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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 250
Author(s):  
Nyurgun P. Lazarev ◽  
Victor A. Kovtunenko

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shuxue Zhao ◽  
Xianfa Lu ◽  
Jiasen Zou ◽  
Zhouying Xu ◽  
Siyu Wei ◽  
...  

Objective. To investigate the influence of cold weather on setup errors of patients with chest and pelvic disease in radiotherapy. Methods. The image-guided data of the patients were collected from the Radiotherapy Center of Cancer Hospital Affiliated to Guangxi Medical University from October 2020 to February 2021. During this period, the cold weather days were December 15, 16, and 17, 2020, and January 7 and 8, 2021. For body fixation in radiotherapy, an integrated plate and a thermoplastic mold were employed in 18 patients with chest disease, while an integrated plate and a vacuum pad were applied in 19 patients with pelvic disease. All patients underwent cone beam computed tomography (CBCT) scans in the first five treatments and once a week thereafter. The obtained data were registered to the planning CT image to get the setup errors of the patient in the translational direction including X, Y, and Z axes and rotational direction including RX, RY, and RZ. Then, the Mann–Whitney U test was performed. The expansion boundary values of the chest and pelvis were calculated according to the formula M PTV = 2.5 ∑ + 0.7 δ . Results. A total of 286 eligible results of CBCT scans were collected. There were 138 chest CBCT scans, including 26 taken in cold weather and 112 in usual weather, and 148 pelvic CBCT scans, including 33 taken in cold weather and 115 in usual weather. The X-, Y-, and Z-axis translational setup errors of patients with chest disease in the cold weather group were 0.16 (0.06, 0.32) cm, 0.25 (0.17, 0.52) cm, and 0.35 (0.21, 0.47) cm, respectively, and those in the usual weather group were 0.14 (0.08, 0.29) cm, 0.23 (0.13, 0.37) cm, and 0.18 (0.1, 0.35) cm, respectively. The results indicated that there was a statistical difference in the Z-axis translational error between the cold weather group and the usual weather group (U = 935.5; p = 0.005 < 0.05 ), while there was no statistical difference in the rotational error between the two groups. The external boundary values of X, Y, and Z axes in the cold weather group were 0.57 cm, 0.92 cm, and 0.99 cm, respectively, and those in the usual weather group were 0.57 cm, 0.78 cm, and 0.68 cm, respectively. There was no significant difference in the translational and rotational errors of patients with pelvic disease between the cold weather group and the usual weather group ( p < 0.05 ). The external boundary values of X, Y, and Z axes were 0.63 cm, 0.79 cm, and 0.68 cm in the cold weather group and 0.61 cm, 0.79 cm, and 0.61 cm in the usual weather group, respectively. Conclusion. The setup error of patients undergoing radiotherapy with their bodies fixed by an integrated plate and a thermoplastic mold was greater in cold weather than in usual weather, especially in the ventrodorsal direction.


2021 ◽  
Vol 1 ◽  
pp. 175-177
Author(s):  
René Kahnt ◽  
Heinz Konietzky ◽  
Thomas Nagel ◽  
Olaf Kolditz ◽  
Andreas Jockel ◽  
...  

Abstract. Within the framework of the “Gesetz zur Suche und Auswahl eines Standortes für ein Endlager für hochradioaktive Abfälle” (Repository Site Selection Act – StandAG), the geoscientific and planning requirements and criteria for the site selection for a repository for high-active nuclear waste are specified. This includes, among others, the modelling of hydrogeological scenarios such as how future cold and warm periods and associated glaciation events can change the (petro-)physical properties specified in the StandAG as well as the natural hydrogeological properties of the overall system through, for example, reactivation of faults or changes in hydraulic gradients and consequently flow directions. The main objective of the AREHS (Effects of Changing Boundary Conditions on the Development of Hydrogeological Systems) project, funded by BASE (Federal Office for the Safety of Nuclear Waste Management; FKZ 4719F10402), is to model the effects of changing external boundary conditions on the hydrogeologically relevant parameters and effects (e.g. hydraulic permeability, porosity, migration pathways, fluid availability, hydraulic gradients) of a generic geological repository in Germany in all three potential host rocks (clay, salt and crystalline rocks) and its surrounding hydrogeological setting (Table 1). Special attention is paid to the cyclic mechanical loading and unloading due to glaciation events and the resulting stress changes (M), as well as induced temperature effects (T) due to permafrost and warm periods. As such processes can cause changes in the coupled far-field regime with groundwater flow and groundwater supply (H), as well as fluid transport due to thermal (T) and chemical (C) gradients, and reactivate faults/fractures (M) and thus create new/additional pathways, they are particularly relevant to the integrity of a repository over a period of 1 million years and must be properly captured with coupled THM(C) modelling. Before a model is set up for the different host rocks, a detailed assessment of relevant processes has been conducted based on NEA-2019 FEP catalogue (NEA, 2019) for high-level waste repositories. The modelling is performed using generic 3D models of typical host rock formations satisfying the StandAG criteria. Although the models for salt and clay rock have been adapted from generic models from recent research projects, for crystalline rock a new generic model had to be developed (Fig. 1) considering discontinuities of different scales that have to be incorporated into the THM(C) models explicitly as DFN (Discrete Fracture Network) networks. This is done by coupling two numerical codes: DFN-lab and 3DEC. A central phase in the overall modelling process is the benchmarking of the models with data from existing models and with field-scale studies. This is done separately for all three host rocks. In addition to extending the modelling capacities for glaciation processes and verifying by corresponding benchmarking tests (analytical solutions and literature comparisons), automated workflows have been developed to generate OpenGeoSys models from GOCAD structure models. Script-based automated workflows improve software quality for site investigation, especially in a sense of modularization as well as reproducibility. The generic workflow concept is currently being tested for the literature-based benchmarks and will, therefore, support a persistent and sustainable benchmarking procedure in the future.


