Anisotropy Coefficient Research Articles

Anisotropy and reproducibility of ultrasound shear wave elastography in patella tendons with and without tendinopathy

PurposeUltrasound shear wave elastography (SWE) is a tool that can be utilized to assess biomechanical properties of tendons. Anisotropy, an ultrasound imaging artifact has been commonly cited as a potential source of error in the accuracy and reproducibility of SWE. The aim of the study was to assess reproducibility in performing SWE of patella tendons and differences in SWE and anisotropy between normal patella tendons and patellar tendinopathy. MethodsAfter obtaining the Institutional Review Board approval and written informed consent, we prospectively measured the shear wave velocity (SWV) of patella tendons with and without tendinopathy in 25 volunteers. SWVs were measured in three anatomic planes: longitudinal, perpendicular transverse, and tilted transverse with the probe tilted 15–30° from the perpendicular transverse plane by three operators with varied levels of experience. Anisotropy coefficient (A) was calculated by formula of A = (SWVLongitudinal − SWVTransverse) / SWVTransverse. ResultsDifferences in SWV and anisotropy coefficient between normal tendons and tendons with tendinopathy were significant (p < 0.05). The intra- and inter-observer reproducibility in performing SWE were moderate to good (intraclass correlation coefficient: 0.81–0.95). The mean difference of 95% Bland-Altman limits of agreement for measuring tendon SWV ranged −0.08 to 0.41 (upper 0.08 to 1.14, lower −1.22 to −0.22) between senior and junior operators. ConclusionThe results of this study suggest that SWE and anisotropy coefficient are feasible tools to differentiate patellar tendinopathy from normal patella tendons. The reproducibility of performing SWE of patella tendons is moderate to good.

Anisotropy induced in magnetic field in GNPs/epoxy composites used as an effective heat dissipation electronic packaging material

AbstractThis article investigates the effect of different magnetic fields on modulating the alignment of graphene nanoplatelets (GNPs) and their impact on the thermal conductivity of epoxy nanocomposites. Various nanocomposite specimens were fabricated with different GNP contents by using magnetically field‐aligned GNPs in the fabrication process to enhance the thermal conductivity. The results showed that the in‐plane thermal conductivity of the Bmf (Bidirectional magnetic field) sample with 5 wt% GNPs added reached 0.75 W m−1 K−1, which is 276.6% higher than that of pure epoxy resin and the anisotropy coefficient (K∥/K⊥) reached 3.3. In addition, temperature rise tests were performed to simulate the thermal conductivity of nanocomposites used as an electronic packaging material, and the results indicated that the composites achieved a significant increase in in‐plane thermal conductivity with a lower amount of filler. This provides valuable insights into the preparation of thermally conductive composites and demonstrates their potential as a thermal management packaging material for next‐generation electronic devices.

ELECTROMAGNETIC MONITORING DURING THE AFTERSHOCK PERIOD OF THE 2003 CHUYA EARTHQUAKE IN THE MOUNTAIN (GORNY) ALTAI: MEASUREMENT METHODOLOGY, RESULTS

The article considers the method of observations, interpretation of data and results of electromagnetic monitoring with a controlled source for one of the seismically active regions of Siberia – Mountain (Gorny) Altai. The monitoring is carried out during the aftershock period in the epicentral zone of the destructive Chuya earthquake of 2003 with M=7.3. For regular observations, a measurement technique has been developed with several modifications of the transient electromagnetics method (TEM) to determine variations in electrical resistivity and anisotropy coefficient. The long-term series of these two geoelectric parameters of the section are presented, compared with the characteristics of the ongoing seismic events. The analysis shows that variations in electrical resistance and electrical anisotropy reflect the development and gradual attenuation of aftershock activity of a powerful earthquake. The advantages of the TEM method and the chosen methodology for monitoring in complex areas are reflected.

Anisotropy in Additively Manufactured Concrete Specimens under Compressive Loading-Quantification of the Effects of Layer Height and Fiber Reinforcement.

