Renormalized solutions of a nonlinear parabolic equation with double degeneracy

In this paper, we consider the initial-boundary value problem of a nonlinear parabolic equation with double degeneracy, and establish the existence and uniqueness theorems of renormalized solutions which are stronger than $BV$ solutions

Hurting without Hitting: The Economic Cost of Political Tension

Political tension causing diplomatic strains rarely escalates into direct violence or war. This paper identifies the economic effects of such non-violent political tension by examining Taiwan’s sovereignty debate. Non-violent events harming the relationship with mainland China lead to an average daily drop of 200 basis points in Taiwanese stock returns. The impact is more severe on firms openly supporting the Taiwanese pro-independence party. Through a series of tests we identify this economic penalty as initiated by mainland authorities, who specifically target political opponents that are economically exposed to mainland China via either investments or exports

BIOMECHANICAL ANALYSIS OF THE PADDLING TECHNIQUE AND THE VELOCITY OF 1000M FULL PADDLING EVENT: A CASE STUDY.

Biomechanical analysis from data obtained by video camera was used to investigate the paddling technique and the velocity of 1000m full paddling event. The results showed the characteristics and the advantages of Meng’s paddling technique. The data also revealed deficiencies and provided a set of kinematics parameters for evaluation, diagnosis and training of paddling techniques

Time periodic solutions for a viscous diffusion equation with nonlinear periodic sources

In this paper, we prove the existence of nontrivial nonnegative classical time periodic solutions to the viscous diffusion equation with strongly nonlinear periodic sources. Moreover, we also discuss the asymptotic behavior of solutions as the viscous coefficient $k$ tends to zero

Transport of pore-water oxygen with/without aeration in subsurface wastewater infiltration system

In this study, three subsurface wastewater infiltration systems (SWISs) at different aeration were set up to study the transport of pore-water oxygen and quantify the amount of trapped gas. Bromide and dissolved oxygen were introduced into SWISs as partitioning tracer and non-partitioning tracer, respectively. A model named CXTFIT based on the convection diffusion equation was used to describe the shape of breakthrough curves for bromide and dissolved air in column experiments. In CXTFIT code, the parameter β obtained from the bromide test ranging from 0.2940 to 0.7600 indicates that the physical nonequilibrium model was relatively suitable for dissolved air transport. Retardation factors obtained by CXTFIT code indicate 2–20% porosity filled with gas. Tracing the transport of air and determining the percentage of porosity filled with trapped gas has lain a foundation for further study on gas clogging in SWISs. Keywords: gas-partitioning tracer, convection diffusion equation, subsurface wastewater infiltration system, dissolved air transport, gas cloggin

Micro/Nano Liquid Crystal Layer–Based Tunable Optical Fiber Interferometers

Miniaturization and integration are the main trends in modern photonic technology. In this chapter, two kinds of micro-/nano liquid crystal (LC) layer–based tunable optical fiber interferometers are proposed. One fiber interferometer is the optical fiber gratings (LPGs), and the other one is the locally bent microfiber taper (LBMT). The working principles of the devices are theoretically analyzed. The preparation process and the functional properties of the devices are experimentally investigated as well

The Strip-Ground Rectangular Patch Antenna

To imitate the broken situation of the conductive threads of the wearable antenna, a strip-ground design of rectangular patch antenna with the conventional substrate is presented to investigate the change of the antenna performance, where the ground is sliced along its E-plane. The strips are symmetrical along the center line of the width of the patch, and the gap ratio of the gap to the solid ground varies with the change of gaps. The conventional patch antenna is used as a reference for comparison with the stripe-ground antennas. And the effect of the coaxial cable, the changes of the impedance, and the cross-polarization of the antenna are investigated. Several antenna prototypes are fabricated and their measured results are in good agreement with the simulations. These results show that the gaps change the performance of the strip-ground antennas, but they can work well if the gap ratio is less than 1 : 4

A deep complementary energy method for solid mechanics using minimum complementary energy principle

In recent years, the rapid advancement of deep learning has significantly impacted various fields, particularly in solving partial differential equations (PDEs) in solid mechanics, benefiting greatly from the remarkable approximation capabilities of neural networks. In solving PDEs, Physics-Informed Neural Networks (PINNs) and the Deep Energy Method (DEM) have garnered substantial attention. The principle of minimum potential energy and complementary energy are two important variational principles in solid mechanics. However,DEM is based on the principle of minimum potential energy, but it lacks the important form of minimum complementary energy. To bridge this gap, we propose the deep complementary energy method (DCEM) based on the principle of minimum complementary energy. The output function of DCEM is the stress function. We extend DCEM to DCEM-Plus (DCEM-P), adding terms that satisfy partial differential equations. Furthermore, we propose a deep complementary energy operator method (DCEM-O) by combining operator learning with physical equations. We train DCEM-O using existing high-fidelity numerical results and the complementary energy together. We present numerical results using the Prandtl and Airy stress functions and compare DCEM with existing PINNs and DEM when modeling representative mechanical problems. The results demonstrate that DCEM outperforms DEM in terms of stress accuracy and efficiency and has an advantage in dealing with complex displacement boundary conditions. DCEM-P and DCEM-O further enhance the accuracy and efficiency of DCEM. In summary, our proposed DCEM marks the first time that complementary energy is extended to the energy-based physics-informed neural network and provides an essential supplementary energy form to the DEM in solid mechanics, offering promising research prospects in computational mechanics.Comment: 58 pages, 30 figure

BINN: A deep learning approach for computational mechanics problems based on boundary integral equations

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are approximated using neural networks and solved through a training process. The loss function is chosen as the residuals of the boundary integral equations. Regularization techniques are adopted to efficiently evaluate the weakly singular and Cauchy principle integrals in boundary integral equations. Potential problems and elastostatic problems are mainly concerned in this article as a demonstration. The proposed method has several outstanding advantages: First, the dimensions of the original problem are reduced by one, thus the freedoms are greatly reduced. Second, the proposed method does not require any extra treatment to introduce the boundary conditions, since they are naturally considered through the boundary integral equations. Therefore, the method is suitable for complex geometries. Third, BINN is suitable for problems on the infinite or semi-infinite domains. Moreover, BINN can easily handle heterogeneous problems with a single neural network without domain decomposition