Homogeneous Problem Research Articles

Homogenisation Problems for Free Discontinuity Functionals with Bounded Cohesive Surface Terms

Homogenisation Problems for Free Discontinuity Functionals with Bounded Cohesive Surface Terms

Integration of biogas and liquid recirculation enhance methane production in high-solid anaerobic digestion of pig manure and rice husks

High-solid anaerobic digestion (HSAD) is a promising technology for treating livestock manure and agricultural waste; however, the wide application has been limited due to homogenization problems. This study established a novel HSAD system by integrating liquid and biogas recirculation (RBL), aiming to enhance the biogas conversion efficiency of high-solid substrates at low costs. Results showed that the highest methane yield was 357 mL/gVSadded in the novel HSAD system (RBL), 30.7 % and 251.7 % higher than those with only liquid recirculation (RL) or with no recirculation (RNo). Biogas recirculation helped enhance dissolution and degradation of organic matter, and prevented the VFAs accumulation, contributing to the enhanced methane production in the novel HSAD system. The net electric energy benefit of RBL was 301.2 kWh for treating 1-ton raw materials, suggesting the high economic feasibility of the novel HSAD system for the sustainable treatment of high-solid organic wastes.

The feasibility study of online virtual education and communication platform

Since the epidemic, the demand for online virtual education in China and even the world is increasing, and the development of online virtual education platform has a good prospect.[1-2] However, because this industry is in the early stage of development, there are certain mechanism problems and Homogenization problem, resulting in poor profitability. This study aims to conduct feasibility analysis for this emerging industry by analyzing the development status and market prospect of the online education platform, and finally provide a new mode of operation of online virtual education platform around personalized customized services.

Fourier Transform Approach to Boundary Domain Integral Equations for Elastic Composites With Domain Decomposition and Multi Reference Parameters

ABSTRACTIn this article, displacement and strain periodic boundary domain integral equations for homogenization problems of elastic composites are derived in the context of FFT homogenization methods. The resolution methods based on regular grids and discrete Green's tensors are presented. The displacement based equations can be used to solve problems in arbitrary domains under periodic and non‐periodic boundary conditions. The strain based integral equation is obtained from the combination of the displacement based equations for different domains, each one having its own reference elasticity tensor. In the latter, the strain values inside every phases are connected to material mismatch parameters on the phase boundary. It was shown that by decomposing suitably domains by stiffness and using adapted reference parameters, the iteration schemes converge faster.

Integrating street-view imagery and points of interest for refining population spatialization: A case study in Wuhan City

Fine-scale population spatialization is the frontier of geosciences, it is essential for sustainable urban planning and effective resource allocation. Various approaches have been proposed to enhance population estimation accuracy using multi-source geospatial data. However, the approaches based on remote sensing data usually suffer from the problem of spatial homogeneity, while the social-sensing-based approach such as point of interest (POI) data cannot distinguish the population distribution around POIs with the same category but different scales. Thus, this study proposes a novel method that incorporates street view imagery (SVI) with POI, to enrich the semantic landscape of street-level objects and provide a visual representation of spatial heterogeneity within an urban environment. Specifically, we extract POI and SVI features at grid-, street-, and community-level, respectively, and then select modelling features based on cross-scale consistency analysis with population. After that, grid-level SVI features are adjusted by community-level SVI features to alleviate its sparsity and transiency. Finally, we train random forest (RF) at the street-level and estimate grid-level population weight for population allocation. Experiments in Wuhan City at a grid size of 100 × 100m show that our method yields higher accuracy compared to WorldPop, GPW datasets, Ye's method, and heterogeneous population attraction of POI modelling (HPA-POI), demonstrating its effectiveness in fine-scale population spatialization.

Application of Gold Nanoparticles for Improvement of Electroporation-Assisted Drug Delivery and Bleomycin Electrochemotherapy.