2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Yuanjun Qi ◽  
Jianbin Li ◽  
Yingjie Zhang ◽  
Qian Shao ◽  
Xijun Liu ◽  
...  

Abstract Background This study aimed to investigate the effect of abdominal compression on tumour motion and target volume and to determine suitable planning target volume (PTV) margins for patients treated with lung stereotactic body radiotherapy (SBRT) based on four-dimensional computed tomography (4DCT). Methods Twenty-three patients diagnosed to have a peripheral pulmonary tumour were selected and divided into an all lesions group (group A), an upper middle lobe lesions group (group B), and a lower lobe lesions group (group C). Two 4DCT scans were performed in each patient, one with and one without abdominal compression. Cone beam computed tomography (CBCT) was performed before starting treatment. The gross target volumes (GTVs) were delineated and internal gross target volumes (IGTVs) were defined. IGTVs were generated using two methods: (1) the maximum intensity projections (MIPs) based on the 4DCT were reconstructed to form a single volume and defined as the IGTVMIP and (2) GTVs from all 10 phases were combined to form a single volume and defined as the IGTV10. A 5-mm, 4-mm, and 3-mm margin was added in all directions on the IGTVMIP and the volume was constructed as PTVMIP5mm, PTVMIP4mm, and PTVMIP3mm. Results There was no significant difference in the amplitude of tumour motion in the left–right, anterior–posterior, or superior-inferior direction according to whether or not abdominal compression was applied (group A, p = 0.43, 0.27, and 0.29, respectively; group B, p = 0.46, 0.15, and 0.45; group C, p = 0.79, 0.86, and 0.37; Wilcoxon test). However, the median IGTVMIP without abdominal compression was 33.67% higher than that with compression (p = 0.00), and the median IGTV10 without compression was 16.08% higher than that with compression (p = 0.00). The median proportion of the degree of inclusion of the IGTVCBCT in PTVMIP5mm, PTVMIP4mm, and PTVMIP3mm ≥ 95% was 100%, 100%, and 83.33%, respectively. Conclusions Abdominal compression was useful for reducing the size of the IGTVMIP and IGTV10 and for decreasing the PTV margins based on 4DCT. In IGTVMIP with abdominal compression, adding a 4-mm margin to account for respiration is feasible in SBRT based on 4DCT.


Author(s):  
Natela Zirakashvili

In Systems Theory, the Mathematical and numerical simulation of strength of thick-wall pipe by using static elastic problems is an important problem and has attracted the attention of many researches, academicians and practitioners. the The present work studies the change in the strength of a quite long isotropic thick-wall pipe (circular cylinder) for the varying pipe diameter, wall thickness and material. The pipe is in the plane deformed state, i.e. plane deformation is considered. Based on the problems of statics of the theory of elasticity, a mathematical model to calculate the strength of the thick-wall pipe was developed and the problems of statics of the theory of elasticity were set and solved analytically in the polar coordinate system. The analytical solution was obtained by the method of separation of variables, which is presented by two harmonious functions. The dependence of the pipe strength on the thickness and material of the pipe wall, when (a) normal stress is applied to the internal boundary (internal pressure) and external boundary is free from stresses and (b) normal stress is applied to the external boundary (external pressure) and the internal boundary is free from stresses, is studied. In particular, the minimum thicknesses of the walls of homogeneous isotropic circular cylinders of different materials and diameters with a plane deformed mode when the pressures in the cylinders do not exceed the admissible values were identified. Some numerical results are presented as tables, graphs and relevant consideration.


