Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

Entropy and Turbulence Structure

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

Inferring metabolic fluxes in nutrient-limited continuous cultures: A Maximum Entropy Approach with minimum information

We propose a new scheme to infer the metabolic fluxes of cell cultures in a chemostat. Our approach is based on the Maximum Entropy Principle and exploits the understanding of the chemostat dynamics and its connection with the actual metabolism of cells. We show that, in continuous cultures with limiting nutrients, the inference can be done with limited information about the culture: the dilution rate of the chemostat, the concentration in the feed media of the limiting nutrient and the cell concentration at steady state. Also, we remark that our technique provides information, not only about the mean values of the fluxes in the culture, but also its heterogeneity. We first present these results studying a computational model of a chemostat. Having control of this model we can test precisely the quality of the inference, and also unveil the mechanisms behind the success of our approach. Then, we apply our method to E. coli experimental data from the literature and show that it outperforms alternative formulations that rest on a Flux Balance Analysis framework.

Relative Lagrangian Formulation of Finite Thermoelasticity

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

An overview of entropy principle

A brief overview of the development from classical linear irreversible thermodynamics to the modern rational thermodynamics with Coleman–Noll and Müller–Liu procedures is presented, emphasizing the basic assumptions and formulation details. The major arguments concerned are the improvement of physical assumptions and mathematical formulation differences. Extended thermodynamics is also briefly commented.

Engineering A Fluorescent Protein Color Switch Using Entropy-driven Beta Strand Exchange

Protein conformational switches are widely used in biosensing. They are typically composed of an input domain (which binds a target ligand) fused to an output domain (which generates an optical readout). A central challenge in designing such switches is to develop mechanisms for coupling the input and output signals via conformational change. Here, we create a biosensor in which binding-induced folding of the input domain drives a conformational shift in the output domain that results in a 6-fold green-to-yellow ratiometric fluorescence change in vitro, and a 35-fold intensiometric fluorescence increase in cultured cells. The input domain consists of circularly permuted FK506 binding protein (cpFKBP) that folds upon binding its target ligand (FK506 or rapamycin). cpFKBP folding induces the output domain, an engineered GFP variant, to replace one of its β-strands (containing T203 and specifying green fluorescence) with a duplicate β-strand (containing Y203 and specifying yellow fluorescence) in an intramolecular exchange reaction. This mechanism employs the loop-closure entropy principle, embodied by folding of the partially disordered cpFKBP domain, to couple ligand binding to the GFP color shift. This proof-of-concept design has the advantages of full genetic encodability, ratiometric or intensiometric response, and potential for modularity. The latter attribute is enabled by circular permutation of the input domain.