Background/Objectives: Electrochemotherapy (ECT) is a safe and efficient method of targeted drug delivery using pulsed electric fields (PEF), one that is based on the phenomenon of electroporation. However, the problems of electric field homogeneity within a tumor can cause a diminishing of the treatment efficacy, resulting only in partial response to the procedure. This work used gold nano-particles for electric field amplification, introducing the capability to improve available elec-trochemotherapy methods and solve problems associated with field non-homogeneity. Methods: We characterized the potential use of gold nanoparticles of 13 nm diameter (AuNPs: 13 nm) in combination with microsecond (0.6-1.5 kV/cm × 100 μs × 8 (1 Hz)) and nanosecond (6 kV/cm × 300-700 ns × 100 (1, 10, 100 kHz and 1 MHz)) electric field pulses. Finally, we tested the most prominent protocols (microsecond and nanosecond) in the context of bleomycin-based electrochemotherapy (4T1 mammary cancer cell line). Results: In the nano-pulse range, the synergistic effects (improved permeabilization and electrotransfer) were profound, with increased pulse burst frequency. Addi-tionally, AuNPs not only reduced the permeabilization thresholds but also affected pore resealing. It was shown that a saturated cytotoxic response with AuNPs can be triggered at significantly lower electric fields and that the AuNPs themselves are non-toxic for the cells either separately or in combination with bleomycin. Conclusions: The used electric fields are considered sub-threshold and/or not applicable for electrochemotherapy, however, when combined with AuNPs results in successful ECT, indicating the methodology's prospective applicability as an anticancer treatment method.

Comparative Study of Cognitive Differences in Rural Landscapes Based on Eye Movement Experiments

With the booming development of rural tourism, the users of rural environments are gradually becoming more diverse. Both tourists and villagers are the main appreciators of rural landscapes, but the cognitive similarities and differences in rural landscape between the two have not yet been explored. Therefore, taking Wangshang Village, located in Shaanxi Province, China as a case study, this research used a combination of quantitative analysis (eye-tracking technology) and qualitative analysis (semi-structured interviews) to compare and analyze the cognitive similarities and differences of rural landscapes between tourists and villagers. The experimental results showed that the cognitive similarities and differences in rural landscapes between tourists and villagers are mainly reflected in their level of cognition, observation methods, and key elements of focus. The reasons for cognitive differences are due to the different living backgrounds of the two groups of subjects, as well as their varying levels of familiarity, novelty, and personal needs towards rural landscapes. In conclusion, studying the cognitive differences between the two groups of participants, tourists and villagers, can help address the homogenization problem faced by rural landscapes. Meanwhile, the results of this study also provide theoretical guidance and methodological support for rural landscape design.

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(Two-scale) gradient Young measures in Orlicz–Sobolev setting are introduced and characterized providing also an integral representation formula for non convex energies arising in homogenization problems with nonstandard growth.

The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms

We consider, for $a,l\geq1$, $b,s,\alpha> 0$, and $p> q\geq1$, the homogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambda u^{q-1}+\beta u^{a-1}\left\vert \nabla u\right\vert ^{b}+mu^{l-1}e^{\alpha u^{s}}$ in a smooth bounded domain $\Omega\subset\mathbb{R}^{N}$. We prove that under certain setting of the parameters $\lambda$, $\beta$ and $m$ the problem admits at least one positive solution. Using this result we prove that if $\lambda,\beta> 0$ are arbitrarily fixed and $m$ is sufficiently small, then the problem has a positive solution $u_{p}$, for all $p$ sufficiently large. In addition, we show that $u_{p}$ converges uniformly to the distance function to the boundary of $\Omega$, as $p\rightarrow\infty$. This convergence result is new for nonlinearities involving a convection term.

Stabilization in a chemotaxis system modelling T-cell dynamics with simultaneous production and consumption of signals

Abstract In a smoothly bounded domain $\Omega \subset \mathbb{R}^n$ , $n\ge 1$ , this manuscript considers the homogeneous Neumann boundary problem for the chemotaxis system \begin{eqnarray*} \left \{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v), \\[5pt] v_t = \Delta v + u - \alpha uv, \end{array} \right . \end{eqnarray*} with parameter $\alpha \gt 0$ and with coincident production and uptake of attractants, as recently emphasized by Dallaston et al. as relevant for the understanding of T-cell dynamics. It is shown that there exists $\delta _\star =\delta _\star (n)\gt 0$ such that for any given $\alpha \ge \frac{1}{\delta _\star }$ and for any suitably regular initial data satisfying $v(\cdot, 0)\le \delta _\star$ , this problem admits a unique classical solution that stabilizes to the constant equilibrium $(\frac{1}{|\Omega |}\int _\Omega u(\cdot, 0), \, \frac{1}{\alpha })$ in the large time limit.

