An optimal path to transition in a duct

This paper is concerned with the transition of the laminar flow in a duct of square cross-section. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown \citep{Biau_JFM_2008} that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the 'optimal' travelling wave associated to its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of a 'edge state' are conducted, to identify an unstable solution which mediates laminar-turbulent transition and relate it to results of the optimisation procedure

Aerospace medicine and biology: A continuing bibliography with indexes (supplement 352)

This bibliography lists 147 reports, articles and other documents introduced into the NASA Scientific and Technical Information System during July 1991. Subject coverage includes: aerospace medicine and psychology, life support systems and controlled environments, safety equipment, exobiology and extraterrestrial life, and flight crew behavior and performance

The Application of Physics Informed Neural Networks to Compositional Modeling

Compositional modeling is essential when simulating processes involving significant changes in reservoir fluid composition. It is computationally expensive because we typically need to predict the states and properties of multicomponent fluid mixtures at several different points in space and time. To speed up this process, several researchers have used machine learning algorithms to train deep learning (DL) models on data from the rigorous phase-equilibrium (flash) calculations. However, one shortcoming of the DL models is that there is no explicit consideration for the governing physics. So, there is no guarantee that the model predictions will honor the thermodynamical constraints of phase equilibrium (Ihunde & Olorode, 2022). This work is the first attempt to incorporate thermodynamics constraints into the training of DL models to ensure that they yield two-phase flash predictions that honor the physical laws that govern phase equilibrium. A space-filling mixture design is used to generate one million different compositions at different pressures (Ihunde & Olorode, 2022). Stability analysis and flash calculations are performed on these compositions to obtain the corresponding phase compositions and vapor fraction (Ihunde & Olorode, 2022). Physics-informed neural network (PINN) and standard deep neural network (DNN) models were trained to predict two-phase flash results using the data from the actual phase-equilibrium calculations (Ihunde & Olorode, 2022). Considering the stochasticity of the deep learning optimization process, we used the seven-fold cross-validation to obtain reliable estimates of average model accuracy and variance (Ihunde & Olorode, 2022). Comparing the PINN and standard DNN models reveals that PINNs can incorporate physical constraints into DNNs without significantly lowering the model accuracy (Ihunde & Olorode, 2022). The evaluation of the model results with the test data shows that both PINN and standard DNN models yield coefficients of determination of ~97% (Ihunde & Olorode, 2022). However, the root-mean-square error of the physics-constraint errors in the PINN model is over 55% lower than that of the standard DNN model (Ihunde & Olorode, 2022). This indicates that PINNs significantly outperform DNNs in honoring the governing physics. Finally, we demonstrate the significance of honoring the governing physics by comparing the resulting phase envelopes obtained from overall compositions computed from the PINN, DNN, and linear regression model predictions (Ihunde & Olorode, 2022)

Applying GSH to a Wide Range of Experiments in Granular Media

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: (i)~static stress distribution, clogging; (ii)~elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; (iii)~rapid dense flow: the $\mu$-rheology, Bagnold scaling and the stress minimum; (iv)~elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and nonlocal fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.Comment: arXiv admin note: substantial text overlap with arXiv:1207.128

Perturbation Theory and Phase Behavior Calculations Using Equation of State Models

Equations of State (EoS) live at the heart of all thermodynamic calculations in chemical engineering applications as they allow for the determination of all related fluid properties such as vapor pressure, density, enthalpy, specific heat, and speed of sound, in an accurate and consistent way. Both macroscopic EoS models such as the classic cubic EoS models as well as models based on statistical mechanics and developed by means of perturbation theory are available. Under suitable pressure and temperature conditions, fluids of known composition may split in more than one phases, usually vapor and liquid while solids may also be present, each one exhibiting its own composition. Therefore, computational methods are utilized to calculate the number and the composition of the equilibrium phases at which a feed composition will potentially split so as to estimate their thermodynamic properties by means of the EoS. This chapter focuses on two of the most pronounced EoS models, the cubic ones and those based on statistical mechanics incorporating perturbation analysis. Subsequently, it describes the existing algorithms to solve phase behavior problems that rely on the classic rigorous thermodynamics context as well as modern trends that aim at accelerating computations

The HBI in a quasi-global model of the intracluster medium

In this paper we investigate how convective instabilities influence heat conduction in the intracluster medium (ICM) of cool-core galaxy clusters. The ICM is a high-beta, weakly collisional plasma in which the transport of momentum and heat is aligned with the magnetic field. The anisotropy of heat conduction, in particular, gives rise to instabilities that can access energy stored in a temperature gradient of either sign. We focus on the heat-flux buoyancy-driven instability (HBI), which feeds on the outwardly increasing temperature profile of cluster cool cores. Our aim is to elucidate how the global structure of a cluster impacts on the growth and morphology of the linear HBI modes when in the presence of Braginskii viscosity, and ultimately on the ability of the HBI to thermally insulate cores. We employ an idealised quasi-global model, the plane-parallel atmosphere, which captures the essential physics -- e.g. the global radial profile of the cluster -- while letting the problem remain analytically tractable. Our main result is that the dominant HBI modes are localised to the the innermost (~<20%) regions of cool cores. It is then probable that, in the nonlinear regime, appreciable field-line insulation will be similarly localised. Thus, while radio-mode feedback appears necessary in the central few tens of kpc, heat conduction may be capable of offsetting radiative losses throughout most of a cool core over a significant fraction of the Hubble time. Finally, our linear solutions provide a convenient numerical test for the nonlinear codes that tackle the saturation of such convective instabilities in the presence of anisotropic transport.Comment: MNRAS, in press; minor modifications from v

Colloidal Gels: Equilibrium and Non-Equilibrium Routes

We attempt a classification of different colloidal gels based on colloid-colloid interactions. We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally we underline typical signatures of different gel types, to be looked in more details in experiments.Comment: topical review, accepted in J. Phys. Condens. Matte

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes