An initial-boundary value problem is considered for one-dimensional isothermal equations of the dynamics of viscous compressible multicomponent media, which are a generalization of the Navier--Stokes equations. We prove the stabilization of the solution to the initial-boundary value problem while the time tends to infinity, without simplifying assumptions for the structure of the viscosity matrix, except for the standard physical requirements of symmetry and positive definitenes.

The thermal lubrication of an entangled polymeric liquid in wall-driven shear flows between parallel plates is investigated by using a multiscale hybrid method coupling molecular dynamics and the hydrodynamics (i.e., the synchronized molecular dynamics method). The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value. The rheological properties of the polymeric liquid drastically change at around the critical drive force. In the weak viscous-heating regime, the conformation of polymer chains is dominated by the local shear flow so that the anisotropy of the bond orientation tensor grows as the drive force increases. However, in the large viscous-heating regime, the conformation dynamics is dominated by the thermal agitation of polymer chains so that the bond orientation tensor recovers more uniform and random structures as the drive force increases, even though the local shear flows are further enhanced. Remarkably, these counter-intuitive transitional behaviors give an interesting re-entrant transition in the stress--optical relation, where a linear formalism in the stress--optical relation approximately holds even though each of the macroscopic quantities behaves nonlinearly. The robustness of the linear stress--optical relation is also confirmed in the spatiotemporal evolution at the hydrodynamic level.

Optimal control has emerged as an indispensable tool in the domain of mechanical robotic systems. The dynamic processes under consideration in this paper are characterized by differential equations with an unknown coefficient. The problem addressed is time-optimal and exhibits bilinear characteristics. To investigate this inverse optimal problem, the classical method has been employed alongside Pontryagin’s Maximum Principle (PMP). This article aims to provide an exact piecewise function for controlling trajectories, specifically accounting for viscous friction. The goal is to determine the reachability set and to find the minimal process time. Notably, no simplifying assumptions were made during the analytical transformations.

This study addresses an alternative use of viscous dampers (VDs) associated with buckling restrained braces (BRBs) as the innovative seismic protection devices. For this, 4, 8 and 12 storey steel frames were designed with 6.5 m equal span length and 4 m storey height. Thereafter, the VDs and BRBs were placed over the height of each frame considering three different configurations. The structures were modeled using SAP2000 finite element program and evaluated by the nonlinear time history analyses subjected to the six natural accelerograms (1976 Gazlı, 1978 Tabas, 1987 Superstition Hills, 1992 Cape Mendocino, 1994 Northridge and 1999 Chi-Chi). The structural response of the structures with and without VDs and BRBs were studied in terms of variation in the displacement, interstorey drift, absolute acceleration, maximum base shear, time history of roof displacement. The results clearly indicated that the application of VDs and BRBs had remarkable improvement in the earthquake performance of the case study frames by reducing the local/global deformations in the main structural systems and satisfied the serviceability.

The most important plastic resins used for wire coating are Polyvinyl Chloride (PVC), Nylon, Polysulfone and Low-high density polyethylene (LDPE / HDPE). In this article,the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adomian decomposition method (ADM). The convergence of the series solution is established. The results are also verified by Optimal Homotopy Asymptotic Method (OHAM). The effect of different emerging parameters such as non-Newtonian parameters α and β, magnetic parameter M and the Brinkman number Br on solutions (velocity and temperature profiles) are discussed through several graphs. Additionally, the current result also compares with the published work already available in the literature.