Femtosecond Bessel laser beam induced concentric rings on SiC for circular symmetry wide-viewing angle structural color

The laser-induced structural coloring technique holds significant potential for various applications due to its precision, controllability, and versatility across different materials. However, laser-induced structural colors face the problems of durability, homogeneity and indistinguishability, which are not conducive to their application as large-scale identifiable markers. In this paper, an innovative approach has been developed to achieve a circular-symmetric structural color display on durable SiC surfaces by fabricating periodic concentric ring structure arrays using the sidelobe light field of a femtosecond zero-order Bessel beam. The research involved a systematic study of the effects of laser power and pulse number on SiC, along with a detailed analysis of the micro-nanostructures evolving on the SiC surface after laser scanning. Additionally, an examination of the characteristics of circular-symmetric structural color displays and their wide viewing angles in periodic circular structures was conducted. Finally, a comparison was made between the structural color display effects of a concentric ring structure generated by a single pulse and the Laser-Induced Periodic Surface Structures (LIPSS) generated by three pulses. This comparison underscores the potential application of alternating between the high saturation color of the concentric ring structure and the low saturation dark light of the LIPSS for anti-counterfeit coding purposes. The findings of this research present promising opportunities for low-cost mass manufacturing in anti-counterfeit labeling and the advanced processing of photonic devices using SiC.

Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting

This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.

Problem perception and problem regulation during online collaborative learning: what is important for successful collaboration?

University students frequently prepare for exams or presentations in self-organized study groups. For this purpose, they often use videoconferencing software. During their collaboration, they need to regulate emerging problems to ensure effective learning. We suppose that regulation is facilitated when (1) the group perceives their regulation problems homogeneously, (2) they choose regulation strategies that have the potential to solve the problems immediately, and (3) they execute these strategies with sufficient intensity. We investigated which problems occur during online collaborative learning via videoconferencing and how homogeneity of problem perceptions, immediacy of the chosen strategies, and intensity of strategy use are related to regulation success. University students (N = 222) from two lectures in pre-service teacher education and educational sciences in 99 study groups. Students collaborated in a self-organized manner, that is, without a teacher present, to study the material of one lecture using videoconferencing software. After the collaboration, group members rated, individually, the intensity of different problems during collaboration, reported which strategies they used to overcome their biggest problem, and rated the success of their problem regulation, their satisfaction with their collaboration, as well as their learning gain. In addition, they answered a knowledge test. We found that most students rated technical issues as their biggest problem. Multilevel modeling showed that homogeneous problem perception moderated by problem intensity-contrary to immediate and intensive strategy use-predicted successful problem regulation and satisfaction with the collaboration but not knowledge gain. Case analyses illustrate the assumed mechanism that a homogeneous problem perception facilitates socially shared regulation. We conclude that even in only slightly structured learning contexts, students might only need to jointly identify their problems, whereas the best possible regulation of these problems seems less relevant. Therefore, training students to foster regulation competencies might prioritize identifying problems.

Analysis of Existing Problems in Chinese A-share Market and Relevant Solutions

China's A-shares have developed rapidly in recent years, with huge market volume and scale, and have become an important direction for corporate financing and mass investment. There are still many problems in the A-share market, which will affect the development of the A-share market. There is a problem of slow delisting in the A-share market, which will lead to bad enterprises not being cleared in time, and the frequency of market update is not enough, which needs to be alleviated by further improving the legal system and changing policies. Some sectors of the A-share market have the problem of downward market, resulting in financing difficulties for companies in these sectors and unable to develop normally. This problem can be fixed by increasing the proportion of companies that pay dividends to attract investors. Listed companies in the A-share market may also have goodwill problems, which will seriously affect investor confidence and reduce the amount of investment. It is necessary to improve the goodwill accounting policy, so that goodwill can be correctly measured and reflected. Finally, A-share market funds have the problem of homogeneity, which leads to vicious competition in a single sector and is unfriendly to small and medium-sized enterprises. The government can mitigate such problems by encouraging innovation and regulating the market, diversifying stock development. It is necessary to study the problems of the A-share market and give solutions of the existing problems, which can make the country, enterprises and investors have a more intuitive understanding of the market so they can make corresponding responses to market changes.