This paper analyzes the effect of print layer heights and loading direction on the compressive response of plain and fiber-reinforced (steel or basalt fiber) 3D printed concrete. Slabs with three different layer heights (6, 13, and 20 mm) are printed, and extracted cubes are subjected to compression (i) along the direction of printing, (ii) along the direction of layer build-up, and (iii) perpendicular to the above two directions. Digital image correlation (DIC) is used as a non-contact means to acquire the strain profiles. While the 3D printed specimens show lower strengths, as compared to cast specimens, when tested in all three directions, this effect can be reduced through the use of fiber reinforcement. Peak stress and peak strain-based anisotropy coefficients, which are linearly related, are used to characterize and quantify the directional dependence of peak stress and strain. Interface-parallel cracking is found to be the major failure mechanism, and anisotropy coefficients increase with an increase in layer height, which is attributable to the increasing significance of interfacial defects. Thus, orienting the weaker interfaces appropriately, through changes in printing direction, or strengthening them through material modifications (such as fiber reinforcement) or process changes (lower layer height, enables attainment of near-isotropy in 3D printed concrete elements.

Experimental and calculation investigations of hydrodynamics and heat exchange in liquid metal turbulent flows in fast reactor fuel assemblies

The formation of velocity and temperature fields in the fuel assemblies of fast reactor core occurs under the influence various factors. It is shown, that the most important factors include a complex multiply connected geometry, subject to deformation during the campaign under the influence of temperature non-uniformity and radiation effects. The results of studies of the velocity fields and shear stress, turbulence microstructure are presented. An intensification of turbulent momentum transfer in channels in azimuthal and radial directions in the area of gaps between the rods is demonstrated. The performed analysis is indicate that there are a significant difference between the experimental dependences for turbulent momentum transfer coefficients in the radial and azimuthal directions and calculated within the framework of semi-empirical models of turbulent momentum transfer as well as the anisotropy coefficients of the turbulent momentum transfer in rod bundles. The results of benchmark on the fuel assembly thermohydraulics showed that the common commercial codes describe experimental data only approximately. It is shown, that the intensification of turbulent momentum transfer in the channels of rod bundles is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the turbulent momentum transfer coefficients in the channels of rod bundles is calculated. The dependence for coefficient of inter-channel turbulent exchange of momentum is obtained and the intensification of inter-channel turbulent exchange in close-packed rod lattices is explained. A dependence for the dissimilarity coefficients of forced inter-channel convective exchange of momentum and mass, as well as energy and mass in rod bundles spaced by wire winding is obtained. The calculation methods and the numerical modeling results for temperature regime of fuel assemblies with randomly distributed initial parameters by the Monte Carlo method are presented as well as the thermomechanical analysis of the temperature field in the fuel assemblies during the campaign. An idea about the equilibrium configuration of a rod bundle in a hexagonal jacket during irradiation, the stress–strain state of an individual fuel rod and a fuel assembly jacket is obtained. The tasks of further investigations discussed.

An approximate method for calculating anisotropy parameters and reflectivity of shales with horizontal fractures

Abstract Shale is a typical medium of transverse isotropy with a vertical axis of symmetry (VTI), and its strong anisotropy is mainly due to the combined effect of intrinsic anisotropy and that induced by horizontal fractures. To calculate the anisotropy parameters of shale, a physical rock model is built based on Hudson's thin-coin fracture model and Schoenberg's linear-sliding model, and an approximate theoretical calculation method for Thomsen's anisotropy parameters of VTI media with horizontal fractures is proposed. These calculation results using the proposed method confirm that this anisotropy contributed to by horizontal fractures cannot be ignored to the overall anisotropy of shale. To simplify Rüger's formula that is an approximate theoretical formula for calculating the anisotropic reflection coefficients of VTI media, a new four-term approximate formula is derived in a standard reflectivity form based on Rüger's and Aki–Richards’ formulas. The simulation results of a VTI theoretical model and logging data of shale reservoirs show that there is only a small difference between the newly derived four-term formula and Rüger's formula for incidence angles &amp;lt;40°, and the new four-term formula can correctly reveal the seismic amplitude-versus-offset (AVO) characteristics of VTI media and fully retain the corresponding anisotropic seismic responses. Compared to Rüger's formula, the proposed new formula only has four terms of unknown parameters and can directly decouple Thomsen's anisotropy parameter ε from them, which helps to alleviate the ill-posed problems of simultaneous inversion of multiple parameters and enhance its application potential in seismic inversion of VTI media as shale.

Selection and justification of drilling and blasting parameters using genetic algorithms

Purpose. Using experimental and theoretical studies to justify the rational location of charges of various types and their technological parameters in the fan, taking into account the physical and mechanical properties and structural features of the rocks in the mountain massif. Methodology. In the experiments, an improved method of geostructural analysis of rocks was used to obtain detailed data on their properties, the block structure of the massif, and the type and direction of development of crack systems. Identification of crack systems, their density, intensity, and direction of development of crack systems is carried out on petrographic sections using microscopic analysis, these are used to calculate the average indicator of the cracking coefficient, while the funneling method – the anisotropy coefficient. The justification of the rational location and the number of charges in each fan was performed using the methods of genetic algorithms and the developed software product. Findings. The coefficient of cracking and anisotropy of physical and mechanical properties of uranium ores was calculated, which was 78 cr/sm2 and 1.4, respectively. According to the developed mathematical models and the software product, the optimization problem was solved using genetic algorithms, which determined the main priorities: the location of the charge in the fan according to the structure of the massif and the rational diameter of the well, which helps to limit the number of oversized blocks of reflected ore. Originality. The regularities are established of the change in the anisotropy coefficient from the cracking coefficient, the nature of the distribution and the number of microcracks (cr/sm2) in the quartz grains, which is present in uranium ore according to a linear law, and the output (in %) of oversized blocks during the destruction of uranium ore from the cracking coefficient – according to the polynomial law. For the first time, the optimal location and the number of charges in each fan, the diameter of the wells, taking into account the type of rock, its strength and fissure, and the geometric parameters of the ore deposit, were determined based on the constructed mathematical models and the developed software product. Practical value. The indicated results of the experimental and theoretical studies will form the basis for the development and substantiation of rational parameters of resource-saving and seismically safe methods for breaking strong rocks of complex structure during the extraction of uranium and iron ores by the energy of the explosion in mines.

High‐resolution stimulated Raman spectroscopy of low‐frequency rotational transitions: Obtention of collisional broadening coefficients in the rotational S branch of CO perturbed by H2

AbstractWe demonstrate the application of high‐resolution quasi‐continuous (q‐cw) stimulated Raman spectroscopy (SRS) to the study of low‐frequency, pure rotational transitions of molecules in diluted samples in order to obtain collisional information. The main problems encountered in the few pioneering q‐cw SRS rotational works, namely weak signals because of the small population differences between the upper and lower states of the transitions and the presence of alternating current (AC) Stark effect, have been addressed: technical improvements in the optical elements that perform the beam mixing, separation, and filtering have allowed us to use a collinear beam geometry and a triple pass configuration to enhance the Raman signals. The distortions in the line profiles caused by AC Stark effect have been measured and included in the numerical treatment of the spectra. With these extended capabilities, we have been able to register stimulated Raman transitions with wavenumbers as low as ∼ 11.5 cm−1, corresponding to the S(0) pure rotational transition of the molecule of CO. We have applied the setup to the study of collisional broadening of CO rotational lines perturbed by H2 and have obtained broadening coefficients for lines from S(0) to S(20) at 77, 180, and 298 K. A comparison between these anisotropic coefficients and those obtained from IR rovibrational experiments shows excellent agreement. This is, to our knowledge, the first demonstration of the use of rotational SRS for the obtention of collisional information in diluted gas samples.

Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level.

The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.

Diffusion tensor imaging of fetal spinal cord: feasibility and gestational-age-related changes.

Diffusion tensor imaging (DTI) of the fetal brain is a relatively new technique that allows evaluation of white matter tracts of the central nervous system throughout pregnancy, as well as in certain pathological conditions. The objectives of this study were to evaluate the feasibility of DTI of the spinal cord in utero and to examine gestational-age (GA)-related changes in DTI parameters during pregnancy. This was a prospective study conducted between December 2021 and June 2022 in the LUMIERE Platform, Necker-Enfants Malades Hospital, Paris, France, as part of the LUMIERE SUR LE FETUS trial. Women with a pregnancy between 18 and 36 weeks of gestation without fetal or maternal abnormality were eligible for inclusion. Sagittal diffusion-weighted scans of the fetal spine were acquired, without sedation, using a 1.5-Tesla magnetic resonance imaging scanner. Theimaging parameters were as follows: 15 non-collinear direction diffusion-weighted magnetic-pulsed gradients with a b-value 700 s/mm2 and one B0 image without diffusion-weighting; slice thickness, 3 mm; field of view (FOV), 36 mm; phase FOV, 1.00; voxel size, 4.5 × 2.8 × 3 mm3 ; number of slices, 7-10; repetition time, 2800 ms; echo time, minimum; and total acquisition time, 2.3 min. DTI parameters, including fractional anisotropy (FA) and apparent diffusion coefficient (ADC), were extracted at the cervical, upper thoracic, lower thoracic and lumbar levels of the spinal cord. Cases with motion degradation and those with aberrant reconstruction of the spinal cord on tractography were excluded. Pearson's correlation analysis was performed to evaluate GA-related changes of DTI parameters during pregnancy. During the study period, 42 pregnant women were included at a median GA of 29.3 (range, 22.0-35.7) weeks. Five (11.9%) patients were not included in the analysis because of fetal movement. Two (4.8%) patients with aberrant tractography reconstruction were also excluded from analysis. Acquisition of DTI parameters was feasible in all remaining cases (35/35). Increasing GA correlated with increasing FA averaged over the entire fetal spinal cord (r, 0.37; P < 0.01), as well as at the individual cervical (r, 0.519; P < 0.01), upper thoracic (r, 0.468; P < 0.01), lower thoracic (r, 0.425; P = 0.02) and lumbar (r, 0.427; P = 0.02) levels. There was no correlation between GA and ADC averaged over the entire spinal cord (r, 0.01; P = 0.99) or at the individual cervical (r, -0.109; P = 0.56), upper thoracic (r, -0.226; P = 0.22), lower thoracic (r, -0.052; P = 0.78) or lumbar (r, -0.11; P = 0.95) levels. This study shows that DTI of the spinal cord is feasible in normal fetuses in typical clinical practice and allows extraction of DTI parameters of the spinal cord. There is a significant GA-related change in FA in the fetal spinal cord during pregnancy, which may result from decreasing water content as observed during myelination of fiber tracts occurring in utero. This study may serve as a basis for further investigation of DTI in the fetus, including research into its potential in pathological conditions that impact spinal cord development. © 2023 International Society of Ultrasound in Obstetrics and Gynecology.

