Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

The Structures of the AR Sequences of Tilted Algebras

In this paper,We give the forms of AR sequences of a tilted algebra with terms all belonging to x(A_T),or all belonging to y(A_T).The sink maps of a tilted algebra which end at the indecompos able projective modules and the source maps of starting at the indecomposable injective modules are also obtained.These results together with the connecting sequecnes given in [3] determine the AR quiver of the tilted algcbra,morever,this can be done directly from the AR quiver of the correspond ing hereditary algebra.

Cascaded tilted fiber Bragg grating for enhanced refractive index sensing

We proposed and experimentally demonstrated a cascaded tilted fiber Bragg grating(TFBG)for enhanced refractive index sensing.The TFBG is UV-inscribed in series in ordinary single-mode fiber(SMF)and reduced-diameter SMF with the same tilt angle,and then excites two sets of superposed spectral combs of cladding modes.The cascaded TFBG with total length of 18 mm has a much wider wavelength range over 100 nm and narrower wavelength separation than that of a TFBG only in the SMF,enabling an enlarged range and a higher accuracy of refractive index measurement.The fabricated TFBG with the merits of enhanced sensing capability and temperature self-calibration presents great potentials in the biochemical sensing applications.

In-fiber photoelectric device based on graphene-coated tilted fiber grating

Graphene and related two-dimensional materials have attracted great research interests due to prominently optical and electrical properties and flexibility in integration with versatile photonic structures.Here,we report an in-fiber photoelec-tric device by wrapping a few-layer graphene and bonding a pair of electrodes onto a tilted fiber Bragg grating(TFBG)for photoelectric and electric-induced thermo-optic conversions.The transmitted spectrum from this device consists of a dense comb of narrowband resonances that provides an observable window to sense the photocurrent and the electrical injection in the graphene layer.The device has a wavelength-sensitive photoresponse with responsivity up to 11.4 A/W,allowing the spectrum analysis by real-time monitoring of photocurrent evolution.Based on the thermal-optic effect of electrical injection,the graphene layer is energized to produce a global red-shift of the transmission spectrum of the TF-BG,with a high sensitivity approaching 2.167×10^(4)nm/A^(2).The in-fiber photoelectric device,therefore as a powerful tool,could be widely available as off-the-shelf product for photodetection,spectrometer and current sensor.

A Review of Formation Mechanism Study on Reservoirs with Tilted Oil-water Contacts

The distribution characteristics of the oil-water contact are the basis for the reservoir exploration and development and reserves evaluation. The reservoir with a tilted oil-water contact has a unique formation mechanism, and the understanding of its distribution and formation mechanism will directly affect the evaluations for the reservoir type, well deployment, selection of well pattern and type, determination of test section, and reserves evaluation. Based on the analysis of reservoir characteristics, petrophysical properties and geological structure in 40 reservoirs worldwide with tilted oil-water contacts, the progress of the research on the formation mechanisms of titled oil-water contacts is summarized in terms of the hydrodynamic conditions, reservoir heterogeneity, neotectonic movement and oil-gas exploitation. According to the formation mechanism of tilted oil-water contacts and the needs of exploration research, different aspects of research methods are summarized and classified, such as the calculation of equipotential surfaces for oil and water in the formation, analysis of formation pressure and analysis of reservoir physical properties and so on. Based upon statistical analysis, it is suggested that the degree of the inclination of the oil-water contact be divided based on the dip of oil-water contact（DipTOWC）. The tilted oil-water contact is divided into three categories： large dip（DipTOWC≥55 m/km）, medium dip（4 m/km≤DipTOWC55 m/km）, and small dip（DipTOWC4 m/km）. The classification and evaluation method can be combined with structure amplitude and reservoir property. The formation mechanism of domestic and international reservoirs with tilted oil-water contacts are summarized in this paper, which have important significance in guiding the exploration and development of the oilfield with tilted oil-water contacts, reserves evaluation, and well deployment.

Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Analytical model of tilted driver–pickup coils for eddy current nondestructive evaluation

A driver-pickup probe possesses better sensitivity and flexibility due to individual optimization of a coil.It is fre-quently observed in an eddy current(EC)array probe.In this work,a tilted non-coaxial driver-pickup probe above a multilayered conducting plate is analytically modeled with spatial transformation for eddy current nondestructive evalua-tion.Basically,the core of the formulation is to obtain the projection of magnetic vector potential(MVP)from the driver coil onto the vector along the tilted pickup coil,which is divided into two key steps.The first step is to make a projection of MVP along the pickup coil onto a horizontal plane,and the second one is to build the relationship between the pr,ojected MVP and the MVP along the driver coil.Afterwards,an analytical model for the case of a layered plate is established with the reflection and transmission theory of electromagnetic fields.The calculated values from the resulting model indicate good agreement with those from the finite element model(FEM)and experiments,which validates the developed analytical model.

Influence of Tilted Angle on Effective Linear Energy Transfer in Single Event Effect Tests for Integrated Circuits at 130 nm Technology Node

A heavy-ion irradiation experiment is studied in digital storage cells with different design approaches in 130？nm CMOS bulk Si and silicon-on-insulator （SOI） technologies. The effectiveness of linear energy transfer （LET） with a tilted ion beam at the 130？nm technology node is obtained. Tests of tilted angles θ=0 ° , 30 ° and 60 ° with respect to the normal direction are performed under heavy-ion Kr with certain power whose LET is about 40？MeVcm 2 /mg at normal incidence. Error numbers in D flip-flop chains are used to determine their upset sensitivity at different incidence angles. It is indicated that the effective LETs for SOI and bulk Si are not exactly in inverse proportion to cosθ , furthermore the effective LET for SOI is more closely in inverse proportion to cosθ compared to bulk Si, which are also the well known behavior. It is interesting that, if we design the sample in the dual interlocked storage cell approach, the effective LET in bulk Si will look like inversely proportional to cosθ very well, which is also specifically explained.

Classification of wintertime large-scale tilted ridges over the Eurasian continent and their influences on surface air temperature

This study investigates the major patterns of large-scale tilted ridges(LSTRS)over the Eurasian continent and their connections with large-scale surface air temperature during boreal winter.A total number of 134 LSTR events with zonal extent exceeding 90°of longitude on the peak day are identified.Using self-organizing map(SOM),the LSTRs are classified into five clusters that are characterized by different spatial distributions and orientations.The leading two clusters are closely associated with extensive and persistent cold events over different places.Considering the first cluster,LSTRs extend from the Ural Mountains to Northeast Asia and are favorable for the amplification and southeastward extension of the Siberian high.Therefore,this cluster is closely associated with the occurrence of extensive and persistent cold events in china.In comparison with the first cluster,the LSTRs of second group are situated to the west,with starting points from the Kola Peninsula,and cause extensive and persistent cold events over Eastern Europe,central Asia,and central Siberia.The results suggest that the vertical coupling between LSTRs and the corresponding anomalous sea level pressure is crucial for the persistent cold temperature events associated with the leading two SOM clusters.

Thermal Convection in a Tilted Rectangular Cell with Aspect Ratio 0.5

Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct nu- merical simulations within both Oberbeck-Boussinesq （OB） approximation and strong non-Oberbeck-Boussinesq （NOB） effects. The considered Rayleigh numbers Ra range from 105 to 107, the working fluid is air at 30OK, and the corresponding Prandtl number Pr is 0.71. Within the OB approximation, it is found that there exist multiple states for Ra = 105 and hysteresis for Ra = 106. For a relatively small tilt angle/3, the large-scale circulation can either orient along one of the the vertical diagonal planes （denoted by Ma mode） or orient parallel to the front wall （denoted by Mp mode）. Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For/Ta = 107 and β = 0°, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, Md and Mp modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed/Ta = 106, it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature Tc for different β ranges are different. NOB effects can either increase or decrease Nu, Re and Tc when β is varied.