РЕЗУЛЬТАТЫ ЭКСПЕРИМЕНТАЛЬНЫХ ИССЛЕДОВАНИЙ НАСОСА-ПОНТОНА ДЛЯ ЛАГУН-НАВОЗОХРАНИЛИЩ

The main methods of preparing organic fertilizers from manure runoff coming from pigbreeding complexes are analyzed. In particular, one of the effective technologies is the technology of homogenization of runoff in lagoons-manure storages. The purpose of the article is to substantiate the design and parameters of the pontoon pump for homogenization and pumping of liquid organic fertilizers (LOF) from lagoons-manure storages. The analysis of studies on the problem of homogenization and pumping of LFO from lagoons-manure storages made it possible to formulate scientific prerequisites for improving the working process of mixing manure runoff in manure storages and pumping them to the place of application to the soil. Their essence lies in the substantiation of the design parameters of the transporting screw - length, diameter and frequency of its rotation. A new design of the pontoon pump is described and a diagram of its location when changing the depth of the lagoon-manure storage is presented. A diagram of the working process for the pontoon pump, consisting of three stages, is developed. The pump flow rate, the total specific energy of the pumped liquid at the pump outlet, and the pressure created by the conveying screw are determined. The analysis of the forces applied to a point in the conveying part of the pontoon pump is performed, which made it possible to determine the trigonometric functions of the angular parameter. Research is conducted using the multifactorial experiment technique. An analytical dependence of the change in the pump pressure on the diameter of the conveying screw casing and the length of the conveying screw at a constant screw rotation frequency is obtained. A graphical dependence of the response surface is constructed. The obtained design parameters ensure the efficient flow of the working process of pumping ZOU from the manure storage lagoon with the specified parameters of pressure and flow rate.

Homogenization for singularly perturbed stochastic wave equations with Hölder continuous coefficients

This work is concerned with the homogenization problem for singularly perturbed stochastic wave equations. Under the assumption that the coefficients are only Hölder continuous, we prove the weak convergence of the original system to a limit equation with an extra Gaussian term by using the technique of Poisson equation in Hilbert space. The optimal convergence rate is also obtained.

Tuning triplet excitons and dynamic afterglow based on host-guest doping

Designing persistent dual-band afterglow materials with thermally activated delayed fluorescence (TADF) and room temperature phosphorescence (RTP) contributed to solving the problems of homogenization and singularity in long afterglow materials. Here, six aryl acetonitrile (CBM) and aryl dicyanoaniline (AMBT) derivatives, used as host and guest materials respectively, were successfully designed and synthesized based on the isomerization effect. Among of them, 0.1 % m-CBM/p-AMBT showed the longest dual-band TADF (540 ms) and RTP lifetimes (721 ms), as well as persistent afterglow over 8 s, whose fluorescence (ΦFL), TADF (ΦT) and RTP (ΦP) quantum yields were 0.11, 0.06 and 0.22 in sequence. More interestingly, some doping systems constructed by CBM and AMBT series compounds showed persistent triple-band emissions composed of TADF, unimolecular and aggregated AMBT series compounds. What’s more, ΦFL, ΦT and ΦP of 1 % o-AMBT@PMMA film were up to 0.17, 0.17, 0.23 in turn, with TADF, RTP and afterglow lifetimes of 606 ms, 727 ms, and 10 s respectively. TADF and RTP emission of CBM/AMBT series doping systems was attributed to host sensitized guest emission. Besides, the comparison displayed AMBT series compounds had bigger intensity ratios between TADF and RTP emission in PMMA films compared to in CBM series compounds. Finally, a series of data encryption were successfully constructed based on different afterglow lifetimes of the doping systems, and a dynamic anti-counterfeiting pattern was prepared by using different temperature responses of TADF and RTP emissions.

Lowest-order nonstandard finite element methods for time-fractional biharmonic problem

In this work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in R2 with clamped boundary conditions. After stating the well-posedness, we focus on some regularity results of the solution with respect to the regularity of the problem data. The spatially semidiscrete scheme covers several popular lowest-order piecewise-quadratic finite element schemes, namely, Morley, discontinuous Galerkin, and C0 interior penalty methods, and includes both smooth and nonsmooth initial data. Optimal order error bounds with respect to the regularity assumptions on the data are proved for both homogeneous and nonhomogeneous problems. The numerical experiments validate the theoretical convergence rate results.

Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains

This paper is concerned with the homogeneous Dirichlet problem for a sublinear elliptic equation with unbounded coefficients in a Lipschitz domain. Bilateral a priori estimates for positive solutions and a priori upper estimates for their gradients are presented as a byproduct of the boundary Harnack principle. These estimates allow us to show the uniqueness of a positive solution of the homogeneous Dirichlet problem under no information about normal derivatives unlike in smooth domains.

Local well-posedness of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator

Based on the local well-posedness for the homogeneous abstract problem, the existence and uniqueness of the local mild and classical solutions have been presented by using Kato’s variable norm technique for the Cauchy problem of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator.