Transverse mode-coupling instability with longitudinal impedance

Transverse mode-coupling instability(TMCI)is a dangerous transverse single-bunch instability that can lead to severe par-ticle loss.The mechanism of TMCI can be explained by the coupling of transverse coherent oscillation modes owing to the transverse short-range wakefield(i.e.,the transverse broadband impedance).Recent studies on future circular colliders,e.g.,FCC-ee,showed that the threshold of TMCI decreased significantly when both longitudinal and transverse impedances were included.We performed computations for the circular electron-positron collider(CEPC)and observed a similar phenom-enon.Systematic studies on the influence of longitudinal impedance on the TMCI threshold were conducted.We concluded that the imaginary part of the longitudinal impedance,which caused a reduction in the incoherent synchrotron tune,was the primary reason for the reduction in the TMCI threshold.Additionally,the real part of the longitudinal impedance assists in increasing the TMCI threshold.

Transverse momentum balance of dijets in Xe+Xe collisions at the LHC

We present a theoretical study of the medium modifications of the p_(T)balance (x_(J)) of dijets in Xe+Xe collisions at■.The initial production of dijets was carried out using the POWHEG+PYTHIA8 prescription,which matches the next-toleading-order (NLO) QCD matrix elements with the parton shower (PS) effect.The SHELL model described the in-medium evolution of nucleus–nucleus collisions using a transport approach.The theoretical results of the dijet xJin the Xe+Xe collisions exhibit more imbalanced distributions than those in the p+p collisions,consistent with recently reported ATLAS data.By utilizing the Interleaved Flavor Neutralisation,an infrared-and-collinear-safe jet flavor algorithm,to identify the flavor of the reconstructed jets,we classify dijets processes into three categories:gluon–gluon (gg),quark–gluon (qg),and quark–quark (qq),and investigated the respective medium modification patterns and fraction changes of the gg,qg,and qq components of the dijet sample in Xe+Xe collisions.It is shown that the increased fraction of qg component at a small x_(J)contributes to the imbalance of the dijet;in particular,the q_(1)g_(2)(quark-jet-leading) dijets experience more significant asymmetric energy loss than the g_(1)q_(2)(gluon-jet-leading) dijets traversing the QGP.By comparing the■of inclusive,■ dijets in Xe+Xe collisions,we observe■.Moreover,ρ_(Xe),P_(b),the ratios of the nuclear modification factors of dijets in Xe+Xe to those in Pb+Pb,were calculated,which indicates that the yield suppression of dijets in Pb+Pb is more pronounced than that in Xe+Xe owing to the larger radius of the lead nucleus.

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.

Suppression of stimulated Brillouin and Raman scatterings using an alternating frequency laser and transverse magnetic fields

A novel scheme to suppress both stimulated Brillouin scattering(SBS) and stimulated Raman scattering(SRS) by combining an alternating frequency(AF) laser and a transverse magnetic field is proposed. The AF laser allows the laser frequency to change discretely and alternately over time. The suppression of SBS is significant as long as the AF difference is greater than the linear growth rate of SBS or the alternating time of the laser frequency is shorter than the linear growth time of SBS. However, the AF laser proves ineffective in suppressing SRS, which usually has a much higher linear growth rate than SBS. To remedy that, a transverse magnetic field is included to suppress the SRS instability. The electrons trapped in the electron plasma waves(EPWs) of SRS can be accelerated by the surfatron mechanism in a transverse magnetic field and eventually detrapped. While continuously extracting energy from EPWs, the EPWs are dissipated and the kinetic inflation of SRS is suppressed. The one-dimensional particle-in-cell simulation results show that both SBS and SRS can be effectively suppressed by combining the AF laser with a transverse magnetic field with tens of Tesla. The total reflectivity can be dramatically reduced by more than one order of magnitude. These results provide a potential reference for controlling SBS and SRS under the related parameters of inertial confinement fusion.