This research provides a computationally efficient numerical tool for predicting 3-D turbulent flows over hydrofoils. It addresses a gap in existing numerical methods by extending the capabilities of the laminar VIScous Vorticity Equation (VISVE) solver to handle 3-D turbulent flow scenarios. The implementation integrates the k − ω SST model into the 3-D VISVE solver using the Finite Volume Method (FVM), extending its capability to handle turbulent flows. The turbulence model is also parallelized to improve computational efficiency. The application of the newly developed model to 3-D hydrofoil cases expands its scope and serves as preparatory work for future rotational propeller applications. Rigorous testing includes a convergence analysis concerning grid numbers and time step sizes, and validation against a Reynolds-Averaged Navier-Stokes (RANS) solver ensures the reliability and accuracy of the enhanced VISVE solver for turbulent flow simulations. The turbulent VISVE solver offers advantages such as reduced computational domain and costs through a vorticity-based approach. Turbulence concentration within boundary layers and free shear flows does not compromise the advantages of the small computational domain. The simplified meshing process, automatically generated by denoting the number of panels on the hydrofoil, makes the solver accessible for researchers and engineers.

A computational methodology for the hydrodynamic analysis of horizontal axis marine current turbines is presented. The approach is based on a boundary integral equation method for inviscid flows originally developed for marine propellers and adapted here to describe the flow features that characterize hydrokinetic turbines. To this purpose, semi-analytical trailing wake and viscous-flow correction models are introduced. A validation study is performed by comparing hydrodynamic performance predictions with two experimental test cases and with results from other numerical models in the literature. The capability of the proposed methodology to correctly describe turbine thrust and power over a wide range of operating conditions is discussed. Viscosity effects associated to blade flow separation and stall are taken into account and predicted thrust and power are comparable with results of blade element methods that are largely used in the design of marine current turbines. The accuracy of numerical predictions tend to reduce in cases where turbine blades operate in off-design conditions.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

Intracranial compliance (ICC) plays a pivotal role in understanding the underlying mechanisms of various brain disorders and is of great clinical importance. Therefore, addressing the challenges in practical application of ICC is crucial for neurosurgeons. This study explored the significance of ICC assessment considering the time-dependency of specific brain disorders through two distinct approaches: short and large time elapsed (TE) in measuring volume or intracranial pressure (ICP) changes in the ICC equation (∆Volume/∆ICP). Variations in ICC values were observed across various ICC assessment methods and different TE values. Notably, the compensatory response of the brain exhibited non-monotonic and variable changes in a large TE for certain brain disorders, diverging from patterns observed in short TE assessments. Furthermore, the recovery behavior of the brain changed under different brain disorders when exposed to short and long TE conditions. These findings emphasized the dynamic nature of ICC and provided valuable insights into the correct practical assessment of ICC by selecting the appropriate TE, as well as considering the differences in strain rates and loading durations on the brain in different brain disorders. These insights also shed light on the reasons why, despite its clinical significance, ICC monitoring has not yet become a standard component of clinical care, unlike ICP monitoring.

In this study, deep neural network (DNN) and transfer learning (TL) techniques were employed to predict the viscous resistance and wake distribution based on the positions of flow control fins (FCFs) applied to containerships of various sizes. Both methods utilized data collected through Computational Fluid Dynamics (CFD) analysis. The position of the flow control fin (FCF) and hull-form information were utilized as input data, and the output data included viscous resistance coefficients and components of propeller axial velocity. The base DNN model was trained and validated using a source dataset from a 1000 TEU containership. Grid search cross-validation technique was employed to optimize the hyperparameters of the base DNN model. Then, transfer learning was applied to predict the viscous resistance and wake distribution for containerships of varying sizes. To enhance the accuracy of feature prediction with a limited amount of dataset, learning rate optimization was conducted. Transfer learning involves retraining and reconfiguring the base DNN model, and the accuracy was verified based on the fine-tuning method of the learning model. The results of this study can provide hull designers for containerships with performance evaluation information by predicting wake distribution, without relying on CFD analysis.

The paper proves the existence of a family of axisymmetric equilibrium figures as solutions of a stationary problem with unknown boundaries for the Navier–Stokes equations corresponding to the slow rotation of a viscous compressible two-layer liquid mass about some axis. It is assumed that the liquids are barotropic, capillary and have different viscosities, the internal fluid being bounded by a closed surface. This interface does not intersect with the external boundary of the cloud. The proof is based on implicit function theorem and carried out in the Hölder spaces.