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Coupled constitutive relations: a second law based higher-order closure for hydrodynamics.

ABSTRACT: In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic descrip- tion is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which cannot be predicted by the classical Navier-Stokes-Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.

SUBMITTER: Rana AS

PROVIDER: S-EPMC6237507 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature

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Coupled constitutive relations: a second law based higher-order closure for hydrodynamics.

Rana Anirudh Singh AS Gupta Vinay Kumar VK Struchtrup Henning H

Proceedings. Mathematical, physical, and engineering sciences 20181017 2218

In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic descrip- tion is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. ...[more]

PMID: 30839822

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Project description:It is increasingly being recognized that physical interactions between distant chromosomal loci influence the expressivity of the genome. Thus, multiple enhancers may converge on a single gene promoter 1,2 and a single enhancer can stochastically loop to multiple promoters 3. Regulatory elements from neighboring domains or from other chromosomes may interact to generate chromatin structures poised for transcription4-8 or repression 9-11. However, a broader perspective on the formation and function of such networks remains largely unexplored. Using the high-resolution 4C (Circular Chromosome Conformation Capture) analysis, we identify here a genome-wide physical network between genomically imprinted domains impinging H19 imprinting control region (ICR). Sequences interacting with the H19 ICR constitutively map at or within most of known imprinted domains both in mouse embryonic stem cells and in vitro-derived embryoid bodies, despite distinct differences in chromatin environments. Moreover, all-to-all 3D DNA FISH analyses revealed that imprinted domains from 7 different chromosomes co-localize with each other in pair-wise patterns, highlighting the dynamic nature of these interactions. The observed interaction network is dependent on CTCF binding sites within the maternally inherited H19 ICR allele and delays reprogramming of epigenetic features at imprinted domains during male germline development. As other imprinted regions can interact with each other in an H19 ICR-dependent manner, the H19 ICR emerges as an organizer of chromosomal networks by specifically recognizing and reconfiguring imprinted domains. We propose that an ancient key regulatory region, such as the H19 ICR, gradually impacted epigenetic modifications via long-range interactions in the germline to facilitate the recruitment of imprinted genes and their formation in clusters during mammalian radiation. Furthermore, the perspective of epigenetic lesions de-stabilizing such chromosomal networks may advance our understanding of how quantitative traits influence human diseases, such as cancer.

Dataset Information

Coupled constitutive relations: a second law based higher-order closure for hydrodynamics.

Publications

Coupled constitutive relations: a second law based higher-order closure for hydrodynamics.

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