Longitudinally extensive transverse myelitis associated with scrub typhus:A case report

Rationale:Longitudinally extensive transverse myelitis(LETM)is a rare inflammatory demyelinating disease predominantly associated with autoimmune and inflammatory disorders.Scrub typhus can cause a variety of neurological complications,which may result in poor recovery and long-term disability.This report reveals a rare linkage between LETM and scrub typhus.Patient concerns:A 24-year-old female presented with a history of fever for 10 days associated with progressive quadriparesis.Physical examination revealed bilateral lower limb weakness(grade 0/5)and bilateral upper limb weakness(grade 2/5)with reduced sensation below the T3 dermatome.Diagnosis:Scrub typhus presenting with longitudinally extensive transverse myelitis.Interventions:Steroid pulse therapy with antibiotics supported by early intensive rehabilitation.Outcomes:Complete recovery was achieved.Lessons:This case report highlights the importance of considering scrub typhus as a potential cause of LETM in endemic regions,particularly in patients presenting with febrile illness and neurological symptoms.

The Effect of Transverse Tibial Bone Transfer in the Treatment of Diabetic Foot

To analyse the effectiveness of performing a transverse tibial bone graft in the treatment of patients with diabetic foot. We retrospectively analysed the clinical details of 51 diabetic foot patients in our hospital from February 2023 to February 2024 and divided them into two groups according to the different treatment modalities, in which the control group received open debridement and the treatment group received transverse tibial bone transfer and compared the differences between the two groups. There were large differences in VAS score, Toronto Clinical Symptom Score, quality of life score, internal lumen diameter, blood flow velocity in the affected limb, perfusion volume, vascular endothelial growth factor, epidermal growth factor and CRP between the two groups after surgery (P < 0.05). Patients with diabetic foot should be treated with transverse tibial bone grafting, which is safer and more effective and can have a significant impact on improving the status of the affected limb, the inflammation and the patient’s quality of life.

Impact of tibial transverse transport in tissue regeneration and wound healing with perspective on diabetic foot ulcers

In this editorial,we comment on an article by Liao et al published in the current issue of the World Journal of Diabetes.We focus on the clinical significance of tibial transverse transport(TTT)as an effective treatment for patients with diabetic foot ulcers(DFU).TTT has been associated with tissue regeneration,improved blood circulation,reduced amputation rates,and increased expression of early angiogenic factors.Mechanistically,TTT can influence macrophage polarization and growth factor upregulation.Despite this potential,the limitations and conflicting results of existing studies justify the need for further research into its optimal application and development.These clinical implications highlight the efficacy of TTT in recalcitrant DFU and provide lasting stimuli for tissue re-generation,and blood vessel and bone marrow improvement.Immunomodu-lation via systemic responses contributes to its therapeutic potential.Future studies should investigate the underlying molecular mechanisms to enhance our understanding and the efficacy of TTT.This manuscript emphasizes the potential of TTT in limb preservation and diabetic wound healing and suggests avenues for preventive measures against limb amputation in diabetes and peripheral artery disease.Here,we highlight the clinical significance of the TTT and its importance in healing DFU to promote the use of this technique in tissue regeneration.

Determining beam transverse absolute position by triangulation of multi-electrode signal phase differences

Accurate measurement of the transverse position of a beam is crucial in particle accelerators because it plays a key role in determining the beam parameters.Existing methods for beam-position measurement rely on the detection of image currents induced on electrodes or narrow-band wake field induced by a beam passing through a cavity-type structure.However,these methods have limitations.The indirect measurement of multiple parameters is computationally complex,requiring external calibration to determine the system parameters in advance.Furthermore,the utilization of the beam signal information is incomplete.Hence,this study proposes a novel method for measuring the absolute electron beam transverse position.By utilizing the geometric relationship between the center position of the measured electron beam and multiple detection electrodes and by analyzing the differences in the arrival times of the beam signals detected by these electrodes,the absolute transverse position of the electron beam crossing the electrode plane can be calculated.This method features absolute position measurement,a position sensitivity coefficient independent of vacuum chamber apertures,and no requirement for a symmetrical detector electrode layout.The feasibility of this method is validated through numerical simulations and beam experiments.

Early postoperative complications after transverse colostomy closure,a retrospective study

BACKGROUND Ostomy is a common surgery usually performed to protect patients from clinical symptoms caused by distal anastomotic leakage after colorectal cancer(CRC)surgery and perforation or to relieve intestinal obstruction.AIM To analyze the complications after transverse colostomy closure.METHODS Patients who underwent transverse colostomy closure from Jan 2015 to Jan 2022 were retrospectively enrolled in a single clinical center.The differences between the complication group and the no complication group were compared.Logistic regression analyses were conducted to find independent factors for overall complications or incision infection.RESULTS A total of 102 patients who underwent transverse colostomy closure were enrolled in the current study.Seventy(68.6%)patients underwent transverse colostomy because of CRC related causes.Postoperative complications occurred in 30(29.4%)patients and the most frequent complication occurring after transverse colostomy closure was incision infection(46.7%).The complication group had longer hospital stays(P<0.01).However,no potential risk factors were identified for overall complications and incision infection.CONCLUSION The most frequent complication occurring after transverse colostomy closure surgery in our center was incision infection.The operation time,interval from transverse colostomy to reversal,and method of anastomosis might have no impact on the postoperative complications.Surgeons should pay more attention to aseptic techniques.

Midpoint transverse process to pleura block for postoperative analgesia following laparoscopic renal cyst decortication:Two case reports

BACKGROUND The midpoint transverse process to pleura(MTP)block,a novel technique for thoracic paravertebral block(TPVB),was first employed in laparoscopic renal cyst decortication.CASE SUMMARY Thoracic paravertebral nerve block is frequently employed for perioperative analgesia during laparoscopic cyst decortication.To address safety concerns associated with TPVBs,we administered MTP blocks in two patients prior to administering general anesthesia for laparoscopic cyst decortication.The MTP block was performed at the T9 level under ultrasound guidance,with 20 mL of 0.5%ropivacaine injected.Reduced sensation to cold and pinprick was observed from the T8 to T11 dermatome levels.Immediately postoperative Numeric Pain Rating Scale scores were 0/10 at rest and on movement,with none exceeding a mean 24 h numeric rating scale>3.CONCLUSION MTP block was effective technique for providing postoperative analgesia for patients undergoing laparoscopic renal cyst decortication.

Acute Transverse Myelitis in Pregnancy—A Case Report and a Literature Review

Purpose: This case report highlights a rare instance of a 26-week pregnant woman presenting with limb numbness, diagnosed with acute transverse myelitis (ATM) following COVID-19 vaccination. Notably, she tested positive for neuromyelitis optica (NMO) but did not exhibit the typical symptoms of blurred vision. Methods: Data were collected from I Seha in governmental hospitals in Bahrain, providing a comprehensive overview of the patient’s clinical journey. Results: The patient was treated with carbamazepine, steroids, and clexane, leading to the successful delivery of a healthy baby at 34 weeks. However, two years postpartum, she reported new episodes of blurred vision and numbness. Subsequent treatment with Rituximab resulted in significant improvement, with a diagnosis of Devic’s disease established. Conclusion: Acute transverse myelitis is a rare condition, particularly during pregnancy, and in this case, symptoms of Devic’s disease were masked by the absence of blurred vision. This condition predominantly affects females in their 20s during childbearing years and can lead to complications such as premature delivery. Effective management includes steroids and antiepileptic drugs, with clexane playing a crucial role in preventing embolisms. A delivery mode may vary based on obstetric factors, and MRI remains the gold standard for diagnosis. Close follow-up is essential for optimal patient outcomes.

Winding Function Model-based Performance Evaluation of a PM Transverse Flux Generator for Applications in Direct-drive Systems

The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.