Author(s):  
Xiaojuan Chen ◽  
Xiaoxiao Ma

In the process of traditional methods, the error rate of external boundary value problem is always at a high level, which seriously affects the subsequent calculation and cannot meet the requirements of current Volterra products. To solve this problem, Volterra's preprocessing method for the external boundary value problem of Integro differential equations is studied in this paper. The Sinc function is used to deal with the external value problem of Volterra Integro differential equation, which reduces the error of the external value problem and reduces the error of the external value problem. In order to prove the existence of the solution of the differential equation, when the existence of the solution can be proved, the differential equation is transformed into a Volterra integral equation, the Taylor expansion equation is used, the symplectic function is used to deal with the external value problem of homogeneous boundary conditions, and the uniform effective numerical solution of the external value problem of the equation is obtained by homogeneous transformation according to the non-homogeneous boundary conditions.


Author(s):  
Veronika Ivanova ◽  

Background: The peculiarities of sensory perception and perception of one's own body in children with autism are the basis for understanding their cognitive and social development difficulties. Objective: The study aims to structure different categories of drawings of children with autism and compare them with the severity of autism measured by CARS2. Methods: 120 children aged 3 to 9 years were studied (X= 6.26, SD = 3.16). Drawings of autistic children. The children have a white sheet, pencils, a children's drawing table, and the experimenter asks them to draw a person. The children were studied with CARS. 2. Clinical method: includes observation, direct work with the child on each of the topics of the methodology used, interview with parents, diagnostic discussion with the clinical team. Psychodiagnostic method: includes an examination of children with mental developmental stairs, assessment of cognitive, communication, socioemotional and sensorimotor functions. CARS 2 Childhood Autism Rating Scale | Second Edition Statistical. Method: includes data processing using the SPSS programme. Descriptive statistics, correlation analysis, a frequency distribution of data are used for data analysis. Results: The results show eight main categories of drawings in autistic children: 1. circles, water; 2. patches of colour covering the human figure or representing a human figure without an external boundary; 3. figures and letters; 4. human figures fenced as a bubble, a human figure composed of parts of objects (the elements are not connected); 5. objects with geometric shapes (buildings, roads with markings, apartment blocks, strange shells; 6. road signs, logos. Conclusions: There is no statistical dependence between the severity of autistic symptomatology and the types of drawings. We can draw some conclusions about how a child with autism perceives his own body from the presented results. Because we see that in mild and moderate degrees of autism CARS 2, the whole variety of drawing categories was evaluated, while in severe and very severe degrees of expression of the disorder circles, colourful spots with vague boundaries predominate. Children with autism often identify with non-living objects, street signs, eccentric houses and towers.


2021 ◽  
Author(s):  
Johnson Johnson ◽  
Ezizanami Adewole

Abstract At inception of a production rate regime, a horizontal well is expected to sweep oil within its drainage radius until the flow transients are interrupted by an external boundary or an impermeable heterogeneity. If the interruption is an impermeable heterogeneity or sealing fault, then the architecture of the heterogeneity must be deciphered in order to be able to design and implement an effective work-over or well re-entry to boost oil production from the reservoir. In this paper, therefore, the behavior of a horizontal well located within a pair of sealing faults inclined at 90 degrees is investigated using flow pressures and their derivatives. It is assumed that the well flow pressure is undergoing infinite activity, and each fault acts as a plane mirror. The total pressure drop in the object well is calculated by superposition principle. Damage and mechanical skin and wellbore storage are not considered. The main objective of our investigation is to establish identifiable signatures on pressure-time plots that represent infinite flow in the presence of adjacent no flow faults inclined at 90degrees. Results obtained show that the flowing wellbore pressure is influenced strongly by object well design, object well distance from each fault, and distance of each image from the object well. Irrespective of object well distance from the fault, there are three (3) images formed. Central object well location yields a square polygon, with two image wells nearer to the object well at equidistance from the object well, and the farthest image well to be 2d2. From the object well For off-centered object well location within the faults, a rectangular polygon is formed, with each image at a different distance from one well to another. Dimensionless pressure and dimensionless pressure derivative gradients during infinite-acting flow are (4.6052/LD) and 2/LD, respectively for all well locations within the faults.


Author(s):  
S. Monsurrò ◽  
A. K. Nandakumaran ◽  
C. Perugia

AbstractIn this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of the Hilbert Uniqueness Method, introduced by J. L. Lions, we study the related boundary exact controllability problem. The key point is to derive an observability inequality by using the so called Lagrange multipliers method, and then to construct the exact control through the solution of an adjoint problem. Eventually, we prove a lower bound for the control time which depends on the geometry of the domain, on the coefficients matrix and on the proportionality between the jump of the solution and the conormal derivatives on the interface.


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