Applications of Solvable Lie Algebras to a Class of Third Order Equations

A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic models for semiconductors considering quantum effects—for example, models for the transmission of electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family. For this family, all point symmetries have been derived. These symmetries are used to determine group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation (ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking into account the Type-II hidden symmetries that appear in the reduced second-order ODEs.

Mechanism of reduction of aeroacoustic sound by porous material: comparative study of microscopic and macroscopic models

The effects of porous material on the aeroacoustic sound generated in a two-dimensional low-Reynolds-number flow ( $Re=150$ ) past a circular cylinder are studied by direct numerical simulation in which the acoustic waves of small amplitudes are obtained directly as a solution to the compressible Navier–Stokes equations. Two models are introduced for the porous material: the microscopic model, in which the porous material is a collection of small cylinders, and the macroscopic model, in which the porous material is continuum characterized by permeability. The corrected volume penalization method is used to deal with the core cylinder, the small cylinders and the porous material. In the microscopic model, significant reduction of the aeroacoustic sound is found depending on the parameters; the maximum reduction of $24.4$ dB from the case of a bare cylinder is obtained. The results obtained for the modified macroscopic model are in good agreement with those obtained for the microscopic model converted by the theory of homogenization, which establishes that the microscopic and macroscopic models are consistent and valid. The detailed mechanism of sound reduction is elucidated. The presence of a fluid region between the porous material and the core cylinder is important for sound reduction. When the sound is strongly reduced, the pressure field behind the cylinder becomes nearly uniform with a high value to stabilize the shear layer in the wake; as a result, the vortex shedding behind the cylinder is delayed to the far wake to suppress the unsteady vortex motion near the cylinder, which is responsible for the aeroacoustic sound.

Metabolic Reaction Network-Based Model Predictive Control of Bioprocesses

Bioprocesses are increasingly used for the production of high added value products. Microorganisms are used in bioprocesses to mediate or catalyze the necessary reactions. This makes bioprocesses highly nonlinear and the governing mechanisms are complex. These complex governing mechanisms can be modeled by a metabolic network that comprises all interactions within the cells of the microbial population present in the bioprocess. The current state of the art in bioprocess control is model predictive control based on the use of macroscopic models, solely accounting for substrate, biomass, and product mass balances. These macroscopic models do not account for the underlying mechanisms governing the observed process behavior. Consequently, opportunities are missed to fully exploit the available process knowledge to operate the process in a more sustainable manner. In this article, a procedure is presented for metabolic network-based model predictive control. This procedure uses a combined moving horizon-model predictive control strategy to monitor the flux state and optimize the bioprocess under study. A CSTR bioreactor model has been combined with a small-scale metabolic network to illustrate the performance of the presented procedure.

Structural properties of nuclei with semi-magic number N(Z) = 40

In this paper, various ground state properties are explored for full isotonic(isotopic) chain of neutron number N [Formula: see text]proton number [Formula: see text] using different families of Relativistic Mean-Field theory. Several properties, such as nucleon separation energies, pairing energies, deformation, radii and nucleon density distributions, are evaluated and compared with the experimental data as well as those from other microscopic and macroscopic models. [Formula: see text] isotonic chain presents ample of support for the neutron magicity and articulates double magicity in recently discovered [Formula: see text]Ca and [Formula: see text]Ni. Our results are in close conformity with the recently measured value of charge radius of [Formula: see text]Ni [S. Kaufmann et al., Phys. Rev. Lett. 124 (2020) 132502] which supports the [Formula: see text] magicity. Contrarily, Zr isotopes ([Formula: see text]) display variety of shapes leading to the phenomenon of shape transitions and shape co-existence. The role of 3s[Formula: see text] state, which leads to central depletion if unoccupied, is also investigated. [Formula: see text]S and [Formula: see text]Zr are found to be doubly bubble nuclei.

A Conservative Macroscopic Model for Binary-mixture Fluidized Beds

Two approaches are commonly used for modeling the vertical mixing of binary-mixture fluidized beds, Computational Fluid Dynamics (CFD) and macroscopic modeling. A common realization of the latter one is the Gibiralo–Rowe (G-R) model, which uses the Two-Phase Theory. This macroscopic model obviously overperforms CFDs regarding computational cost; however, determining its coefficients is a still challenging issue. Although several methods were published for solving this, the general problem with most of them remains their neglecting the conservation of mass. In the present new procedure, the mass conservation is applied to correct the values of the G-R model coefficients estimated from known equations. The present model was validated on a wide variety of fluidized bed systems. The results show that this conservative and macroscopic model gives more accurate predictions than the recently published other macroscopic models, and this one is, in general, better than the CFD model from the perspective of prediction accuracy as well.

On the Verification of the Pedestrian Evacuation Model

In this article we deal with numerical solution of macroscopic models of pedestrian movement. From a macroscopic point of view, pedestrian movement can be described by a system of first order hyperbolic equations similar to 2D compressible inviscid flow. For the Pedestrian Flow Equations (PFEs) the density ρ and the velocity v are considered as the unknown variables. In PFEs, the social force is also taken into account, which replaces the outer volume force term used in the fluid flow formulation, e.g., the pedestrian movement is influenced by the proximity of other pedestrians. To be concrete, the desired direction μ of the pedestrian movement is density dependent and is incorporated in the source term. The system of fluid dynamics equations is thus coupled with the equation for μ. The main message of this paper is the verification of this model. Firstly, we propose two approaches for the source term discretization. Secondly, we propose two splitting schemes for the numerical solution of the coupled system. This leads us to four different numerical methods for the PFEs. The novelty of this work is the comparative study of the numerical solutions, which shows, that all proposed methods are in the good agreement.

Mesoscopic Modeling and Rapid Simulation of Incremental Changes in Epidemic Scenarios

In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what-if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that attempts to strike a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors such as at the individual entity level. The mesoscopic approach offers the possibility of incorporating complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also provides an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple data (SIMD). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what-if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what-if scenario tree evaluation has been implemented in software on modern GPUs. Synthetic simulation scenarios are explored and presented here to demonstrate the basic feasibility and computational characteristics of our approach. Results from the experiments on large population data illustrate the overall modeling methodology and computational run time performance on large numbers of synthetically generated what-if scenarios.

Model-Based Dynamic Toll Pricing: An Overview

In this paper, we review some of the most recent research regarding design, simulation, implementation and evaluation of dynamic tolling schemes. Analyzing the structure of the reviewed studies, we identify the common elements and the differences in the approaches chosen by different authors, presenting an overview of the methods for price definition and of the simulation techniques as well as a discussion on the newest technology applications in the field. Optimization revealed to be the dominant price definition method, while control-based algorithms are notably employed for managed lanes toll pricing schemes. Regarding traffic and driver behavior simulation we observed a great variety of solutions throughout the reviewed papers, with a prevalence of macroscopic models for the former and logit models for the latter. Still few papers include models for externalities quantification, while AI paradigms are gaining importance in the field.