Технологические режимы раздачи и обжима при локальном нагреве

The processes of spread and reduction of a heated rough piece under visco-plasticity conditions are viewed. The ratio for force stress calculating in operations, damage to the material of the rough pieces is obtained. In the branches of special en-gineering, high-strength alloys based on titanium and aluminum are used. In the branches of special engineering, high-strength alloys based on titanium and aluminum are used. These alloys have mechanical properties anisotropy. Processing of these alloys is difficult. For this reason, the pressure treatment operation is performed with heating of the deformation zone. The material in the deformation zone exhibits viscous properties. Deformation hardening and softening (stress relaxa-tion) of the material take place simultaneously. Besides, the lower the deformation rate, the greater the softening. In this regard, a constitutive equation representing these processes is found. The factor of hardening and softening creates condi-tions for reducing the power mode of pressure treatment operations and increasing the degree of primary part forming. Stress relaxation calculation with the help of analytical dependencies is necessary at the stage of expansion and pressing development. The calculated ratios are recorded as a function of the speed of these operations. In this case, the specified deformation (the change in the degree of forming) is taken into account, adjusted depending on the speed and mechanical characteristics of the bearing alloy anisotropy. The calculated ratios are obtained under conditions of a flat voltage scheme, which corresponds to expansion and pressing. Stress equilibrium equation and yield condition of anisotropic material are used. The joint solutions of this equation and yield conditions determine values of the meridional and circumferential stress-es arising in the piece part material. The values of the stresses allow calculating the forces of operations. It is shown that the speed of expansion and pressing and mechanical properties anisotropy affect the damage to the material of the «green body». Dependences for the calculation of damage are obtained on the basis of energy and deformation strength criteria. These dependencies allow predicting the quality of products. It is also shown that anisotropy affects the technological modes of expansion and pressing. As the anisotropy coefficient increases, the stresses and forces of operations decrease. Calculations of stresses, forces and material damage in the process of expansion of anisotropic titanium alloy VT14 at 875 ℃ are made.

Multi-scale soot formation simulation providing detailed particle morphology in a laminar coflow diffusion flame

The macroscopic simulation of soot production in flames by CFD approaches often assumes of spherical particles or considers ad-hoc formulas in order to take the particle fractal aggregates’ morphology into account. On the other hand, numerically simulated aggregates can be generated by Discrete Element Modeling (DEM) simulations at the nanoscopic scale. However, the change in thermodynamic conditions, surface growth, oxidation, and nucleation mechanisms are commonly neglected by this approach. This work combines these complementary approaches to investigate the detailed morphology of soot along 4 different particle trajectories in a diffusion flame. The proposed multi-scale approach shows remarkably larger and more compact aggregates near the wings of the flame as compared to the centerline, in agreement with previous experimental studies. This approach allows to analyse the particle polydispersity and morphological parameters beyond the fractal dimension, such as anisotropy coefficient and monomers overlapping coefficient. It becomes possible to reveal clear morphological signatures of soot formed along different streamlines in the flame. Finally, we have also observed a positive correlation between primary particle diameter and aggregate gyration diameter due to the predominance of surface reactions over aggregation. The proposed post-processing of CFD results based on DEM methods, bringing new information on soot morphology, is a proof of concept of a more accurate procedure for validating soot models used in CFD codes as compared to existing methods in the literature.

Anisotropy origins of coefficient of friction and scratch hardness in nano scratching monocrystalline copper

The monocrystalline Cu material mechanical properties at the micro and nano scale show complex anisotropy and size effects. However, the anisotropy of scratch hardness and coefficient of friction (COF) in micro-nano scratching monocrystalline Cu has not been well explained. In this paper, we conducted the nano-scratching experiments and corresponding molecular dynamics (MD) simulation under ramp normal force mode along two representative crystal orientations thereby investigating the anisotropy origins of scratch hardness and COF. The research results indicate that, for monocrystalline Cu materials, the scratch hardness and COF are closely related to the atomic slip resistance Fslip caused by the activated <1 1 0> {1 1 1} slip systems.

