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In this paper, we study an optimal control problem for a stationary Navier–Stokes hemivariational inequality with control constraints and its numerical approximation. The hemivariational inequality is the weak formulation of a stationary incompressible fluid flow problem, modeled by the Navier-Stokes equations subject to a nonleak boundary condition and a subdifferential condition of friction type. We investigate the stability of the solution of the hemivariational inequality with respect to perturbations in the density of external force and superpotential, and demonstrate the existence of a solution for the optimal control problem with the external force density as the control. Moreover, we consider the numerical solution of the optimal control problem and show its convergence. As an example and for definiteness, the numerical solution is defined through the finite element method. [ABSTRACT FROM AUTHOR]

We numerically investigate the hydrodynamic interactions between two microswimmers in viscoelastic fluids at low Reynolds number regimes using the fictitious domain method. In the Newtonian fluid, after contact, pushers rotate toward each other and remain in a "trapped" state for a long time, induced by a counterclockwise viscous torque. We believe it is related to the asymmetrical surrounding vortexes. As the pushers approach, two positive vortexes merge into one, disrupting the vortex balance and inducing a net counterclockwise torque on the swimmers. But in the Giesekus viscoelastic fluids, an clockwise elastic torque modifies the pushers' rotations during early contact. Subsequently, two negative vortexes around the pushers merge, generating a clockwise torque that causes the swimmers to separate. Additionally, a huge elastic stretching effect is observed at the rear of the pullers, which restricts their swimming behavior through elastic force. Post-collision, the pullers rapidly separate with a large scattering angle in both Newtonian and viscoelastic fluids. However, neutral swimmers separate with unchanged orientations, and their trajectories remain consistently aligned across various Weissenberg numbers. Furthermore, the elastic force impedes the relative motions of the swimmers and alters the pressure and viscosity force. [ABSTRACT FROM AUTHOR]

The thermal-controlled fracture method has been increasingly focused upon in the high-quality cutting of advanced ceramic materials due to its excellent characteristics. The successful application of this method in cutting ceramics mainly depends on the volumetric heating effect. However, most ceramics are treated using the surface heating mode. For the surface heating mode, the processing quality, including fracture trajectory and fracture quality, is far lower than the industrial application standards. This work was conducted to reveal the mechanism of this processing quality. Experiments involving cutting ceramics in single-surface heating mode indicate that the fracture trajectories of the upper and lower surfaces display a significant inconsistency, and the fracture quality is worse than that using the dual-surface heating mode. A cutting model was established to calculate the thermal stress distribution and to simulate the crack-propagation behaviors. The simulation results show good agreement with the experiment and provide the stress distribution, and are used to understand the reason for the processing quality problem. The mechanism of the trajectory deviation and uneven distribution of the fracture quality is revealed based on the simulation and calculation results. This study helps provide a deep understanding of the processing problems arising from this method and thus helps to innovate high-quality processing methods in this field. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a dynamic adhesive contact model where the body is composed of a viscoelastic material with long memory. The adhesion process is modeled by a bonding field on part of the contact surface and on which the contact and the friction are modeled by nonmonotone Clarke subdifferential conditions with adhesion. Meanwhile, on another part of the contact surface, the contact is comprised of a normal compliance contact condition while the memory effects of the obstacle are considered, the friction is modeled by a version of Coulomb's law of dry friction and the friction bound is dependent on the normal stress. The variational form of the model generates a system of a doubly-history dependent variational–hemivariational inequality as well as a differential equation. Then, on the basis of the proof of abstract variational–hemivariational inequality, the existence and uniqueness results of the contact problem are established. [ABSTRACT FROM AUTHOR]

Motivation Topologically associating domains (TADs) are fundamental building blocks of 3D genome. TAD-like domains in single cells are regarded as the underlying genesis of TADs discovered in bulk cells. Understanding the organization of TAD-like domains helps to get deeper insights into their regulatory functions. Unfortunately, it remains a challenge to identify TAD-like domains on single-cell Hi-C data due to its ultra-sparsity. Results We propose scKTLD, an in silico tool for the identification of TAD-like domains on single-cell Hi-C data. It takes Hi-C contact matrix as the adjacency matrix for a graph, embeds the graph structures into a low-dimensional space with the help of sparse matrix factorization followed by spectral propagation, and the TAD-like domains can be identified using a kernel-based changepoint detection in the embedding space. The results tell that our scKTLD is superior to the other methods on the sparse contact matrices, including downsampled bulk Hi-C data as well as simulated and experimental single-cell Hi-C data. Besides, we demonstrated the conservation of TAD-like domain boundaries at single-cell level apart from heterogeneity within and across cell types, and found that the boundaries with higher frequency across single cells are more enriched for architectural proteins and chromatin marks, and they preferentially occur at TAD boundaries in bulk cells, especially at those with higher hierarchical levels. Availability and implementation scKTLD is freely available at https://github.com/lhqxinghun/scKTLD. [ABSTRACT FROM AUTHOR]

The main idea of this manuscript is to study an adhesive contact problem with long memory which is governed by a hemivariational inequality and a fractional differential equation. We first prove the existence of a unique solution of the fractional differential hemivariational inequality system. Subsequently, we consider a fully discrete scheme of this system and then focus on deriving error estimates for numerical solutions. To the tail of this manuscript, we present two numerical simulation examples for the adhesive contact problem, which provide numerical evidence to support our theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical method for an optimal control problem governed by an obstacle problem. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem with a simple method. The connection between the two formulations is established through some convergence results. A sufficient condition is derived to decide whether a solution of the first-order optimality system is a global minimum. The method with a second-order in time dissipative system is developed to solve the optimality system numerically. Several numerical examples are reported to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Rationale: An LC–MS/MS method was established to measure tigecycline in dried blood spots (DBSs). Methods: The DBS specimens obtained by applying 30 μl of blood to filter paper were extracted with hydrogen oxide and subsequently precipitated protein with perchloric acid, then the extract was directly analyzed by liquid chromatography tandem mass spectrometry. A Hypersil GOLD aQ column was utilized for separating the analytes, and detection was carried out in positive and selective reaction monitoring modes. The precursors to product ion transitions m/z 586.3 → 513.1 and m/z 586.3 → 569.2 were monitored for tigecycline, and m/z 473.2 → 456.0 and m/z 473.2 → 367.0 for 9‐amino minocycline as internal standard. Results: The validation parameters of specificity and selectivity, linearity (0.02–5 μg ml−1), sensitivity (limit of quantification 0.02 μg ml−1), intra‐ and interday precision (within 15%) and relative error (within ±15%) were acceptable. The recoveries were from 84.65% to 90.49% and from 85.41% to 95.72% for tigecycline and internal standard, respectively, and the matrix effect was not evident to influence accuracy. The impact of hematocrit on measurement of the analyte was negligible, and after preserving at ambient temperature for 24 h and at 4°C for 1 month it remained steady. Conclusions: The advantages of nonintrusive blood collection and micro‐volume sample requirements make DBS a potent surrogate to conventional venepuncture for sampling. [ABSTRACT FROM AUTHOR]

In this paper, we study a dynamic contact problem with Clarke subdifferential boundary conditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. The weak form of the model is governed by an evolutionary hemivariational inequality coupled with an integral equation. We study a fully discrete approximation scheme of the problem and bound the errors. Under appropriate solution regularity assumptions, optimal-order error estimates can be derived. Finally, a numerical example is also included to support our theoretical analysis. Particularly, it gives numerical evidence on the theoretically predicted optimal convergence order. [ABSTRACT FROM AUTHOR]