A New Potential Indicator in Differentiating Patients with Lumbar Spinal Stenosis and Lumbar Intervertebral Disc Degeneration

Background: Center of pressure (CoP) trajectory is one of the gait parameters that is widely used for clinical assessments. Moreover, the CoP trajectory could be adversely affected by anatomic and mechanical factors that involve foot function, which was shown to be correlated with musculoskeletal diseases. The aim of this study is to compare angle-associated parameters of gait in patients with different lumbar spinal disorders. Methods: The subjects suffered from the same levels of spine impairment, including patients with lumbar spinal stenosis (LSS) and lumbar intervertebral disc degeneration (LIDD) were recruited in this study. The spatio-temporal angular parameters associated with the CoP of the subjects during their gait were collected and examined. The measurements were used to calculate the CoP angle and symmetry angle (SA). Then the butterfly diagram (BD) intersection angle was introduced as a new potential parameter in gait assessment. Results: The results of the current study showed that CoPs and SAs did not vary between the two groups (P > 0.05). The BD intersection angle, however, indicated some variations between patients with LSS and LIDD (P < 0.05). Conclusion: While the results showed that CoP angles and SAs did not differ between the LSS and LIDD groups, it is hypothesized that such disorders that affect the gait could be reflected in the BD intersection angle. Therefore, the BD intersection angle is suggested as a clinical indicator in clarifying patients with lumbar spinal disorders.

Incipient Motion of Gravel Bedload Considering the Secondary Flow in Bend

The transport of gravel bedload in river bend is one of the basic problems of river dynamics. However, both the complicated bend flow structure and the stochastic bedload transport make explaining the problem theoretically difficult. Flow is the power of the bedload transport, so obtaining the precise theoretical flow structure is fundamental. Through considering the velocity-dip phenomenon and giving the matched boundary conditions, we have obtained the completed three-dimensional bend flow structure in the previous study. Combining the flow structure and the influences of the two-way exposure, we did further research on the incipient motion of the gravel bedload in bend in this paper. It turns out that, because of the existence of the secondary flow, the particle in bend forced by both the longitude and the transverse velocities in the plane. The two-way velocities form an intersection angle which influences the incipient velocity and direction of the particle movement. Moreover, the non-uniform distribution of the bend flow structure along the cross-section decides the differences of the intersection angle, incipient velocity, transport speed of the bedload in the bed surface. Then, the above differences result in the change of the sediment gradation and partition behaviour of the bedload transport.

On the Diophantine equations z^2 = f(x)^2 ± f(x)f(y) + f(y)^2

Using the theory of Pell equation, we study the non-trivial positive integer solutions of the Diophantine equations $z^2=f(x)^2\pm f(x)f(y)+f(y)^2$ for certain polynomials f(x), which mean to construct integral triangles with two sides given by the values of polynomials f(x) and f(y) with the intersection angle $120^\circ$ or $60^\circ$.

The role of fault intersection in fluid flow patterns and the formation of world-class unconformity-related uranium deposits, Athabasca Basin, North Canada

&lt;p&gt;The epigenetic uranium deposits in the eastern part of the Athabasca Basin are classified as unconformity-related ore deposits. Their explicit spatial association to reactivated basement faults is observed within the regional structural NNE trend Wollaston-Mudjatik transition zone, marked by elongated dravite, illite, and chlorite alteration zones. Accordingly, geochemical studies have advocated a circulation and focalization of large amount of one or more fluids to carry and precipitate aqueous chemical materials. At the deposit-scale, the uranium deposits are found mainly at the intersection between two or more fault sets, and described as elongated-like bodies varying in orientation from E-W to NNE direction along the regional transitional zone. Furthermore, some orebodies show a change of orientation and dip of their structures. Thus, what is the hydro-mechanical response of reactivated and inherited fault architecture (e.g., intersection zone) under different stress states (e.g., reverse, strike-slip, and normal faulting regime), and its potential contribution to the shape and orientation of orebodies at deposit scale?&lt;/p&gt;&lt;p&gt;Using hydro-mechanical numerical modeling, this project demonstrates the role that fault intersections play in controlling mineralized fluids by examining the various fluid flow patterns observed when reactivated intersected faults are under various stress states. Numerical modeling is performed using 3-Dimensional Distinct Element Code (3DEC). The numerical models are subdivided into two categories: 1) simplified 3-D models of two intersecting faults, 2) 3-D complex models of fault network at different deposits sites (e.g., the Cigar Lake deposit). While the first simple models attempt to evaluate the effects of intersection angle, burial depth, fluid pressure, basin permeability and stress states on the fluid flow patterns; the second models investigate the stress state under which certain orebodies may have formed.&lt;/p&gt;&lt;p&gt;Our preliminary results from simplified models show that at defined intersection angles, the fluid flow deviates from the main fault toward the secondary fault at their intersection point. The deviation in fluid flow is referred to the value of intersection angle at which the shear stress varies along the secondary fault, leading to the opening of secondary fault. Additionally, the burial depth does not affect the flow along the basement faults, whereas, the overlying highly permeable basin reduces the horizontal flow along the basement faults toward the intersection zone, and reorients a part of the flow toward the basin. &amp;#160;In the complex models (the Cigar Lake model), considering a compressional regime, the E-W fault set is reactivated once the maximum stress is oriented N40W to N65W, which is in agreement with field observations.&lt;/p&gt;

Numerical simulation investigations of coalbed methane drainage performance with multilateral well

