Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This ...generalizes early results of Chang-Yang 7 and the first named author 32, and complements Fontana's inequality of two dimensions 15. The blow-up analysis in the current paper is far more elaborate than that of 32, and particularly clarifies several ambiguous points there. In precise, we prove the existence of isothermal coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.
•Calculation of cross-scale anisotropic thermal transport in carbon fiber composites.•Use of the dual coordinate system to describe thermal conductivity anisotropy.•The mechanism of interface ...rotation affecting interfacial thermal resistance.•The heat transport properties of fiber tortuosity and orientation within the resin substrate were investigated.
The thermal conductivity parameter of materials is a fundamental factor for thermal management and the study of heat transfer processes. In the present work, we constructed the microscopic topology and interfacial structure of the fiber structure based on the homogenization of finite elements and molecular dynamics theory. For the anisotropy of fiber thermal conductivity, we proposed an anisotropic cross-scale heat transport model for carbon fiber/epoxy resin (CF/ER) composites, with consideration of interfacial thermal resistance (ITR). Based on the numerical validation of the reliability of the method, we established a dual coordinate system to analyze the mechanism of the geometric topological parameters on the structural anisotropic heat transport. The fiber volume fraction significantly affected the effective thermal conductivity (ETC) within a range of 10% to 15%, with ETC growth rates of up to 50%. The fiber orientation angle influenced the main heat transfer direction, and when the fiber volume fraction was 40%, increasing the fiber orientation angle to 90° could enhance the ETC in the axial direction up to 130.28%. Meanwhile, the larger orientation angle could reduce the interfacial phonon heat dissipation and achieve the better phonon transmission effect. The change of fiber structure could effectively modulate the ETC, while the fiber length and cross-sectional shape would have less effect on the ETC. With the introduction of fiber tortuosity, the heat transport could be regulated by changing the tortuosity. Within the variation range of tortuosity from 1 to 3, the ETC regulation of the composite could be achieved from 12% to 42% in the axial direction and 14% to 34% in the radial direction. With increasing curvature, the ETC variation trend became gradually nonlinear. The study serves as a theoretical basis for the preparation and thermal properties evaluation of fiber-reinforced composites.
The numerically efficient solution describing the sound radiation from a circular source located in a flat, rigid baffle is obtained. For this purpose, a half-space was divided into two subregions ...coupled through continuity equations. The Helmholtz equation was solved in both subregions. The proposed method can be used for circular baffled sources in the case when fluid–structure interactions are included, as well as for an input from a waveguide or cavity. The validity and numerical efficiency of the presented solution were tested assuming that a clamped circular plate is a source. The numerical simulations show that the results given by the proposed method agree with those given by the known integral solution. The exceptions are the field points at which the integral formulas fail and provide incorrect values of the sound pressure. Hence, the presented formulas can be the only method to perform accurate calculations at troublesome field points. The numerical efficiencies of the obtained formulas and integral ones were compared by estimating the value of the appropriate time ratios. The numerical analysis shows that the proposed method can be used to significantly improve calculations of the sound power and the sound pressure.
•Improvement in calculations of the sound pressure and the sound power.•Formulas to efficiently calculate the sound field from a baffled circular source.•Proposed formulas versus the known integral solution.
SUMMARY
Within the field of seismic modelling in anisotropic media, dynamic ray tracing is a powerful technique for computation of amplitude and phase properties of the high-frequency Green’s ...function. Dynamic ray tracing is based on solving a system of Hamilton–Jacobi perturbation equations, which may be expressed in different 3-D coordinate systems. We consider two particular coordinate systems; a Cartesian coordinate system with a fixed origin and a curvilinear ray-centred coordinate system associated with a reference ray. For each system we form the corresponding 6-D phase spaces, which encapsulate six degrees of freedom in the variation of position and momentum. The formulation of (conventional) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between Cartesian and ray-centred phase-space perturbations. Such transformation can also be used for defining initial conditions for dynamic ray tracing in Cartesian coordinates and for obtaining the coefficients involved in two-point traveltime extrapolation. As a step towards extending dynamic ray tracing in ray-centred coordinates to higher orders we establish detailed information about the higher-order properties of the transformation between the Cartesian and ray-centred phase-space perturbations. By numerical examples, we (1) visualize the validity limits of the ray-centred coordinate system, (2) demonstrate the transformation of higher-order derivatives of traveltime from Cartesian to ray-centred coordinates and (3) address the stability of function value and derivatives of volumetric parameters in a higher-order representation of the subsurface model.
Surrogate-assisted evolutionary algorithms (SAEAs) have been proven to be very effective in tackling low-dimensional expensive problems. However, it remains a challenge to solve high-dimensional ...expensive problems (HEPs) with the curse of dimensionality. Therefore, this paper proposes a surrogate-assisted improved multioperator differential evolution (SA-IMODE) algorithm to address HEPs up to 2000 dimensions. Specifically, this paper proposes a novel relationship classification model-based environment selection strategy (RCES), in which a classification model is used to distinguish between “good” and “bad” solutions to assist in environment selection. By doing this, the “unpromising” solutions are thrown away directly without evaluation to reduce the number of expensive fitness evaluations. Moreover, the solution-improvement data point and error samples are added to construct the training dataset to improve the model's prediction accuracy. Two coordinate systems are utilized to produce five types of DE operators to suit different fitness landscapes. An adaptive strategy is also used to select suitable DE operators to generate promising offspring. Furthermore, a local search mechanism is applied to refine the best solution in the current population to accelerate the algorithm's convergence. The systematic experiment results show SA-IMODE has a significant advantage over thirteen state-of-the-art algorithms on benchmark problems.
The geometric and distributive properties of voids significantly influence anisotropic coalescence behaviour. However, this problem has received little attention owing to the complexity of ...considering all the properties in the current analytical framework of limit analysis. To address this issue, this study proposes an analytical framework based on an elliptic coordinate system, including the determination of the ligament zone, characterization of plastic flow, and derivation of the void coalescence criterion, for porous materials with various geometric and distributive properties, including size, shape, spacing, and orientation. This framework is motivated by our observations that the evolution of the void geometry and surrounding plastic flow can be well characterized by the grid of the elliptic coordinate system. Subsequently, an analytical function is proposed to determine the ligament zone and coalescence direction with various void properties. A hollow nonaxisymmetric cylindrical unit cell is proposed to describe this ligament zone, and the corresponding trial velocity field is derived by extending the previous Gurson-like velocity field into the elliptic cylindrical coordinate system. The rationality of the field is validated by comparing its equivalent strain rate field with numerical simulations. Finally, a coalescence criterion is derived via the limit analysis of the proposed unit cell undergoing internal necking. Two heuristic adjustments are formulated for the overflow phenomenon in the rigid zone and outer ligament zones. Numerical assessments with various void properties confirm the accuracy of the analytical model. The coalescence criterion can predict the independent and coupling effects of geometric and distributive properties on anisotropic void coalescence. This study provides possible solutions to future plasticity problems of ellipsoidal inclusions.
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•The anisotropic coalescence behaviours are described in elliptic coordinate system.•An analytical function is proposed to determine the intervoids ligament zone.•The Gurson-like trial velocity field is extended into the proposed coordinate system.•The coalescence criterion agrees with the numerical assessments on void properties.•The effects of void properties on anisotropic coalescence are identified.
When simulating the propagation of seismic waves in some special structures, such as tunnels and boreholes, finite difference forward modeling in the polar system has higher accuracy than the ...traditional Cartesian system. In actual situations, the polar space is the most irregular. To solve this problem, a forward modeling method for an irregular polar coordinate system is proposed to improve the simulation accuracy. First, an irregular surface of the polar space was meshed into an irregular polar system. After the transformation, the undulating surface was mapped into a plane one, and the wavefield was then computed in an irregular polar system. The Lebedev staggered grid was used to solve the wave equations in the irregular polar system. In addition, the artificial absorption boundary, cylindrical free boundary, and circumferential boundary conditions were used to absorb the boundary reflection. We selected three polar space models to demonstrate the new method in this study. The results show that the proposed elastic simulation method in an irregular polar coordinate system can produce more accurate and stable simulation results when modeling seismic wave propagation in an irregular polar space. Elastic full waveform inversion further shows that the irregular polar system elastic simulation method can accurately simulate the wavefield in an undulating polar space.
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•A mathematical dimension extension method combing spherical coordinate and moving coordinate system was developed.•Bidirectional heat transfer model for characterizing gangue ...endothermic relaxation behavior was established.•Evolution on single-gangue-ball temperature field along the high-temperature path in a longwall gob was derived.•Specific measures to enhance spontaneous ignition prediction accuracy during coal mining were proposed.
The collapse of overlying strata in a goaf during coal mining forms many gangue blocks that vary in size and shape. Because the heat released by the coal–oxygen reaction diffuses around the wind flow, endothermic relaxation occurs when the heated gas contacts the gangue. However, only a few studies have addressed this issue. In this study, we first propose a method to investigate the thermal relaxation behavior by expanding the mathematical space of the problem and then establish a bidirectional heat transfer model of a single-gangue-ball in spherical coordinates combined with the energy conservation law, which is solved numerically using the finite difference method. Finally, the reason for the fluctuation of the solid temperature distribution in the gob is determined by extracting the calculation results and comparing them with the gangue temperature curve under transient heat conduction, and the effects of some key factors on the thermal relaxation efficiency of the gangue are quantitatively investigated. The results show that (i) along the high-temperature path of the goaf, the gangue temperature exhibits the same trend as the ambient temperature, and its external and internal temperature difference decreases gradually with an increase in burial depth; (ii) compared with the change in temperature rise under transient heat conduction, the relaxation phenomenon can result in a calculation error of up to 1.3 °C; (iii) the heat transfer efficiency is related to the gangue characteristics and its surface heat transfer resistance, and the accuracy of spontaneous combustion prediction can be guaranteed by increasing the initial temperature, reducing the heat transfer radius, or decreasing the air flow rate. In this study, the thermal relaxation behavior of the gangue in a gas–solid dual medium in a longwall gob is investigated, and a foundation is laid for the establishment of a four-dimensional temperature field model for the gangue in the future.
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