Global smooth solutions of the compressible Navier–Stokes equations with density-dependent viscosity

AbstractIn this paper we study a free boundary problem for the viscous, compressible, heat conducting, one-dimensional real fluids. More precisely, the viscosity is assumed to be a power function of density, i.e., μ(ρ)=ρα, where ρ denotes the density of fluids and α is a positive constant. In addition, the equations of state include and are more general than perfect flows which only depend linearly on temperature. The global existence (uniqueness) of smooth solutions is established with α∈(0,12] for general, large initial data, which improves the previous results. Moreover, it is also shown that the solutions will not develop vacuum, mass concentration or heat concentration in a finite time provided the initial data are bounded and smooth, and do not contain vacuum

The High-dimensional Phase Diagram and the Large CALPHAD Model

When alloy systems comprise more than three elements, the visualization of the entire phase space becomes not only daunting but is also accompanied by a data surge. Addressing this complexity, we delve into the FeNiCrMn alloy system and introduce the Large CALPHAD Model (LCM). The LCM acts as a computational conduit, capturing the entire phase space. Subsequently, this enormous data is systematically structured using a high-dimensional phase diagram, aided by hash tables and Depth-first Search (DFS), rendering it both digestible and programmatically accessible. Remarkably, the LCM boasts a 97% classification accuracy and a mean square error of 4.80*10-5 in phase volume prediction. Our methodology successfully delineates 51 unique phase spaces in the FeNiCrMn system, exemplifying its efficacy with the design of all 439 eutectic alloys. This pioneering methodology signifies a monumental shift in alloy design techniques or even multi-variable problems

Global existence of solutions for compressible Navier–Stokes equations with vacuum

AbstractIn this paper, we will investigate the global existence of solutions for the one-dimensional compressible Navier–Stokes equations when the density is in contact with vacuum continuously. More precisely, the viscosity coefficient is assumed to be a power function of density, i.e., μ(ρ)=Aρθ, where A and θ are positive constants. New global existence result is established for 0<θ<1 when the initial density appears vacuum in the interior of the gas, which is the novelty of the presentation

Mass accumulation rate changes in Chinese loess during MIS 2, and asynchrony with records from Greenland ice cores and North Pacific Ocean sediments during the Last Glacial Maximum

Sensitivity-corrected quartz optically stimulated luminescence (OSL) dating methods have been widely accepted as a promising tool for the construction of late Pleistocene chronology and mass or dust accumulation rates (MARs or DARs) on the Chinese Loess Plateau (CLP). Many quartz OSL ages covering marine isotope stage (MIS) 2 (equal to L1-1 in Chinese loess) have been determined for individual sites within the CLP in the past decade. However, there is still a lack of detailed MAR or DAR reconstruction during MIS 2 across the whole of the CLP. Here, we present detailed MARs determined for eight sites with closely-spaced quartz OSL ages covering MIS 2, and relative MARs suggested by a probability density analysis of 159 quartz OSL ages ranging from 30 to 10 ka ago, from 15 sites on the CLP. The results show enhanced dust accumulation during the Last Glacial Maximum (LGM), with particularly rapid dust accumulation from 23 to 19 ka ago (the late LGM). In contrast, MARs determined for the last deglaciation (from 19 to 12 ka ago) are low. The MAR changes during MIS 2 in Chinese loess are mainly controlled by the East Asian winter monsoon (EAWM) intensity, which is forced by Northern Hemisphere ice volume. The MAR changes also indicate that dust accumulation during MIS 2 is generally continuous at millennial time scales on the CLP. Comparison of Asian-sourced aeolian dust MARs in Chinese loess with those preserved in Greenland ice cores and North Pacific Ocean sediments indicates that rapid dust accumulation occurred from 26 to 23 ka ago (the early LGM) in Greenland ice cores and North Pacific Ocean sediments, suggesting a several kilo-year difference in timing when compared with the rapid dust accumulation during the late LGM in Chinese loess. This asynchronous timing in enhanced dust accumulation is probably related to both changes in the EAWM intensity and changes in the mean position of zone axis of the Westerly jet, both of which are greatly influenced by Northern Hemisphere ice volume. This study highlights the possible influence of changes in the mean position of zone axis of the Westerly jet on long-range transport of Asian-sourced dust.</p

Late Holocene anti-phase change in the East Asian summer and winter monsoons

Changes in East Asian summer and winter monsoon intensity have played a pivotal role in the prosperity and decline of society in the past, and will be important for future climate scenarios. However, the phasing of changes in the intensity of East Asian summer and winter monsoons on millennial and centennial timescales during the Holocene is unclear, limiting our ability to understand the factors driving past and future changes in the monsoon system. Here, we present a high resolution (up to multidecadal) loess record for the last 3.3 ka from the southern Chinese Loess Plateau that clearly demonstrates the relationship between changes in the intensity of the East Asian summer and winter monsoons, particularly at multicentennial scales. At multimillennial scales, the East Asian summer monsoon shows a steady weakening, while the East Asian winter monsoon intensifies continuously. At multicentennial scales, a prominent similar to 700-800 yr cycle in the East Asian summer and winter monsoon intensity is observed, and here too the two monsoons are anti-phase. We conclude that multimillennial changes are driven by Northern Hemisphere summer insolation, while multicentennial changes can be correlated with solar activity and changing strength of the Atlantic meridional overturning circulation. (C) 2018 Elsevier Ltd. All rights reserved

Strengthening of CoNiFeV0.5Mo0.2 Medium Entropy Alloy Wire Rods with Loading-Unloading Cycles

Changes in the texture as well as mechanical properties of CoNiFeV0.5Mo0.2 medium entropy alloy wire rods during loading&ndash;unloading are investigated. The intensity of the recrystallization texture {001}&lt;110&gt; component and fraction of low angle grains increase with the loading&ndash;unloading cycles and the alloy strength increases (934 MPa to 1083 MPa) due to dislocation increment in the loading&ndash;unloading cycles. The loading modulus (El) and average modulus (Esecant) for a hysteresis loop decrease slightly, whereas the unloading modulus (Eun) increases, the Eun increment of 5-TC-UTand 10-TC-UT are 22 and 137 GPa

Strengthening of CoNiFeV_0.5Mo_0.2 Medium Entropy Alloy Wire Rods with Loading-Unloading Cycles

Changes in the texture as well as mechanical properties of CoNiFeV0.5Mo0.2 medium entropy alloy wire rods during loading–unloading are investigated. The intensity of the recrystallization texture {001} component and fraction of low angle grains increase with the loading–unloading cycles and the alloy strength increases (934 MPa to 1083 MPa) due to dislocation increment in the loading–unloading cycles. The loading modulus (El) and average modulus (Esecant) for a hysteresis loop decrease slightly, whereas the unloading modulus (Eun) increases, the Eun increment of 5-TC-UTand 10-TC-UT are 22 and 137 GPa