Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.

Semi-analytical Evaluation of Entropy Generation in 1-D Heat Conduction with Variable Thermal Conductivity

In the present study, steady state heat transfer in a slab is analysed by applying the principle of variation calculus to the entropy generation minimization. The governing equation of the phenomena is obtained by minimizing the total entropy generation over the slab by considering the irreversibility and variation of thermal conductivity as a function of spatial co-ordinates. The governing equation is solved to obtain the temperature distribution, internal heat generation due to irreversibility, entropy generation number and entropy transport into system. The apparent heat sources that come into existence because of the irreversibility in heat diffusion have made the minimization of entropy generation feasible.

Balanced Dynamics and Moisture Quasi-Equilibrium in DYNAMO Convection

Tropical convection that occurs on large-enough space and time scales may evolve in response to large-scale balanced circulations. In this scenario, large-scale midtropospheric vorticity anomalies modify the atmospheric stability by virtue of thermal wind gradient balance. The convective vertical mass flux and the moisture profile adjust to changes in atmospheric stability that affect moisture and entropy transport. We hypothesize that the convection observed during the 2011 DYNAMO field campaign evolves in response to balanced dynamics. Strong relationships between midtropospheric vorticity and atmospheric stability confirm the relationship between the dynamic and the thermodynamic environments, while robust relationships between the atmospheric stability, the vertical mass flux, and the saturation fraction provide evidence of moisture adjustment. These results are important because the part of convection that occurs as a response to balanced dynamics is potentially predictable. Furthermore, the diagnostics used in this work provide a simple framework for model evaluation, and suggest that one way to improve simulations of large-scale organized deep tropical convection in global models is to adequately capture the relationship between the dynamic and thermodynamic environments in convective parameterizations.

Mechanisms in the hypersonic laminar near wake of a blunt body

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

Eddy Viscosity and Reynolds Stress Models of Entropy Generation in Turbulent Channel Flows

This paper presents new models of entropy production for incompressible turbulent channel flows. A turbulence model is formulated and analyzed with direct numerical simulation (DNS) data. A Reynolds-averaged Navier–Stokes (RANS) approach is used and applied to the turbulence closure of mean and fluctuating variables and entropy production. The expression of the mean entropy production in terms of other mean flow quantities is developed. This paper presents new models of entropy production by incorporating the eddy viscosity into the total shear stress. Also, the Reynolds shear stress is used as an alternative formulation. Solutions of the entropy transport equations are presented and discussed for both laminar and turbulent channel flows.