Seismic Stability Analysis of Tunnel Faces in Heterogeneous and Anisotropic Soils Using Modified Pseudodynamic Method

This work assesses the seismic stability of tunnel faces advanced in heterogeneous and anisotropic soils based on the plastic limit theorem. A discretized kinematic velocity field respecting the normal flow rule is generated via a point-to-point discretization technique. The distribution of soil parameters in the depth direction including cohesion, friction angle, and unit weight are considered by four kinds of profiles. The variation in cohesion with shear direction caused by consolidation and sedimentation is considered by including an anisotropy coefficient. The seismic acceleration is represented by the modified pseudodynamic method (MPD) rather than the conventional pseudodynamic method (CPD). Based on the energy equilibrium equation, an upper-bound solution is derived. The accuracy and rationality of the proposed procedure are substantiated by comparing with the solutions obtained by conventional log-spiral mechanism and CPD. A parametric study indicates that nonlinear profiles tend to predict a smaller required face pressure than the constant and linear profiles due to the convexity of nonlinear profiles. The over-consolidated soil is more sensitive to the anisotropy coefficient than normally consolidated soil. Moreover, the adverse effect of horizontal seismic acceleration is much greater than that of vertical acceleration, and the resonance effect is more prone to happen, especially for shallow-buried tunnels.

Systematic Investigations of the Structural, Elastic, and Thermal Properties of c‐BAs by First‐Principles Calculations

The structure, elastic properties, and thermodynamic properties of cubic boron arsenide (c‐BAs) under high temperature and high pressure are studied based on first‐principles calculations. The obtained equilibrium structure and mechanical properties are in good agreement with other theoretical results. First, the phonon dispersion spectra at zero pressure and high pressure are calculated. The results show that c‐BAs is dynamically stable under pressure of 0–110 GPa. Second, the lattice constants, elastic constants, Young's modulus, bulk modulus, shear modulus, Poisson's ratio, B/G, sound velocity, and Debye temperature of c‐BAs under zero pressure and high pressure are calculated. c‐BAs are predicted to be unstable above 112.3 GPa in accordance with the elastic stability criterion. Furthermore, it is indicated by the calculated B/G ratio that c‐BAs is brittle at zero GPa and begins to tend to be ductile as pressure rises to 46.4 GPa. The calculated elastic anisotropy coefficients indicate that c‐BAs has elastic anisotropy. The thermodynamic properties of c‐BAs are investigated at high temperatures and pressures by combining generalized density function theory and the quasiharmonic Debye model. It is suggested by the calculated elastic and thermodynamic properties that c‐BAs can be used as candidate structures for the fabrication of efficient solar cells and thermoelectric materials.

Fitting the charged-optimized many-body potential for the Al-O-Se-Zn system

A charge-optimized many-body (COMB3) potential has been developed for the Al-O-Se-Zn system using first-principles data. This work updates COMB3 for zinc and extends it to include selenium as well as other pairwise and three-body interactions that were not developed previously. We tested the empirical potential for known crystalline phases and find reasonable agreement between the calculated structural, elastic, and vibrational properties and experimental data. We use the anisotropic coefficients of the thermal expansion method to calculate the temperature-dependent properties of a few selected materials. We then compare the total energy of the system and its first- and second-order positional derivatives, as well as the second-order strain derivative with respect to the atomic potential energy surface to thermal properties obtained from molecular dynamics simulations using the fitted COMB3 potential. The results of our temperature-dependent calculations show reasonable agreement with previous work for temperatures below the system’s melting point. With this fitting, we could utilize a versatile, charge-dependent empirical potential to model the interface between ZnSe and Al2O3 by molecular dynamics simulations.

Investigating the dynamic influence of passive effects on undulatory locomotion in viscous environment and unleashing the potential of hybrid friction

This study encompasses the passive interdependence of body material (internal damping, stiffness, and geometry) and environmental (frictional anisotropy and frictional coefficients) properties on the performance and adaptability of undulatory locomotion. Undulatory locomotion is modeled in viscous and hybrid environments. The body’s ability to adapt passively results in different locomotion gaits, such as swimming and crawling. Results show that, in swimming gaits, body stiffness dominates frictional forces, whereas in crawling gaits, frictional forces dominate body stiffness. Our result showed that the interdependence between endogenous and exogenous dynamics can be utilized to achieve the desired speed. The hybrid frictional environment is modeled as the combination of dry and viscous frictions and recognized as a valuable asset in the modeling of undulatory locomotion in granular media. In the hybrid environment the respective ratios of dry and viscous frictions play an essential role in the speed optimization. The optimal combination of dry and viscous frictions can be found depending on the characteristics of the body and environment. We validate the viscous based frictional model using the properties of the body of Caenorhabditis Elegans from the state of the art, in a viscous environment. The results can be employed to design robotic solutions to perform optimally in different environments and with customized body properties.

