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We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in R2$\mathbb {R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result. [ABSTRACT FROM AUTHOR]

This paper proposes a full-automatic high-efficiency Mueller matrix microscopic imaging (MMMI) system based on the tissue microarray (TMA) for cancer inspection for the first time. By performing a polar decomposition on the sample's Mueller matrix (MM) obtained by a transmissive MMMI system we established, the linear phase retardance equivalent waveplate fast-axis azimuth and the linear phase retardance are obtained for distinguishing the cancerous tissues from the normal ones based on the differences in their polarization characteristics, where three analyses methods including statistical analysis, the gray-level co-occurrence matrix analysis (GLCM) and the Tamura image processing method (TIPM) are used. Previous MMMI medical diagnostics typically utilized discrete slices for inspection under a high-magnification objective (20×–50×) with a small field of view, while we use the TMA under a low-magnification objective (5×) with a large field of view. Experimental results indicate that MMMI based on TMA can effectively analyze the pathological variations in biological tissues, inspect cancerous cervical tissues, and thus contribute to the diagnosis of postoperative cancer biopsies. Such an inspection method, using a large number of samples within a TMA, is beneficial for obtaining consistent findings and good reproducibility. [ABSTRACT FROM AUTHOR]

Accelerated durability evaluation aims to quantify the fatigue damage of automotive components in a shorter time. The quality of accelerated editing directly affects the evaluation's efficiency and accuracy. In this paper, an index-controlled accelerated spectrum editing method is proposed, and the equivalent fatigue damage model of the component is derived. Taking an automotive steering knuckle as the verification object, the proposed accelerated editing method is evaluated from multiple perspectives. The evaluation results show that the proposed method has apparent advantages in compression efficiency, damage consistency, and retaining the frequency domain impact on the component. [ABSTRACT FROM AUTHOR]

The thermoelectric generator (TEG) can convert heat to electricity and is widely used. To overcome the limitation for low efficiency of thermoelectric materials, optimizing the performance of TEG in given system is necessary. This study proposes a method to match individual TEG components to the system environment based on two boundary conditions—temperature and heat flux. With this method, TEG geometrical parameters can be determined to optimize the system performance by varying temperature as an independent variable. Using this method, the TEG in an undersea Radioisotope thermoelectric generator (u‐RTG) is optimized. The TEG system exhibits an output power of 14.10 W when powered by a 200 W heat source. The simulate result in the comprehensive system model of u‐RTG is 14.04 W, which has 0.45% deviation from the TEG optimization result. It is proved that the TEG optimized by this method matches the system, the optimization results are accurate. [ABSTRACT FROM AUTHOR]

A 3 × 3 Mueller matrix polarimeter, as one of the primary polarization measurement tools, has attracted intensive interest in various fields of polarization optics. In this paper, from a novel viewpoint with more mathematical analysis of the basic configuration and the working performance of a 3 × 3 Mueller matrix polarimeter, we systematically study the relationship between Mueller matrix measurement errors with the configuration and characteristics of polarizers in the polarimeter. We figure out that, mathematically, there is an optimal orientation angle configuration (0°, 60°, and 120°) of polarizers, which inherently ensures a minimal relative measurement error in general. Moreover, we interpret the internal source of such a robust error resistance under this optimized configuration mathematically for the first time. Simulation and practical experiments show the effectiveness of our mathematical analyses, and compared to the frequently used orientation angle configuration, the average relative error is reduced by up to 32% under such an optimized configuration. [ABSTRACT FROM AUTHOR]

A stochastic contour path finite‐difference time‐domain (S‐CP‐FDTD) algorithm is presented for electromagnetic wave propagation in metallic enclosures with uncertain slot size. The correlation coefficient between the field and size of slot was set to one. This new algorithm can efficiently obtain the mean and variance of the field. The simulation results indicate that the efficiency of the S‐CP‐FDTD method is much higher than that of the Monte Carlo (MC) method, that is, the S‐FDTD method only takes about 3% of the computation time of the MC method with excellent accuracy. The proposed method can be used to predict the influence of slots in metal structures with random sizes on the field. [ABSTRACT FROM AUTHOR]

The alloy materials of automotive chassis are subjected to sequential time‐varying loads due to road unevenness. The continuous change of the loading mode and the stress ratio leads to cyclic plasticity of the material, which induces cyclic hardening. The estimation of hardening effects seriously affects the structural's fatigue properties. Therefore, herein, a hardening model and the corresponding fatigue life prediction model are proposed. Then, the loading sequence effect's influence on an Al–Mg–Si alloy's cyclic hysteretic characteristics is analyzed. The steering knuckle is taken as the verification object. The acquired load spectrum is transformed into three sequential forms according to the equivalent damage principle for the verification test. The test results verify the conjecture of the loading sequence effect and confirm the accuracy of the proposed prediction model. [ABSTRACT FROM AUTHOR]

The random parameters remain hard to tackle for a long time in electromagnetic (EM) computations. Aiming at the time‐dependent uncertainty in the axially symmetric structures, the formulations of the stochastic finite‐difference time‐domain (S‐FDTD) method are derived, and the effectiveness is verified by a cylindrical ring structure. The simulation results indicate that the efficiency of S‐FDTD method is much higher than that of the polynomial chaos (PC) method and the Monte Carlo (MC) method, that is, the S‐FDTD method only takes about 3% of the computation time of the PC method and 0.03% of the computation time of the MC method with slightly lower accuracy. Thus the uncertainty in the EM calculation of axisymmetric cylindrical coordinates is possible to tackle, such as the uncertainties in the calculations of lightning electromagnetic pulse, high altitude electromagnetic pulse and so on. [ABSTRACT FROM AUTHOR]

A system-generated electromagnetic pulse (SGEMP) occurs when the system is exposed to an X-ray or $\gamma $ -ray beam. And the presence of air will greatly alter the fields of SGEMP. In this article, 1-D simulations are performed with a newly developed relativistic swarm model to investigate the air effects on SGEMP. For comparison, the equilibrium model and the non-relativistic swarm model are also used in simulations. The simulation results are divided into different pressure regions for discussion, that is, the high-pressure region (I and II), the transition region, and the intermediate pressure region. In the high-pressure region, the air plasma will dramatically reduce the electric field generated by the primary current. And the electric field increases with decreasing air density in high-pressure region I, due to the decreases of the ionization source of primary electrons interacting with air molecules. Then the electric field decreases with decreasing air density in high-pressure region II, mainly because of cascading ionization begins to dominate the generation of secondary electrons. In the transition region, the electric field is reduced to a minimal level, as the cascading rate saturates with the increase of electron energy. As air density continues to decrease, the electric field rises again and begins to oscillate in the intermediate region, where the relativistic effect becomes important. This investigation will be helpful in understanding future results of both experiment and simulation. [ABSTRACT FROM AUTHOR]

We consider the initial boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain Ω ⊂ ℝ2. Given any k distinct points in the domain, we develop a new inner‐outer gluing method to construct solutions that blow up exactly at those k points as t goes to a finite time T. Moreover, we obtain a precise description of the blowup. © 2021 Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for the energy critical heat equation{ut=Δu+u3in R4×(0,T),u(⋅,0)=u0in R4. (1){ut=Δu+u3in R4×(0,T),u(⋅,0)=u0in R4. (1)We find that for given points q1,q2,...,qkq1,q2,...,qk and any sufficiently small T>0T>0 there is an initial condition u0u0 such that the solution u(x,t)u(x,t) of (1) blows up at exactly those kk points with a type Ⅱ rate, namely larger than (T−t)−12(T−t)−12. In fact ∥u(⋅,t)∥∞∼(T−t)−1log2(T−t)‖u(⋅,t)‖∞∼(T−t)−1log2⁡(T−t). The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin-Talenti bubbles. [ABSTRACT FROM AUTHOR]

We construct infinite time blow-up solution to the following heat equation with Sobolev critical exponent and drift terms u t = Δ u + ∇ b (x) · ∇ u + u n + 2 n - 2 in R n × (0 , + ∞) , u (· , 0) = u 0 in R n , where b(x) is a smooth bounded function in R n with n ≥ 5 and the initial datum u 0 is positive and smooth. Let q j ∈ R n , j = 1 , … , k , be distinct nondegenerate local minimum points of b(x). Assume that an eigenvalue condition (1.6) is satisfied. We prove the existence of a positive smooth solution u(x, t) which blows up at infinite time near those points with the form u (x , t) ≈ ∑ j = 1 k α n μ j (t) μ j (t) 2 + | x - ξ j (t) | 2 n - 2 2 , as t → + ∞. Here ξ j (t) → q j and 0 < μ j (t) → 0 exponentially as t → + ∞ . [ABSTRACT FROM AUTHOR]

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics. [ABSTRACT FROM AUTHOR]

Since tungsten is considered as the optional divertor target material for the future fusion devices, e.g., China Fusion Engineering Test Reactor (CFETR), it is crucial to have a good screening of the tungsten impurity to keep a low core tungsten concentration. In this paper, based on the two-point model, possible divertor plasma parameters are predicted in high recycling regime for CFETR. Further analysis of tungsten ionization lengths shows that when target temperature is low enough (less than 15 eV), the increase of upstream density may cause an increase of ionization length, and thus a degradation of divertor tungsten screening effect may happen. The 2-D simulations of tungsten transport are then performed by using Osm-Eirene-Divimp edGE [onion skin model (OSM)-EIRENE-DIVvertor IMPurities (DIVIMP)] code package. The target plasma parameters, in the region of those predicted by the two-point model, are set as input in OSM-EIRNEN to generate the background plasma. DIVIMP code is used to further simulate the tungsten impurity transport process. The results reveal that although the decrease of target plasma temperature may reduce the tungsten impurity prompt redeposition rate, the benefit of a lower erosion rate can make compensation. Therefore, to control the core tungsten concentration, lower target plasma temperature is preferred in high recycling regime. [ABSTRACT FROM AUTHOR]