Discontinuous Research Articles

Embedded delta shocks

In 1977 Korchinski presented a new type of shock discontinuity in conservation laws. These singular solutions were coined δ-shocks since there is a time dependent Dirac delta involved. A naive description is that such δ-shock is of the overcompressive type: a single shock wave belonging to both families, the four characteristic lines of which impinge into the shock itself. In this work, we open the fan of solutions by studying two-family waves without intermediate constant states but possessing central rarefactions or comprising δ-shocks.

AB1041 BIOLOGICS IN ADULT’S ONSET STILL’S DISEASE: TREATMENT STRATEGIES AND SAFETY IN SINGLE CENTER COHORT WITH LONG-TERM FOLLOW-UP

Background:Adult-onset Still’s disease (AOSD) is a rare systemic inflammatory disorder. In recent years biological disease modifying antirheumatic drugs (bDMARDs) are becoming increasingly important for its treatment.Objectives:To evaluate disease outcomes, treatment strategies and their long-term safety in a cohort of AOSD patients treated with bDMARDs.Methods:A single-center retrospective study of patients diagnosed with AOSD until 2019 was conducted. Patients were included if they: a) were 16 years old or older, b) met the Yamaguchi criteria and c) had received a bDMARDDemographics, clinical and laboratory parameters were collected at the time of diagnosis.Data regarding treatment lines included: the previous and concomitant conventional disease modifying antirheumatic drugs (cDMARDs), the type of initial bDMARD, switches, survival and corticosteroids discontinuation. Adverse events related to treatment and disease outcomes including death and amyloidosis were also recorded.Results:Sixteen patients with AOSD (Table 1) refractory to cDMARDs were administered biologics. The median duration of follow-up was 14 years (range 1-24). Consistent with recent literature1, two distinct disease patterns were recognized: the systemic form (SF) and the chronic articular form (CAF). In the SF the leading clinical symptoms were fever, pericarditis and pleuritis. In CAF the leading clinical symptom was persistent RA-like arthritis.Table 1.Some clinical and laboratory features of patients with FMF or MEFV mutations accompanied by demyelination diseaseCasesAge/SexDiseasesMEFV mutationsThe onset age/diagnostic age for FMFThe onset age for DD/MS/Presenting manifestations/MRI findingsTreatment for FMF /DD/MSCase 1(F1)17/FFMF+DDM694V homozygous3/515OB (-)Fusiform plaques in the cingulate gyrus; plaques in T4-6ColchicineIL-1 RAGlatiramer acetateCase 2(F1)46/FFMF+MSM694V homozygous8/928Optic nerve involvementOB(+)Plaques (+)ColchicineGlatiramer acetateCase 3(F1)17/FFMF+MSM694V heterozygous3/515Loss of the right eye, vertigoOB(+)PlaquesColchicinePulse steroidBeta-interferonTeriflunomideCase 4(F2)36/FMS+MEFV mutationM694V/R202Q-27Headache, blurred vision, optic nerve atrophyOB(+)Plaques (+)Glatiramer acetateCase 5(F2)16/FMS?+FMF+Cutaneous vasculitisM694V/R202Q16/1611Headache, blurred visionNo LP (denied by pt)Plaques-F: Female, F1: Family 1, F2: Family 2; DD: Demyelination disease;MS: Multiple sclerosis;MRI: Magnetic resonance imaging; OB:Oligoclonal band; LP: Lumbar punctionTable 1.Summary of patient characteristics at the time of diagnosisCharacteristicsResultsAge at the time of diagnosis median, (range) years32.5 (18-64)Sex (N)11 female, 5 maleFever14 (87.5%)Rash8 (50%)Lymphadenopathy2 (12.5%)Arthritis15 (93.75%)Pleuritis7 (43.7%)Pericarditis9 (56.25%)Hepatosplenomegaly2 (12.5%)Elevated liver enzymes2 (12.5%)Hyperferritinaemia4 (25%)Patients with the SF were treated with anakinra (n=4), tocilizumab (TCZ; n=3), canakinumab (n=1) and anti-TNFa (1 adalimumab, 1 etanercept) (n=2). Patients with the CAF received anti-TNFa (3 infliximab, 1 etanercept) (n=4) and TCZ (n=2). The median time from biologic initiation to corticosteroids discontinuation was 6.5 months, (range 2-32), (Table 2). 9 patients (56.25%) remained on treatment with the initial bDMARD, 4 patients (25%) received treatment with two and 3 patients (18.75%) with ≥ 3 bDMARDs. All patients with the CAF were on bDMARD at the end of follow-up, while 4/10 patients (40%) with the SF discontinued it. During follow-up only one serious adverse event was attributed to bDMARD (allergic reaction to infliximab infusion). There were no cases of amyloidosis or deathsConclusion:Dichotomous phenotype in AOSD can determine treatment strategy for initial biologic treatment. Inhibition of IL-1 and IL-6 was the preferred therapeutic option for systemic form while inhibition of TNF and IL-6 was the preferred option for the chronic articular form. All of the above bDMARDs have favorable long-term safety profile in patients with AOSD.