Tilted Axis Rotation of ^(57)Mn in Covariant Density Functional Theory

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.

Giant Enhancement of Diffusion in a Tilted Egg-Carton Potential

Diffusion of a particle on a tilted periodic surface such as the egg-carton potential is investigated using Langevin Monte Carlo simulations. It is found that the effective diffusion coefficient of the particle related to the one- dimensional case can be greatly enhanced, when the local minima of such potential along the x and y directions are close to vanishing. A relation between the group diffusion and the phase diffusion is used to analyze the enhancement mechanism of the diffusion.

Third-order aberration analysis of tilted-pupil optical systems

The aberration field of an optical system with a tilted pupil is explored through expanding the vector expressions of the third-order wavefront aberrations. First, the vector forms of the wavefront aberrations are modified to obtain the aberration expressions with the pupil tilted; full field displays of coma and astigmatism in this situation are given. Then, the third-order aberration formulas with the pupil decentered and tilted simultaneously are derived and discussed. Finally, an example is taken to certify the validity of aberration distribution properties.

Stable Superwetting Surface Prepared with Tilted Silicon Nanowires

Large-scale uniform nanostructured surface with superwettability is crucial in both fundamental research and engineering applications.A facile and controllable approach was employed to fabricate a superwetting tilted silicon nanowires(TSNWs) surface through metal-assisted chemical etching and modification with low-surface-energy material.The contact angle(CA) measurements of the nanostructured surface show a large range from the superhydrophilicity(the CA approximate to 0°) to superhydrophobicity(the CA up to 160°).The surface becomes antiadhesion to water upon nanostructuring with a measured sliding angle(a) close to 0°.Moreover,the fluorinated TSNWs surface exhibits excellent stability and durability because strong chemical bonding has been formed on the surface.

A 795 nm gain coupled distributed feedback semiconductor laser based on tilted waveguides

The 795 nm distributed feedback lasers have great application in pumping the Rb D1 transition.In this paper,in order to realize specific 795 nm lasing,we designed tilted ridge distributed feedback lasers based on purely gain coupled effect induced by periodic current injection windows through changing the angle of the tilted ridge.The fabricated devices were cleaved into 2 mm-cavity-length,including 5 tilted angles.The peak output powers of all devices were above 30 mW.Single longitudinal mode lasing was realized in all tilted Fabry-Perot cavities using periodic current injection windows,with side mode suppression ratio over 30 dB.The total wavelength range covered 8.656 nm at 20℃.It was disclosed theoretically and experimentally that the output powers,threshold currents,and central wavelengths of the tilted ridge purely gain coupled DFB lasers were relevant to the tilted angles.The results will be instructive for future design of DFB laser arrays with different central wavelengths.

Effect of interface anisotropy on tilted growth of eutectics:A phase field study

Interfacial energy anisotropy plays an important role in tilted growth of eutectics. However, previous studies mainly focused on the solid-solid interface energy anisotropy, and whether the solid-liquid interface energy anisotropy can significantly affect the tilted growth of eutectics still remains unclear. In this study, a multi-phase field model is employed to investigate both the effect of solid-liquid interfacial energy anisotropy and the effect of solid-solid interfacial energy anisotropy on tilted growth of eutectics. The findings reveal that both the solid-liquid interfacial energy anisotropy and the solid-solid interfacial energy anisotropy can induce the tilted growth of eutectics. The results also demonstrate that when the rotation angle is within a range of 30°-60°, the growth of tilted eutectics is governed jointly by the solid-solid interfacial energy anisotropy and the solid-liquid interfacial energy anisotropy;otherwise, it is mainly controlled by the solid-solid interfacial energy anisotropy. Further analysis shows that the unequal pinning angle at triple point caused by the adjustment of the force balance results in different solute-diffusion rates on both sides of triple point. This will further induce an asymmetrical concentration distribution along the pulling direction near the solid-liquid interface and the tilted growth of eutectics. Our findings not only shed light on the formation mechanism of tilted eutectics but also provide theoretical guidance for controlling the microstructure evolution during eutectic solidification.

