Restrictions on the Material Coefficients in the Constitutive Theories for Non-Classical Viscous Fluent Continua

This paper considers conservation and balance laws and the constitutive theo-ries for non-classical viscous fluent continua without memory, in which in-ternal rotation rates due to the velocity gradient tensor are incorporated in the thermodynamic framework. The constitutive theories for the deviatoric part of the symmetric Cauchy stress tensor and the Cauchy moment tensor are de-rived based on integrity. The constitutive theories for the Cauchy moment tensor are considered when the balance of moments of moments 1) is not a balance law and 2) is a balance law. The constitutive theory for heat vector based on integrity is also considered. Restrictions on the material coefficients in the constitutive theories for the stress tensor, moment tensor, and heat vector are established using the conditions resulting from the entropy inequa-lity, keeping in mind that the constitutive theories derived here based on inte-grity are in fact nonlinear constitutive theories. It is shown that in the case of the simplest linear constitutive theory for stress tensor used predominantly for compressible viscous fluids, Stokes’ hypothesis or Stokes’ assumption has no thermodynamic basis, hence may be viewed incorrect. Thermodynamically consistent derivations of the restrictions on various material coefficients are presented for non-classical as well as classical theories that are applicable to nonlinear constitutive theories, which are inevitable if the constitutive theo-ries are derived based on integrity

From START to FINISH : the influence of osmotic stress on the cell cycle

Peer reviewedPublisher PD

Bayesian Orthogonal Least Squares (BOLS) algorithm for reverse engineering of gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>A reverse engineering of gene regulatory network with large number of genes and limited number of experimental data points is a computationally challenging task. In particular, reverse engineering using linear systems is an underdetermined and ill conditioned problem, i.e. the amount of microarray data is limited and the solution is very sensitive to noise in the data. Therefore, the reverse engineering of gene regulatory networks with large number of genes and limited number of data points requires rigorous optimization algorithm.</p> <p>Results</p> <p>This study presents a novel algorithm for reverse engineering with linear systems. The proposed algorithm is a combination of the orthogonal least squares, second order derivative for network pruning, and Bayesian model comparison. In this study, the entire network is decomposed into a set of small networks that are defined as unit networks. The algorithm provides each unit network with P(D|H_i), which is used as confidence level. The unit network with higher P(D|H_i) has a higher confidence such that the unit network is correctly elucidated. Thus, the proposed algorithm is able to locate true positive interactions using P(D|H_i), which is a unique property of the proposed algorithm.</p> <p>The algorithm is evaluated with synthetic and <it>Saccharomyces cerevisiae </it>expression data using the dynamic Bayesian network. With synthetic data, it is shown that the performance of the algorithm depends on the number of genes, noise level, and the number of data points. With Yeast expression data, it is shown that there is remarkable number of known physical or genetic events among all interactions elucidated by the proposed algorithm.</p> <p>The performance of the algorithm is compared with Sparse Bayesian Learning algorithm using both synthetic and <it>Saccharomyces cerevisiae </it>expression data sets. The comparison experiments show that the algorithm produces sparser solutions with less false positives than Sparse Bayesian Learning algorithm.</p> <p>Conclusion</p> <p>From our evaluation experiments, we draw the conclusion as follows: 1) Simulation results show that the algorithm can be used to elucidate gene regulatory networks using limited number of experimental data points. 2) Simulation results also show that the algorithm is able to handle the problem with noisy data. 3) The experiment with Yeast expression data shows that the proposed algorithm reliably elucidates known physical or genetic events. 4) The comparison experiments show that the algorithm more efficiently performs than Sparse Bayesian Learning algorithm with noisy and limited number of data.</p

Microbiome to Brain:Unravelling the Multidirectional Axes of Communication

The gut microbiome plays a crucial role in host physiology. Disruption of its community structure and function can have wide-ranging effects making it critical to understand exactly how the interactive dialogue between the host and its microbiota is regulated to maintain homeostasis. An array of multidirectional signalling molecules is clearly involved in the host-microbiome communication. This interactive signalling not only impacts the gastrointestinal tract, where the majority of microbiota resides, but also extends to affect other host systems including the brain and liver as well as the microbiome itself. Understanding the mechanistic principles of this inter-kingdom signalling is fundamental to unravelling how our supraorganism function to maintain wellbeing, subsequently opening up new avenues for microbiome manipulation to favour desirable mental health outcome

Giesekus Constitutive Model for Thermoviscoelastic Fluids based on Ordered Rate Constitutive Theories

This paper presents derivation of Giesekus constitutive model in Eulerian description based on ordered rate constitutive theories for thermoviscoelastic fluids for compressible and incompressible cases in contra-, co-variant and Jaumann bases. The ordered rate constitutive theories for thermoviscoelastic fluids of orders (m, n) consider convected time derivative of order m of the deviatoric Cauchy stress tensor in a chosen basis (i.e. co-, contra-variant or Jaumann) as dependent variable in the development of constitutive theories for the stress tensor. Its argument tensors consist of density, temperature, convected time derivatives of the deviatoric Cauchy stress tensor of up to order m-1 and convected time derivative of up to order n of the conjugate strain tensor. In addition, constitutive theory for the heat vector compatible with the constitutive theory for the deviatoric stress tensor is also presented in co-, contra-variant and Jaumann bases. It is shown that the Giesekus constitutive model is a subset of the rate constitutive theory of orders m = n = 1. It is also shown that the deviatoric Cauchy stress tensor (contra-, co-variant or Jaumann basis) naturally results as dependent variable in the constitutive theory, and that currently used Giesekus constitutive model in deviatoric polymer Cauchy stress tensor is not derivable based on axioms and principles of the constitutive theory in continuum mechanics. Numerical studies are presented for fully developed flow between parallel plates for a dense polymeric liquid using the Giesekus constitutive model derived in this paper as well as currently used model