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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 237
Author(s):  
Calogero Vetro

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument.


2022 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Handong He ◽  
Yanrong Liu ◽  
Jing Cui ◽  
Di Hu

Knowing the GIS expression of geological phenomena is an important basis for the combination of geology and GIS. Regional geological structures include folds, faults, strata, rocks, and other typical geological phenomena and are the focus of geological GIS research. However, existing research on the GIS expression of regional geological structure focuses on the expression of the spatial and attribute characteristics of geological structures, and our knowledge of the expression of the semantic, relationship, and evolution processes of geological structures is not comprehensive. In this paper, a regional geological structure scene expression model with the semantic terms positional accuracy, geometric shape, relationship type, attribute type, and time-type attributes and operations is proposed. A regional geological structure scenario markup language (RGSSML) and a method for mapping it with graphics are designed to store and graphically express regional geological structure information. According to the geological time scale, a temporal reference coordinate system is defined to dynamically express the evolution of regional geological structures. Based on the dynamic division of the time dimension of regional geological structures, the expression method of “time dimension + space structure” for the regional geological structure evolution process is designed based on the temporal model. Finally, the feasibility and effectiveness of the regional geological structure scene expression method proposed in this paper is verified using the Ningzhen Mountain (Nanjing section) as an example. The research results show that the regional geological structure scene expression method designed in this paper has the following characteristics: (1) It can comprehensively express the spatial characteristics, attribute characteristics, semantics, relationships, and evolution processes of regional geological structures; (2) it can be used to realize formalized expression and unified storage of regional geological information; and (3) it can be used to realize dynamic expression of the regional geological structure evolution process. Moreover, it has significant advantages for the expression of regional geological structure semantics, relationships, and evolution processes. This study improves our knowledge of the GIS expression of regional geological structures and is expected to further promote the combination and development of geology and GIS.


Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 22
Author(s):  
Wolf-Dieter Richter

The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is continued here in dimension four and above. To this end, the notions of geometric vector product and geometric exponential function are extended to arbitrary finite dimensions and some usual algebraic rules known from usual complex numbers are replaced with new ones. An application for the construction of directional probability distributions is presented.


2022 ◽  
Author(s):  
Khaled H. Khafagy ◽  
Siddhant Datta ◽  
Tom G. Stoumbos ◽  
Daisaku Inoyama ◽  
Aditi Chattopadhyay

Author(s):  
N. A. Skibitskaya ◽  
◽  
I. O. Burkhanova ◽  
M. N. Bolshakov ◽  
V. A. Kuzmin ◽  
...  

Evaluation of rock wettability is an important task, since this parameter determines the distribution of water and oil in the reservoirs and their relative and phase permeability. The reliability of evaluation the wettability of rock samples depends on the drilling-in conditions during core sampling and core sample preparation methods. The investigation of the surface properties of the core from the Orenburg oil and gas condensate field showed that using of polymer-colloidal drilling mud leads to hydrophilization of the samples' surface. To obtain information on the actual wettability values of rock samples taken from wells drilled with polymer-colloidal drilling mud a method for estimating the relative (predominant) wettability of rocks based on petrophysical and lithological studies data is proposed. The authors suggest that the extraction of oil and gas source rock samples leads to irreversible changes in surface properties that cannot be restored. Keywords: selective wettability; relative wettability; predominant wettability; polymer-colloidal drilling mud; residual gas saturation; trapped gas saturation; pore space structure; extraction.


2021 ◽  
Vol 6 (4) ◽  
pp. 22-31
Author(s):  
Guzel R. Vahitova ◽  
Anzhela A. Kazaryan ◽  
Timur F. Khaybullin

Aim. Due to the depletion of reserves of the main oil and gas complexes, the greatest interest is attributed to hard-to-recover reserves, complex-built objects of the sedimentary cover, the development of which was unprofitable until recently. One of these is the oil-bearing complex of the Achimov deposits of the Malobalykskoye field in Western Siberia. This article is devoted to the facies analysis and typification of reservoir rocks of the Achimov deposits in order to increase the reliability of determining the boundaries of the reservoirs, their interpretation and assessment of the petrophysical properties of the reservoirs. At the same time, special attention is paid to the facies analysis, which determines the characteristics of the reservoir. The Achimov deposits are a promising source of increasing resources and maintaining production at a high level. With their increasing importance, there are problems that complicate the search and assessment of deposits. Such problems include a high degree of reservoir compartmentalization, sharp facies variability, complex pore space structure, high clay content, low permeability values, etc. Materials and methods. The work is based on a comprehensive interpretation of the data of the lithological description of the core, the results of laboratory studies of the core and well logging data analysis of the Achimov deposits of the Malobalykskoye field. The methods used in the interpretation of GIS data, statistical analysis, comparison. Due to the fact that the reservoir properties of sand bodies are determined by the peculiarities of their formation in different conditions of sedimentation, it is necessary to establish a relationship between the petrophysical characteristics of rocks and their facies nature by substantiating petrofacies models. The use of the latter in geological modeling makes it possible to more effectively predict the reservoir properties (reservoir properties) of various facies lithotypes. Results. The paper presents the results of facies analysis and typification of the reservoirs of the Achimov deposits of the Malobalykskoye field, on the basis of which the boundaries of the reservoirs and the effective oilsaturated thicknesses were refined. Conclusions. Based on the results of the study, it can be concluded that it is necessary to develop refined petrophysical models for reservoirs with complex geological structure that take into account the facies features of rocks.