Continuous and discontinuous nominal expressions in flexible (or “free”) word order languages: Patterns and correlates

AbstractThis study explores continuous and discontinuous word order patterns of multi-word nominal expressions in flexible word order languages (traditionally referred to as “free word order” or “non-configurational” languages). Besides describing syntagmatic patterns, this paper seeks to identify any functional or other correlates that can be associated with different word orders. The languages under investigation are a number of Australian languages as well as Vedic Sanskrit, all of which have long been known for their syntagmatic flexibility. With respect to continuous order, evidence from several of these languages suggests that default ordering is primarily governed by functional templates. Deviations from default order, while maintaining continuity, can be attributed to different types of “focus” interpretations or heaviness effects. With respect to discontinuous order, I identify three sub-types. The most widespread one, “Left-Edge Discontinuity”, involves one element placed in or near utterance-initial position. It shows a clear, if not an absolute, correlation with different kinds of focus interpretations, similarly to deviations from the default order in continuity. The other two types of discontinuity are linked to the behaviour of specific function words. Besides teasing out cross-linguistic similarities, this paper also sheds light on language-specific characteristics that affect the forms and functions of complex (i.e. multi-word) nominal expressions in flexible word order languages, such as the nature of 2nd position (“Wackernagel”) elements.

Asymptotically Stable Stationary Solutions of the Reaction–Diffusion–Advection Equation with Discontinuous Reaction and Advection Terms

We study the Lyapunov asymptotic stability of the stationary solution of the spatially one-dimensional initial–boundary value problem for a nonlinear singularly perturbed differential equation of the reaction–diffusion–advection (RDA) type in the case where the advection and reaction terms undergo a discontinuity of the first kind at some interior point of an interval. Sufficient conditions are derived for the existence of a stable stationary solution with a large gradient near the point of discontinuity. An asymptotic method of differential inequalities is used to prove the existence and stability theorems. The resulting stability conditions can be employed to create mathematical models and develop numerical methods for solving “stiff” problems arising in various applications, for example, when simulating combustion processes and in nonlinear wave theory.

Stability and asymptotic properties of a linearized hydrodynamic medium model for dispersive media in nanophotonics

We analyze the stability of a linearized hydrodynamical model describing the response of nanometric dispersive metallic materials illuminated by optical light waves that is the situation occurring in nanoplasmonics. This model corresponds to the coupling between the Maxwell system and a PDE describing the evolution of the polarization current of the electrons in the metal. We show the well posedness of the system, polynomial stability and optimal energy decay rate. We also investigate the numerical stability for a discontinuous Galerkin type approximation and several explicit time integration schemes.

Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener–Hopf method does yield an exact solution of the discrete scattering problem, using which, as the main result of the paper, the transmission coefficients for energy flux are obtained. It is assumed that a wave mode is incident from either side of the step and the question addressed is what fraction of incident energy is transmitted across the atomic step discontinuity. A total of ten configurations are presented that arise due to various placements of discrete Dirichlet and Neumann boundary conditions on the waveguide. Numerical illustrations of a measure of ‘conductance’ are provided.

Application of matrix bandwidth reduction technique in implicit discontinuous Galerkin

Application of matrix bandwidth reduction technique in implicit discontinuous Galerkin

Characterizing Sliding Surfaces of Cyber-Physical Systems

When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution function of the closed-loop system is not anymore piecewise continuous along the trajectory, mainly due to if statements inside the control algorithm. As a consequence, an unwanted chattering effect may occur. This behavior is often difficult to observe even in simulation. We propose here a set-membership method based on interval analysis to detect different types of discontinuities. One of them is the sliding surface where the state trajectory jumps indefinitely between two distinct behaviors. As an application, we consider the validation of a sailboat controller. We show that our approach is able to detect and explain some unwanted sliding effects that may be observed in rare and specific situations on our actual sailboat robots.

Fully hydromechanical coupled hydraulic fracture simulation considering state transition of natural fracture

The natural fracture in the reservoir presents different properties in the inactivated and the activated state. To model the hydromechanical behaviors of the natural fractures in the two states, the element partition method(EPM) is employed. The EPM is a fracture simulation method, which allows a crack run across an element without introducing any extra degrees of freedom. For the element containing an inactivated fracture segment, it is treated as a potential partitioned element, but its permeability is related to the normal stress to the embedded fracture. A Mohr-Coulomb type of activation criterion is developed for the inactivated fracture. Once the fracture is activated, this potential element is transformed into a partitioned element. The constitutive relation with consideration of shear dilation and the fully hydromechanical coupled equation of a partitioned element are derived. Based on this method, the activation process of a fracture and its propagation are simulated. The simulation results suggest that the present method can capture the full hydromechanical properties of a natural fracture from its inactivated to activated state. Besides the natural fracture, the randomized cavities are another type of discontinuities in some reservoir. The effect of the cavity on hydraulic fracture(HF) is also considered. It is suggested that the cavity strongly repels the HF due to the surrounding stress concentration, but whether the HF can connect with the cavity depends. If there are some cracks adjunct to the cavity, the HF may connect with the cavity through these adjunct cracks. The simulation results suggest that the present method is a simple and efficient simulation method for the HF in the complex reservoir. It can comprehensively consider the behaviors of the natural fracture and cavity.

Seabed Mapping Using Shipboard Multibeam Acoustic Data for Assessing the Spatial Distribution of Ferromanganese Crusts on Seamounts in the Western Pacific

Cobalt-rich ferromanganese crusts (Fe–Mn crusts), potential economic resources for cobalt, nickel, platinum, and other rare metals, are distributed on the surface of seamounts, ridges, and plateaus. Distribution of Fe–Mn crust deposits and their geomorphological characteristics are prerequisites to selecting possible mining sites and to predicting the environmental impact of deep-sea mining activity. Here, we map the spatial distribution of Fe–Mn crust deposits on seamount summits and flanks in the Western Pacific using shipboard multibeam echo sounder (MBES) data and seafloor images from a deep-towed camera system (DCS) and evaluate the relationship between acoustic backscatter variations and the occurrence of Fe–Mn crusts. We find a positive correlation between high backscatter intensity, steep seabed slope gradients, and the occurrence of Fe–Mn crusts. However, our analysis was not effective to distinguish the spatial boundary between several seabed types that occur over small areas in mixed seabed zones, particularly where transition zones and discontinuous seabed types are present. Thus, we conclude that MBES data can be a valuable tool for constraining spatial distribution of Fe–Mn crust deposits over a large exploration area.

Research and application of PLA fibres

This work is focused on characterization of spinning process of PLA fibres. PLA polymer with high melting point was modified by two hydrolytic additives in amounts (0 and 1 wt. %). Fully drawn (FDY) PLA fibres were prepared by melt spinning technique in the company Chemosvit Fibrochem a. s. (Svit, Slovakia). Preparation of PLA fibres was done by two different processes of continuous and discontinuous type. Different drawing ratios, take-up speeds and spin finishes for optimal fibre properties were used. Physical and mechanical properties of prepared FDY fibres, such as elongation and tenacity were measured. Prepared PLA fibres with different hydrolytic additives were process able in manufacturing process and this material could be used for various textile and composite applications.

Enhancement of microCT images of steel cracks using mathematical filters

MicroCT has become a powerful and widely used tool for non-destructive testing and can be used for mapping the complex 3D structures of cracks and their interactions. The materials of most oil and gas transport pipes, buried or submerged, such as high strength low alloy steels, for example, are likely to suffer corrosion degradation and fracture due to the corrosive environment. Similarly, cracks are one of the most severe types of discontinuity in a welded joint since they are strong stress concentrators. High tensile stresses develop in the weld region as a result of the localized thermal expansion and contraction, associated with the welding thermal cycle. To better characterize the cracking behavior, it is important to gain information about the evolution of the 3D crack network. However, the search for improving image quality in the inspection of steel samples using X-ray beams is still challenging because of spreading effects that can cause noise in the 3D image. For this purpose, we performed microCT tests to verify cracks due corrosion and loss of weld adhesion cracks applying mathematical filters to improve the final image quality. To enhance details of the grey scale microCT slices, the image was improved using anisotropic diffusion (AD) and unsharp mask (UM) filters, which have been found to be highly effective for enhancement of digital fractured media. With the results was possible to verify cracks around 0.66 mm for corrosion cracks and 4.27 mm for cracks due to loss of weld adhesion, as well as the cracks network in the 3D visualization of the inspected materials.

Controlling the pinning time of a receding contact line under forced wetting conditions

HypothesisThe contact line pinning that appears in a flow coating process over substrates patterned with chemical or physical heterogeneities has been recently applied to deposit micro- and nanoparticles with great precision. However, the mechanism underlying pinning of a receding contact line at the nanoscale is not yet well understood. In the case of a contact line pinned at a chemical heterogeneity, we hypothesise that it is possible to establish a relation between the pinning time, the contact line velocity and the liquid/plate/heterogeneity affinity that can help to optimize particle deposition. MethodsWe use large-scale molecular dynamic (MD) simulations of a finite liquid bridge formed between two parallel, non–identical, smooth solid plates. The top plate slides relative to the bottom plate inducing a displacement of the four different contact lines of the liquid bridge. The introduction of a chemical heterogeneity on the bottom plate by modifying locally the liquid–solid affinity provokes the transient pinning of the contact line in contact with the bottom substrate. By means of this simple MD simulation, we can study the mechanism of contact line pinning and its relation with the liquid/heterogeneity affinity and the contact line velocity. Additionally, we compare this mechanism with the case of the receding contact line pinned on a physical heterogeneity (a simple step discontinuity). FindingsWe propose an analytical model that predicts the values of the dynamic contact angles in the general case of a capillary liquid bridge confined between two parallel plates with different wettabilities versus the relative velocity of the top plate. These predictions are successfully validated by the results of the large–scale MD simulations. The model allows thus to predict the value of the dynamic contact angles for the different contact lines of the system versus the relative speed of the moving plate. Once the chemical heterogeneity is introduced in the bottom plate, we show that when the receding contact line reaches the patch it remains temporarily pinned while the receding contact angle evolves with time. Once the receding angle reaches the value of the equilibrium contact angle of the patch, the receding contact line overcomes pinning. A geometrical model able to predict the pinning time is proposed and validated by our MD simulations. The pinning time depends not only on the relative plate velocity and plate wettability properties but also on the separation distance between the plates confining the capillary bridge. The model can consequently be used to select the substrate wettability or meniscus geometry suitable to impose the pinning time required for specific applications.

The 2^k Neighborhoods for Grid Path Planning

Grid path planning is an important problem in AI. Its understanding has been key for the development of autonomous navigation systems. An interesting and rather surprising fact about the vast literature on this problem is that only a few neighborhoods have been used when evaluating these algorithms. Indeed, only the 4- and 8-neighborhoods are usually considered, and rarely the 16-neighborhood. This paper describes three contributions that enable the construction of effective grid path planners for extended 2k-neighborhoods; that is, neighborhoods that admit 2k neighbors per state, where k is a parameter. First, we provide a simple recursive definition of the 2k-neighborhood in terms of the 2k-1-neighborhood. Second, we derive distance functions, for any k ≥ 2, which allow us to propose admissible heuristics that are perfect for obstacle-free grids, which generalize the well-known Manhattan and Octile distances. Third, we define the notion of canonical path for the 2k-neighborhood; this allows us to incorporate our neighborhoods into two versions of A*, namely Canonical A* and Jump Point Search (JPS), whose performance, we show, scales well when increasing k. Our empirical evaluation shows that, when increasing k, the cost of the solution found improves substantially. Used with the 2k-neighborhood, Canonical A* and JPS, in many configurations, are also superior to the any-angle path planner Theta* both in terms of solution quality and runtime. Our planner is competitive with one implementation of the any-angle path planner, ANYA in some configurations. Our main practical conclusion is that standard, well-understood grid path planning technology may provide an effective approach to any-angle grid path planning.

A 3-D hydraulic fracture propagation model applied for shale gas reservoirs with multiple bedding planes

Rock layering, a critical factor in determining fracture height growth, is pervasive in Longmaxi shale formation in the southwest of China. This formation has characteristics of large burial depth, low porosity and multiple bedding layers that hamper reaching the target fracture height even after increasing the pumping rate and treatment size. Hence, it becomes much significant to develop a fracture propagation model considering the effect of bedding layers on fracture height growth. This paper introduces a coupled 3-D hydraulic fracture propagation model and investigates the influence of shear displacement discontinuities along bedding planes on fracture height growth. Our model addresses rock deformation and fluid flow. Rock deformation is governed by a fully three-dimensional displacement discontinuity method (3D DDM). The fluid flow model employs a finite difference method (FDM) being able to capture fluid movement along vertical fractures and bedding planes. Additionally, a propagation criteria determines whether the fracture would penetrate bedding planes. In this paper, we selected two different fracture geometries and analyzed profiles of fracture width, pressure and two types of shear displacement discontinuities. From numerical investigations, we found that the maximum width can be obtained at the junction after the vertical fracture penetrated the bedding planes as a result of the decrement of the compressive stress acting on the bedding planes. As the fracture penetrates the bedding planes, a certain amount of fluid would leak into the planes, which leads to fracture height containment. Moreover, the slope utilized for characterizing the correlation between leak-off volume and fracture height, is regarded as a tool to identify the number of BPs that fracture penetrates through. This paper illustrates the potential application of our 3-D fracture propagation model for Longmaxi shale formation with multiple bedding layers. Shear displacements along bedding planes are regarded as a primary mechanism of fracture height containment.

Problematizando as Práticas de Criminalização dos Movimentos Sociais: uma Análise Documental

Este trabalho teve como objetivo fazer um levantamento, revisão e análise da literatura acerca do tema “Criminalização dos Movimentos Sociais”. Foram utilizadas para a análise dissertações coletadas no ano de 2013 encontradas sobre esse tema no banco de dados da Biblioteca Digital Brasileira de Teses e Dissertações (BDTD). Para a análise das dissertações foram utilizadas as pistas deixadas pelo trabalho realizado por Michel Foucault através de suas ferramentas arqueológicas e genealógicas de análise que nos forneceu a possibilidade de uma crítica e uma problematização das práticas discursivas (saber) e não discursivas (poder e subjetivação) que atravessam e compõem os trabalhos analisados, guiado pela visão de uma história descontínua que deflagra acontecimentos em sua singularidade. Verificamos que as séries recortadas das dissertações trazem à mídia, a justiça, a polícia e o governo como principais elementos de uma prática de criminalização dos movimentos sociais, sem esquecer-se de apontar as resistências promovidas por esses grupos contra esse processo.

Comparative transcriptome analysis of olfactory epithelium in large yellow croaker: Evidence for olfactory adaptation to feed phagostimulant in fish

To investigate the olfactory adaptation to feed phagostimulant in fish, we utilized three types of phagostimulants. Dimethyl-beta-propiothetin hydrochloride (Dmpt), taurine (Tau) and l-tryptophan (Trp) mixed with feed for the diets of large yellow croaker (Larimichthy crocea) for 7 days. The fish displayed a significant behavioral preference for 0.50% Dmpt, so we mixed feed with 0.50% Dmpt, 3.50% Tau and 1.63% Trp, and the fish showed a downtrend of mean percentage of ingested feed (MPIF) in Dmpt and Trp group of 7 days, but showed an up- and a downtrend of MPIF in Tau group of 7 days. Then, we sequenced olfactory epithelium tissues of Day 7 to detected the differentially expressed genes (DEGs), and found 37 (6 up- and 31 down-regulated) olfactory receptor related DEGs in Dmpt group, 22 (18 up- and 4 down-regulated) in Tau group and 16 (15 up- and 1 down-regulated) olfactory receptor related DEGs in Trp group; we analyzed the expression level of significantly changing genes of these DEGs in 7 days by RT-qPCR, and we found that the expression of genes showed a downtrend in 7 days of Dmpt and Trp group but an up- and a downtrend in 7 days of Tau group. According to the behavioral adaptation process and adaptive expression trend of olfactory related receptor DEGs, we sequenced the transcriptome of olfactory epithelium in Tau group of Day 1 and Day 5, and analyzed the olfactory transduction pathway. Based on the expression level of DEGs, especially OR, ACIII, CAMKII, CNG and CNGA3 in this pathway, we speculated the positive olfactory effect of Tau and the higher concentration of Ca2+ entering into olfactory sensory cell in Day 5, which suggested that the fish had been medium adaptation stage in Day 5 and later adaptation stage in Day 7. Using this data, we initially prove the olfactory adaptation to feed phagostimulant (phased and discontinuous types of olfactory stimulants) in fish, and provide new insights into utilization of phagostimulant in aquaculture.

A novel reliability analysis method based on Gaussian process classification for structures with discontinuous response

Reliability analysis techniques combining with various surrogate models have attracted increasing attention because of their accuracy and great efficiency. However, they primarily focus on the structures with continuous response, while very rare researches on the reliability analysis for structures with discontinuous response are carried out. Furthermore, existing adaptive reliability analysis methods based on importance sampling (IS) still have some intractable defects when dealing with small failure probability, and there is no related research on reliability analysis for structures involving discontinuous response and small failure probability. Therefore, this paper proposes a novel reliability analysis method called AGPC-IS for such structures, which combines adaptive Gaussian process classification (GPC) and adaptive-kernel-density-estimation-based IS. In AGPC-IS, an efficient adaptive strategy for design of experiments (DoE), taking into consideration the classification uncertainty, the sampling uniformity and the regional classification accuracy improvement, is developed with the purpose of improving the accuracy of Gaussian process classifier. The adaptive kernel density estimation is introduced for constructing the quasi-optimal density function of IS. In addition, a novel and more precise stopping criterion is also developed from the perspective of the stability of failure probability estimation.The efficiency, superiority and practicability of AGPC-IS are verified by three examples

НАБЛИЖЕННЯ РОЗРИВНОЇ ФУНКЦІЇ ДВОХ ЗМІННИХ РОЗРИВНИМИ ІНТЕРЛІНАЦІЙНИМИ СПЛАЙНАМИ З ВИКОРИСТАННЯМ ТРИКУТНИХ ЕЛЕМЕНТІВ

Робота присвячена розробці методу наближення розривних функцій за допомогою оператора інтерлінації функцій двох змінних. Ці оператори відновлюють функції (можливо, наближено) за відомими їх слідами на заданій системі ліній. Саме такі експериментальні дані використовуються в дистанційних методах, зокрема в комп’ютерній томографії. Тобто вони надають можливість будувати оператори, інтеграли від яких по вказаних лініях (лінійні інтеграли) будуть дорівнювати інтегралам від самої відновлюваної функції. Отже, інтерлінація – математичний апарат, природно пов’язаний із задачею відновлення характеристик об’єктів за їх відомими проекціями. Існує багато практично важливих наукових та технічних галузей, в яких об’єкти дослідження математично описуються величинами, що зазнають розрив. Такі об’єкти часто виникають також і в задачах, які використовують дистанційні методи. На сьогоднішній день не існує загальної теорії описів явищ та процесів, що описуються розривними функціями. В статті будуються та досліджуються оператори розривної інтерлінації для наближення розривних функцій двох змінних за відомими її слідами (проекціями) на системі ліній з використанням довільних трикутних елементів. На основі створених сплайн-інтерлінантів будується метод наближення функцій, які мають розриви першого роду та область визначення яких розбивається на трикутні елементи. Причому побудовані розривні конструкції включають в себе, як окремий випадок, класичні неперервні інтерлінаційні сплани. В якості експериментальних даних виступають односторонні сліди функції на системі заданих ліній, саме такі дані використовуються в томографії. В роботі наведені теореми про інтерлінаційні властивості та похибку побудованих розривних конструкцій. Побудований метод наближення дозволяє наблизити розривну функцію, уникаючи явища Гіббса. Розглянуто приклади, які підтверджують ефективність запропонованого методу. Запропонований метод наближення розривних функцій можна буде використати для математичного моделювання розривних процесів в медичних, геологічних, космічних та інших дослідженнях.

Preliminary numerical study on long-wavelength wave propagation in a jointed rock mass

Non-destructive exploration using elastic waves has been widely used to characterize rock mass properties. Wave propagation in jointed rock masses is significantly governed by the characteristics and orientation of discontinuities. The relationship between spatial heterogeneity (i.e., joint spacing) and wavelength for elastic waves propagating through jointed rock masses have been investigated previously. Discontinuous rock masses can be considered as an equivalent continuum material when the wavelength of the propagating elastic wave exceeds the spatial heterogeneity. However, it is unclear how stress-dependent long-wavelength elastic waves propagate through a repetitive rock-joint system with multiple joints. A preliminary numerical simulation was performed in in this study to investigate long-wavelength elastic wave propagation in regularly jointed rock masses using the three-dimensional distinct element code program. First, experimental studies using the quasi-static resonant column (QSRC) testing device are performed on regularly jointed disc column specimens for three different materials (acetal, aluminum, and gneiss). The P- and S-wave velocities of the specimens are obtained under various normal stress levels. The normal and shear joint stiffness are calculated from the experimental results using an equivalent continuum model and used as input parameters for numerical analysis. The spatial and temporal sizes are carefully selected to guarantee a stable numerical simulation. Based on the calibrated jointed rock model, the numerical and experimental results are compared.