A novel multilateral well for coalbed methane extraction was proposed in the study. There is a main wellbore at the longitudinal center of coal seam and four lateral wells at the horizontal center in the multilateral-well system. Compared with traditional drainage holes, multilateral-well system has a better performance on coalbed methane development. A hydraulic-mechanical coupling model of multilateral well was established, the pressure and permeability ratio distribution of the gas extraction process were analyzed comprehensively. The sensitivity analysis of lateral number, length distribution and intersection angle of multilateral-well system were studied. The results indicate that there is a minimum gas pressure distribution around the multilateral well and the overall permeability of coal seams increases with production time and the permeability around the multilateral well is larger than the area away from the multilateral well which induced by the gas desorb and matrix shrink. The quantity of lateral wells has a positive effect on cumulative production. When the total length of lateral wells is equal, the uniformity and symmetry of lateral length distribution are two key factors on the gas extraction performance. The minimum intersection angle has a positive effect on cumulative production. This study provides a better alternative for traditional drainage hole to obtain greater coalbed methane performance.

Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation

Previous research showed that pulsed functional magnetic stimulation can activate brain tissue with optimum intensity and frequency. Conventional stimulation coils are always set as a figure-8 type or Helmholtz. However, the magnetic fields generated by these coils are uniform around the target, and their magnetic stimulation performance still needs improvement. In this paper, a novel type of stimulation coil is proposed to shrink the irritative zone and strengthen the stimulation intensity. Furthermore, the electromagnetic field distribution is calculated and measured. Based on numerical simulations, the proposed coil is compared to traditional coil types. Moreover, the influential factors, such as the diameter and the intersection angle, are also analyzed. It was demonstrated that the proposed coil has a better performance in comparison with the figure-8 coil. Thus, this work suggests a new way to design stimulation coils for transcranial magnetic stimulation.

The Effect of Modifying Double Continuous Flow Intersections Layout Geometric Features on their Operation

Introduction: Continuous flow interventions were first introduced as an alternative to improve traffic operations in the intersections with severe congestion caused by heavy left-turn movements. Objective: This study quantified the effect of modifying the intersection angles of Double Continuous Flow Intersections (DCFI) on their operational characteristics. Mainly, the effects of changing the intersection angle between the different approaches of the main intersection and the angle of the minor cross-over intersections were investigated. Methods: VISSIM software simulation models were used for modifying several design features related to the DCFI and the operational performance was compared between the different simulation scenarios. Results and Discussion: Changes to the cross-over intersection angle increase the safety levels by providing better channelization of traffic movements on the minor intersections of the DCFI and reduce the intersection footprint to be used at high-density urban locations. Increasing the cross-over intersection angle and changing the layout geometry have adverse effects on the capacity of the conventional DCFI. This is mainly because of the added curvature in the intersection approaches which reduces the vehicle speeds, therefore reducing the overall capacity of the modified intersection when compared to the conventional DCFI. However, the total footprint for the intersection is reduced for the modified layout geometry, which improves the capacity of the DCFI. Conclusion: The study has explored the effects of modifying the DCFI intersection angles to fit the limited space in major urban areas on the capacity and performance of the intersection. It showed that DCFI designs could be applied in areas with limited space availability and skewed intersection angles.

An Analytical Model for Fracture Initiation from a Particular Radial Borehole in Hydraulic Fracturing Guided by Multiradial Boreholes

Radial drilling-fracturing, the combination of the hydraulic fracturing and radial borehole, is a technology that can guide the hydraulic fractures to directionally propagate and efficiently develop low permeability reservoir. In this paper, an analytical model of two radial boreholes (a basic research unit) is established to predict fracture initiation pressure (FIP) from one particular radial borehole and the interference between radial boreholes when the hydraulic fracturing is guided by multi-radial boreholes. The model is based on the stress superposition principle and the maximum tensile stress criterion. The effects of in situ stress, wellbore pressure, and fracturing fluid percolation are considered. Then, sensitivity analysis is performed by examining the impact of the intersection angle between radial boreholes, the depth difference between radial boreholes, the radius of radial boreholes, Biot coefficient, and the number of radial boreholes. The results show that FIP declines with the increase of radial boreholes number and the decrease of intersection angle and depth difference between radial boreholes. Meanwhile, the increase of radial borehole number and the reduction of intersection angle and depth difference strengthen the interference between radial boreholes, which conduce to the formation of the fracture network connecting radial boreholes. Besides, FIP declines with the increase of radial borehole radius and the decrease of Biot coefficient. Large radius and low Biot coefficient can enlarge the influence range of additional stress field produced by radial boreholes, enhance the mutual interference between radial boreholes, and guide fracture growth between radial boreholes. In hydraulic fracturing design, in order to reduce FIP and strengthen the interference between radial boreholes, the optimization design can be carried out by lowering intersection angle, increasing radius and number of boreholes, and reducing the depth difference between boreholes when the conditions permit. The research clarifies the interference between radial boreholes and provides the theoretical basis for optimizing radial boreholes layout in hydraulic fracturing guided by multi-radial boreholes.

Quantitative evaluation of eddy current distribution by relative entropy and cross entropy

Koch curve exciting coil of an eddy current probe can adjust the eddy current distributing in more directions at a small domain to enhance the sensitivity of eddy current probe for short defect detection. In this study, a relative entropy and a cross entropy of tangential intersection angle spectrum are proposed to evaluate the eddy current distributions in the different directions when the eddy current probe is positioned at different lift-off distances and excited by different exciting frequency alternative currents. The eddy current distributions induced by a circular and a fractal Koch curve exciting coils are analyzed by the two entropy indices. With the increasing of the lift-off distance or the decreasing of the exciting frequency, the eddy current distributions induced by the Koch curve exciting coil are close to those induced by the circular exciting coil.