Energies ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 32
Author(s):  
Yugao Wang ◽  
Xiaochen Liu ◽  
Zhilei Wang ◽  
Chuan Dong ◽  
Jun Shen ◽  
...  

Oxidative depolymerization of low-rank coals is promising for obtaining benzene carboxylic acids (BCAs). However, it is hindered by the low yield of BCAs along with a large number of alphatic acids. Thermal dissolution could modify the physico-chemical structural features of low-rank coals, which is expected to improve the oxidation of LRCs. In this paper, lignite and subbituminous coal were firstly subjected to thermal dissolution with cyclohexane at 250 °C for 2 h. Then, the raw coal and the corresponding thermal insoluble portion (TIP) were oxidized by NaOCl under the same conditions. The residual yields of TIPs oxidation were both lower than those of raw coals oxidation, indicating that TIPs were more easily oxidized than the raw coals. The yield of BCAs obtained by TIPs oxidation was above 19% higher than that from the oxidation of raw coals. Meanwhile, the selectivity of BCAs was improved in the resulting oxidation products from TIPs compared with that from the raw coals. The relationship between BCAs generation and thermal dissolution of low rank coals was investigated by ultimate analysis, Fourier transform infrared spectroscopy, and nitrogen adsorption-desorption analysis. The results suggested that thermal dissolution could enrich aromatic portion in the remaining TIPs, resulting in an increasing of the yield and selectivity of BCAs. Simultaneously, thermal dissolution raised the specific surface area and expanded the looser space structure of TIPS, which were beneficial for the sufficient collision between aromatic structures and oxidant, facilitating the oxidative depolymerization of TIPs. This investigation would provide a novel route for promoting BCAs production by mild oxidative depolymerization of low-rank coals.


Metals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 2024
Author(s):  
Jun Liang ◽  
Chunjing Wu ◽  
Zihang Zhao ◽  
Weizhong Tang

In order to promote the industrialization of the large deformation technology of carbon fiber composites, this paper studies a new method of forming of helical carbon fiber reinforced aluminum matrix composite. The purpose is to solve the problem of large deformation of carbon fiber with low elongation and metal matrix with high elongation. By introducing carbon fiber with helical space structure into the aluminum matrix, the helical carbon fiber reinforced aluminum matrix composites were prepared and the subsequent drawing deformation was carried out. Here we systematically studied the large plastic deformation behavior of helical carbon fiber reinforced aluminum matrix composite via a combination of numerical simulations and experiments, and analyzed the deformation law and stress of helical carbon fiber in the deformation process. We found that the plastic deformation of the composite causes local stress concentration around the helical carbon fiber, and the helical carbon fiber will move synchronously with the aluminum matrix during the deformation, and receive the pressure from the aluminum matrix. Second, the best process parameters obtained from the simulation, that is, the drawing die angle α = 7°, when five-pass drawing experiments were carried out, the total deformation reached 58%, and the average elongation of a single pass was 18.9%. The experimental show carbon fiber reinforced aluminum matrix composite with helical space structure can achieve large deformation and high strength. The experimental and simulation are in general agreement, which verifies the correctness of the carbon fiber helical structure model.


Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 488
Author(s):  
Hongxing Zhang ◽  
Naying Zhou ◽  
Wenfang Liu ◽  
Xin Wu

A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity. Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time steps perform well long-term when stabilizing Hamiltonian errors, regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincaré sections and fast Lyapunov indicators is applied to investigate the effects of the parameters, including the four free deformation parameters, on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances, as the magnitude of the magnetic parameter or any one of the negative deformation parameters increases. However, they are weakened when the angular momentum or any one of the positive deformation parameters increases.


2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Mihai Marciu

AbstractIn the present paper a new cosmological model is proposed by extending the Einstein–Hilbert Lagrangian with a generic functional $$\tilde{f}(R,P)$$ f ~ ( R , P ) , which depends on the scalar curvature R and a term P which encodes a possible influence from specific cubic contractions of the Riemann tensor. After proposing the corresponding action, the associated modified Friedmann relations are deduced, in the case where the generic functional has the following decomposition, $$\tilde{f}(R,P)=f(R)+g(P)$$ f ~ ( R , P ) = f ( R ) + g ( P ) . The present study takes into account the power-law and the exponential decomposition for the specific form of the corresponding generic functional. For the analytical approach the specific method of dynamical system analysis is employed, revealing the fundamental properties of the phase space structure, discussing the dynamical consequences for the cosmological solutions obtained. It is revealed that the cosmological solutions associated to the critical points can explain various dynamical eras, with a high sensitivity to the values of the corresponding parameters, encoding different effects due to the geometrical nature of the specific couplings.


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