Laminated Solid Timber Slab with Transverse Prestressing Using the Strategy of Interleaved Vertical Displacement of Lamellae

This article presents a study on the structural behavior of transversely prestressed laminated timber slabs,focusing on an innovative approach:vertically misaligned lamellae.This misalignment,achieved by sliding vertically the wooden lamellae rather than aligning them,enhances the slab’s cross-section moment of inertia,thereby improving load-bearing capacity and stiffness.Testing involved two groups of structural size specimens:one with vertically aligned lamellae(control group)and the other with misaligned lamellae(study group).Results showed the study group exhibited 42%superior stiffness and 10%less load capacity compared to the control.Failures typically occurred individually in the lamellae,particularly in those with defects or lower modulus of elasticity,concentrated in the middle third of the slabs’free span where tensile stresses peak.Despite a higher number of failed lamellae,the study group demonstrated promising performance.Analysis of prestressing bar indicated no damage at all in the thread,suggesting potential for reducing bar diameter.These findings offer crucial insights into applying these slabs in timber construction as well as to any kind of construction.

Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

Evaluation of the Clinical Advantages of Laparoscopic Transverse Abdominal Wall Suspension in the Treatment of Pelvic Organ Prolapse

Objective:To evaluate the clinical advantages of laparoscopic transverse abdominal wall suspension in treating pelvic organ prolapse.Methods:Sixty patients diagnosed with moderate to severe pelvic organ prolapse and underwent surgical treatment in our hospital between January 2022 and December 2023 were selected.According to different surgical methods,they were divided into an observation group(given laparoscopic transverse abdominal wall suspension)and a control group(given transvaginal mesh implantation),with 30 subjects/group.The data on perioperative-related indicators,quality of life scores,postoperative recurrence,and complications of the two groups of patients were collected.Results:The postoperative hospitalization days and intraoperative bleeding volume of the observation group were significantly lower than those of the control group,but had longer operation time than that of the control group(P<0.05).The differences between the two groups were statistically significant 6 months after surgery,and the Pelvic Floor Disease Quality of Life Impact Questionnaire(PFIQ-7)score of the observation group was significantly higher than the control group(P<0.05).Both groups of patients completed 12 months of follow-up without any postoperative recurrence.The number of complications in the observation group was slightly lower than that of the control group(P>0.05).Conclusion:Laparoscopic transverse abdominal wall suspension was more effective in treating pelvic organ prolapse and is an ideal surgical procedure.

Safety Length Simulation of Natural Gas Pipeline Subjected to Transverse Landslide

The safety of natural gas pipeline is often severely threatened by the transverse landslide. At home and abroad, it is the first time to study the safe length of the pipeline when affected by landslide, and take the safe length of the pipeline as an engineering practical index. Therefore, it is of great significance to study the influence of transverse landslide affecting the safety of natural gas pipeline when a certain length of pipeline is thrusted, and to establish practical index and simulation method for prediction and prevention of the landslide hazards to gas pipeline. Based on the current research results, this study could be divided into three steps: First of all, with the help of ANSYS finite element software, the model of transverse landslide acting on the gas pipeline can be set up, then the length value of gas pipeline safely withstanding transverse landslide can be calculated;Secondly, using the strength reduction method, which is commonly used in the research of landslide stability, can establish three-dimensional model of the landslide and pipes in the ABAQUS finite element software, next, under the same landslide pushed length, the calculation results will be obtained;Finally, to draw reliable conclusions, all calculated results of the former two methods will be linked to synthetically and comparatively analyze, then the length value of common X80 gas pipeline safely bearing transverse landslide can be got. All results can provide some references for engineering and design.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Early hemodynamics after tibial transverse transport in patients with nonarterial stenosis and arterial stenosis diabetic foot

