health monitoring system is installed after the bridge is reinforced. To achieve an easy assessmentof the bridge’s safety status by directly using transferred data, a real-time safety warning system is createdbased on a five-level safety standard. The threshold for each safety level will be determined by theoretical calculationsand the outcomes of static loading tests. The highest risk threshold will be set at the ultimate limit statevalue. The remaining levels, namely middle risk, low risk, and very low risk, will be determined usingreduction coefficients of 0.95, 0.9, and 0.8, respectively.

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO2, H2O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)T, between gaseous and liquid states along any isotherm from critical (Tc) to Boyle (TB) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρrs(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρBW(T) = 2ρPA(T) = 3ρPB(T) = 3ρRS(T)/2 for T TB. These simple relationships arise, because the higher virial coefficients (bn, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T TB) within the gas phase. The Boyle-work line (p/ρBW)T is related exactly at lower densities as T → TB, and accurately for liquid densities, by ρBW(T) = −(b2/b3)T. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρRS(0) = (2/3)ρBW(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below TB are obtainable from b2(T). A BW-line ground-state crystal density ρBW(0) can be defined by the pair potential minimum. The Ar2 pair potential, ∅ij(rij) determines b2(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅ij(rij) for all fluid states, without any adjustable parameters.

Performance characterization, of rigid polyurethane foam with refined alkali lignin and modified alkali lignin

The two kinds of rigid polyurethane （PU） foams were prepared with respectively adding the refined alkali lignin and alkali lignin modified by 3-chloro-1,2-epoxypropane to be instead of 15% of the polyether glycol in weight. The indexes of mechanical performance, apparent density, thermal stability and aging resistance were separately tested for the prepared PU foams. The results show that the mechanical property, thermal insulation and thermal stability for PU foam with modified alkali lignin are excellent among two kinds of PU foams and control samples. The additions of the refined alkali lignin and modified alkali lignin to PU foam have little effect on the natural aging or heat aging resistance except for decreasing hot alkali resistance apparently. Additionally, the thermal conductivity of modified alkali lignin PU foam is lowest among two kinds of PU foams and control samples. The alkali lignin PU foam modified by 3-chloro-1,2-epoxypropane could be applied in the heat preservation field.

A general method to calculate passive earth pressure on rigid retaining wall for all displacement modes

A general analytical method to calculate the passive rigid retaining wall pressure was deduced considering all displacement modes. First, the general displacement mode function was setup, then the hypotheses were made that the lateral passive pressure is linear to the corresponding horizontal displacement and the soil behind retaining wall is composed of a set of springs and ideal rigid plasticity body, the general analytical method was proposed to calculate the passive rigid retaining wall pressure based on Coulomb theory. The analytical results show that the resultant forces of the passive earth pressure are equal to those of Coulomb＇s theory, but the distribution of the passive pressure and the position of the resultant force depend on the passive displacement mode parameter, and the former is a parabolic function of the soil depth. The analytical results are also in good agreement with the experimental ones.

Experimental investigation on seismic performance of rigid frame tied-arch bridge with split-piers

A novel seismic design method, namely split-pier seismic design, is proposed. A vertical gap and connect elements are set in split-piers. The lateral stiffness of piers is reduced by cracking of the connect elements under severe earthquake, and the seismic response of bridges is reduced by avoiding the site predominant periods. A model of tied-arch rigid frame bridge with split-piers was designed. Seismic performance was investigated by pseudo-static experimentation on the scale model, The failure process of split-piers, the hysteresis characteristic and the effect of split-piers on the superstructure are presented. Results show that the split-pier has better seismic performance than common ductile piers do.

Vibration analysis of maglev three-span rigid frame bridge considering magnetic force

The dynamic interaction between the maglev vehicle and the three-span rigid frame bridge is discussed. With the consideration of magnetic force, the interaction model is developed. Numerical simulations are performed to study the dynamic characteristics of the bridge during vehicle movement along the bridge. The results show that a reasonable value of the linear stiffness ratio of columns to beams is between 2. 0 and 3.0. The dynamic responses of the bridge are aggravated with the decrease in bending rigidity and the increase in vehicle speed and the span ratio of the bridge. It is suggested that a definite way is to control impact coefficients and acceleration in the dynamic design of the bridge. It is unsuitable to adopt the moving load model and the moving mass model in the design. The proposed results can serve in the design of high-speed maglev three-span rigid frame bridges.

Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

Synthetic analysis is conducted to the wind tunnel experiment results of zero lift drag coefficient and lift coefficient for large aspect ratio winged rigid body.By means of wind tunnel experiment data,the dynamics model of the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended.The research indicates that the change trends of zero lift drag coefficient and lift coefficient to Mach number are similar.The calculation result and wind tunnel experiment data all verify the validity of the amended dynamics model by which to estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body,and thus providing some technical reference to aerodynamics character analysis of the same types of winged rigid body.

Analysis on the resistive force in penetration of a rigid projectile

According to the dimensionless formulae of DOP(depth of penetration) of a rigid projectile into different targets,the resistive force which a target exerts on the projectile during the penetration of rigid projectile is theoretically analyzed.In particular,the threshold V_C of impact velocity applicable for the assumption of constant resistive force is formulated through impulse analysis.The various values of V_C corresponding to different pairs of projectile-target are calculated,and the consistency of the relative test data and numerical results is observed.

Pseudo-rigid-body Model for Corrugated Cantilever Beam Used in Compliant Mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.

Automatic Generation of Optimally Rigid Formations Using Decentralized Methods

In this paper, decentralized methods of optimally rigid graphs generation for formation control are researched. The notion of optimally rigid graph is first defined in this paper to describe a special kind of rigid graphs. The optimally rigid graphs can be used to decrease the topology complexity of graphs while maintaining their shapes. To minimize the communication complexity of formations, we study the theory of optimally rigid formation generation. First, four important propositions are presented to demonstrate the feasibility of using a decentralized method to generate optimally rigid graphs. Then, a formation algorithm for multi-agent systems based on these propositions is proposed. At last, some simulation examples are given to show the efficiency of the proposed algorithm.

关于弱α-skew Armendariz环和α-rigid环

研究了弱-αskew Armendariz环、-αrigid环、α-SC环以及半交换环的关系.设α是环R的一个自同态,nil(R)是R的理想,如果R是α-SC环,那么R是弱-αskew Armendariz环.

Oblique perforation of thick metallic plates by rigid projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.

RIGID FINITE ELEMENT AND ITS APPLICATIONS IN ENGINEERING

Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.

Non-limit passive soil pressure on rigid retaining walls

This paper aims to reveal the depth distribution law of non-limit passive soil pressure on rigid retaining wall that rotates about the top of the wall(rotation around the top(RT) model). Based on Coulomb theory, the disturbance degree theory, as well as the spring-element model, by setting the rotation angle of the wall as the disturbance parameter, we establish both a depth distribution function for sand and a nonlinear depth distribution calculation method for the non-limit passive soil pressure on a rigid retaining wall under the RT model, which is then compared with experiment. The results suggest that under the RT model: the non-limit soil pressure has a nonlinear distribution; the backfill disturbance degree and the lateral soil pressure increase with an increase in the wall rotation angle; and, the points where the resultant lateral soil pressure acts on the retaining wall are less than 2/3 of the height of the wall. The soil pressure predicted by the theoretical calculation put forward in this paper are quite similar to those obtained by the model experiment, which verifies the theoretical value, and the engineering guidance provided by the calculations are of significance.

Seismic response analysis of continuous rigid frame bridge considering canyon topography effects under incident SV waves

To evaluate the importance of the canyon topography effects on large structures, based on a rigid frame bridge across a 137-m-deep and 600-m-wide canyon, the seismic response of the canyon site is analyzed using a two-dimensional finite element model under different seismic SV waves with the assumptions of vertical incidence and oblique incidence to obtain the ground motions, which are used as the excitation input on the pier foundations of the bridge with improved large mass method. The results indicate that canyon topography has significant influences on the ground motions in terms of inci- dent angle. The peak ground acceleration values vary greatly from the bottom of the canyon to the upper comers. Under ver- tical incident SV waves, at the upper comers of canyon the peak ground accelerations greatly increase; whereas the peak ground accelerations diminish at the bottom comers of canyon. Under oblique incident SV waves, the shaking of the canyon slope perpendicular to the incidence direction is much more severe than that of the opposite side of canyon. And the ground surface has been characterized by larger deformations in the case of oblique incident waves. It is also concluded that the low piers and frame of the continuous rigid frame bridge ape more sensitive to the multi-support seismic excitations than the flexible high piers. The canyon topography as well as the oblique incidence of the waves brings the continuous rigid frame bridge severe responses, which should be taken into account in bridge design.

INDENTATION OF A TRANSVERSELY ISOTROPIC PIEZOELECTRIC HALF-SPACE BY A RIGID SPHERE

This paper exactly analyzes the problem of a rigid sphereindenting a transversely isotropic piezoelectric half-space. Thepotential theory method is employed and generalized to included thepiezoelec- tric effect. By using the previous results of elasticity,an exact solution is derived. It is found that all the elastoelectricvariables can be expressed in terms of elementary functions.