Application of Magnetic Resonance Diffusion Tensor Imaging in Diagnosis of Lumbosacral Nerve Root Compression

The aim of this study was to assess the value of 3.0T magnetic resonance (MR) Diffusion tensor imaging (DTI) in the diagnosis of lumbosacral nerve root compression. The radiology reports, and clinical records of 34 patients with nerve root compression caused by lumbar disc herniation or bulging and 21 healthy volunteers who had undergone magnetic resonance imaging (MRI) and DTI scan were retrospectively reviewed. The differences in fractional anisotropy (FA) and apparent diffusion coefficient (ADC) between compressed and non-compressed nerve roots from patients and the normal nerve roots from healthy volunteers were compared. Meanwhile, the nerve root fiber bundles were observed and analyzed. The average FA and ADC values of the compressed nerve roots were 0.254 ± 0.307 and 1.892 ± 0.346 10^-3mm2/s, respectively. The average FA and ADC values of the non-compressed nerve roots were 0.377 ± 0.659 and 1.353 ± 0.344 10^-3mm2/s, respectively. The FA value of compressed nerve roots was significantly lower than that of non-compressed nerve roots (P < 0.01). The ADC value of compressed nerve roots was significantly higher than that of non-compressed nerve roots. There were no significant differences between the left and right nerve roots of normal volunteers in FA and ADC values (P > 0.05). The nerve roots at different levels of L3-S1 had significantly different FA and ADC values (P < 0.01). Incomplete fiber bundles with extrusion deformation, displacement or partial defect were observed in the compressed nerve root fiber bundles. The real diagnosis of the clinical situation of the nerve can provide neuroscientists with an important computer tool to help them infer and understand the possible working mechanism from the experimental data of behavior and electrophysiology. The compressed lumbosacral nerve roots can be accurately localized through 3.0T magnetic resonance DTI, which is instructive for accurate clinical diagnosis and preoperative localization.

A nonlinear scheme preserving maximum principle for heterogeneous anisotropic diffusion equation

We present a new nonlinear method in order to preserve the maximum principle for the diffusion problem with heterogeneous anisotropic coefficient. It is well-known that for diffusion problems with general discontinuous coefficients, the existing cell-centered finite volume schemes on general meshes cannot unconditionally satisfy the discrete maximum principle (DMP), i.e., there are always certain severe restrictions on the mesh-cell geometry or locations of discontinuity in order to preserve DMP. To deal with the issue we propose a nonlinear method of modifying discrete flux of linear second-order schemes into a new conservative flux. Then the resulting scheme keeps conservation and accuracy, and has the structure preserving maximum principle without imposing those severe restrictions. Specifically, we will start with the diamond scheme whose flux is linear and has second-order accuracy, but has no the structure preserving maximum principle. Then the nonlinear correction method is applied to get a scheme satisfying the discrete maximum principle unconditionally. We give some theoretical analysis including the coercivity property and a prior estimation. Numerical results show that the accuracy of our new scheme is superior to the existing scheme preserving maximum principle, and in some cases the accuracy can even be improved by one order of magnitude.

Impacts of anisotropy coefficient and porosity on the thermal conductivity and P-wave velocity of calcarenites used as building materials of historical monuments in Morocco

Impacts of anisotropy coefficient and porosity on the thermal conductivity and P-wave velocity of calcarenites used as building materials of historical monuments in Morocco