BACKGROUND The diagnosis of peripheral arteriopathy in the diabetic foot is complicated by diabetes and its advanced complications.It has been found that diabetic foot can be categorized into arterial stenosis and non-arterial stenosis,both of which have significant differences in hemodynamic characteristics.AIM To evaluate the early hemodynamic changes in diabetic foot patients with nonarterial stenosis and arterial stenosis treated by tibial transverse transport(TTT)using high-frequency color Doppler ultrasonography(HFCDU)and a laser Doppler flowmeter.METHODS Twenty-five patients with Wagner grades 3-5 diabetic foot ulcers were treated with TTT,and the wound healing time and rate were recorded.Patients were grouped according to the results of preoperative lower-extremity ultrasonography.Cases with≥50%stenosis in any of the femoral,popliteal,posterior tibial,anterior tibial,and peroneal arteries of the affected limb were classified as the arterial stenosis group(n=16);otherwise,they were classified as the nonarterial stenosis group(n=9).Before and one month after surgery,HFCDU was used to evaluate the degree of lower limb artery lesions and hemodynamic changes in patients.The degree of femoral-popliteal atherosclerotic stenosis,the degree of vascular stenosis and occlusion of the lower-knee outflow tract,and the degree of medial arterial calcification were scored;the three scores were added together to obtain the total score of lower extremity arteriopathy.PeriScanPIM3,a laser Doppler flowmeter system,was used to detect alterations in plantar microcirculation before and 1 mo after surgery.Wound healing and hemodynamic indices were compared between the two groups.RESULTS The wound healing time of the diabetic foot was significantly shorter in the nonarterial stenosis group than in the arterial stenosis group(47.8±13 vs 85.8±26,P<0.05),and the wound healing rate of both groups was 100%.The preoperative total lower extremity arteriopathy scores were lower in the nonarterial stenosis group than those in the arterial stenosis group(18.89±8.87 vs 24.63±3.52,P<0.05).The nonarterial stenosis group showed higher preoperative popliteal artery(POA)blood flow than the arterial stenosis group(204.89±80.76 cc/min vs 76.75±48.49 cc/min,P<0.05).Compared with the baseline(before surgery),the postoperative POA blood flow of the affected limb in the nonarterial stenosis group decreased one month after surgery(134.11±47.84 cc/min vs 204.89±80.76 cc/min,P<0.05),while that in the arterial stenosis group increased(98.44±30.73 cc/min vs 61.69±21.70 cc/min,P<0.05).Although the POA blood flow in the arterial stenosis group was obviously improved one month after surgery,it was still lower than that in the nonarterial stenosis group(98.44±30.73 cc/min vs 134.11±47.84 cc/min,P<0.05).The nonarterial stenosis group had higher preoperative plantar microcirculation than the arterial stenosis group(56.1±9.2 vs 33.2±7.5,P<0.05);compared with the baseline,the plantar microcirculation in the arterial stenosis group was significantly improved one month after surgery(51.9±7.2,P<0.05),while that in the nonarterial stenosis group was reduced(35.9±7.2,P<0.05).CONCLUSION Based on preoperative HFCDU findings,diabetic foot patients can be divided into two categories:Those with nonarterial stenosis and those with arterial stenosis,with obvious differences in hemodynamic changes in the early postoperative period between them.In the early stage after TTT,the blood flow volume and velocity and the plantar microcirculation perfusion of the affected limb of the diabetic foot with nonarterial stenosis decreased compared with the baseline,while those of the diabetic foot with arterial stenosis improved significantly compared with the baseline,although both had smoothly healed diabetic foot ulcers.

Solving elastic wave equations in 2D transversely isotropic media by a weighted Runge-Kutta discontinuous Galerkin method

Accurate wave propagation simulation in anisotropic media is important for forward modeling, migration and inversion. In this study, the weighted Runge-Kutta discontinuous Galerkin (RKDG) method is extended to solve the elastic wave equations in 2D transversely isotropic media. The spatial discretization is based on the numerical flux discontinuous Galerkin scheme. An explicit weighted two-step iterative Runge-Kutta method is used as time-stepping algorithm. The weighted RKDG method has good flexibility and applicability of dealing with undulating geometries and boundary conditions. To verify the correctness and effectiveness of this method, several numerical examples are presented for elastic wave propagations in vertical transversely isotropic and tilted transversely isotropic media. The results show that the weighted RKDG method is promising for solving wave propagation problems in complex anisotropic medium.

Poroelastodynamic responses and elastic moduli of a transversely isotropic porous cylinder under forced deformation test

Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.