On the Onsager-Casimir reciprocal relations in a tilted Weyl semimetal

The Onsager-Casimir reciprocal relations are a fundamental symmetry of nonequilibrium statistical systems.Here we study an unusual chirality-dependent Hall effect in a tilted Weyl semimetal Co_(3)Sn_(2)S_(2) with broken time-reversal symmetry.It is confirmed that the reciprocal relations are satisfied.Since two Berry curvature effects,an anomalous velocity and a chiral chemical potential,contribute to the observed Hall effect,the reciprocal relations suggest their intriguing connection.

REPETITIVE CLUSTER-TILTED ALGEBRAS

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected.

Design and Simulation of Silicon-based NiCrAu MEMS Torsion Micromirror with Tilted Back-electrode

Torsion micromirror is a key structure of optical devices in micro-electro-mechanical system(MEMS), such as MEMS optical switches, MEMS variable optical attenuator, MEMS scanning micromirror array and so on. A silicon-based NiCrAu MEMS torsion micromirror is theoretically analyzed. It is shown that in order to have 15° rotation, the driven voltage should be about 20V and the thickness of the supporting beam must be controlled in the range of submicron orders of magnitude. This very thin beam makes the structure more unstable and unreliable, and also makes the fabrication more complicated. Based on parallel back-electrode analysis and testing, a tilted back-electrode has been designed to replace the parallel back-electrode in order to decrease the driven voltage and difficulty of fabricating processing. By theoretical analysis and simulation, a conclusion can be drown that the thickness can be improved from submicron to micron by using tilted back-electrode when using the same driven voltage. Tilted back-electrode is very effective to improve the stability and reliability of the micromirror structure.

What Is the Association between an Anteriorly Tilted Pelvis and Trendelenburg Gait?

Lower back pain (LBP) is a widespread, painful medical condition that has been plaguing society for many years. Present conservative rehabilitation focus is on lumbo-pelvic hip stability exercises in individual planes. However, a functional integrative rehabilitative approach addressing lumbo-pelvic misalignment in the sagittal (anteriorly tilted pelvis) and frontal (Trendelenburg gait) planes has not been presented. The aforementioned patho-biomechanical conditions and their management are often discussed estranged from each other rather than functionally integrated. This paper serves as a short communication which discusses the lumbo-pelvic anatomy, identifies the anatomical and biomechanical associations between the anteriorly tilted pelvic and Trendelenburg gait. Through an analysis of relevant literature, recommendations were made on the improvement of flexibility of the hip flexors, taut iliofemoral and pubofemoral ligaments to resolve the primary abnormal force-couple, with improved flexibility of the erector spinae and quadratus lumborum to resolve the secondary abnormal force-couple. In addition, improved flexibility of the hip flexors should coincide with closed-kinetic chain concentric strengthening of the ipsi-lateral hip abductors and contralateral external obliques. Patient education is also needed for self-re-alignment of the lower extremity to a neutral position and neutral foot stance. Biokineticists/exercise therapists should also review the patient’s gait biomechanics to determine whether sartorius synergistic dominance is in play. In conclusion, the association between an anteriorly tilted pelvis and Trendelenburg gait, is in regard to taut anterior acetabulofemoral ligaments and femoral retroversion torsion angle that is both preceded and followed by the biomechanical influence of various anatomical structures. These anatomical and biomechanical factors must be evaluated by the biokineticists/exercise therapists before prescribing a rehabilitative programme to ensure successful rehabilitation of lumbo-pelvic hip complex.