Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals

The dynamics of free and forced vibrations of a chain of particles are investigated in a harmonic model taking into account the retardation of interactions between atoms. It is found that the retardation of interactions between particles leads to the non-existence of stationary free vibrations of the crystal lattice. It is shown that in the case of a stable lattice, forced vibrations, regardless of the initial conditions, pass into a stationary regime. A non-statistical dynamic mechanism of the irreversible thermodynamic equilibration is proposed.

From Lithological Modelling to Groundwater Modelling: A Case Study in the Tiber River Alluvial Valley

This study presents the results of a research project financed by the Lazio Regional Government. The research focused on defining an integrated model of recent alluvial deposits in the Tiber River. To achieve this objective, geological boreholes were made to monitor the aquifer and in situ and laboratory tests carried out. The data obtained was used to detail stratigraphic aspects and improve the comprehension of water circulation beneath the recent alluvial deposits of the Tiber River in the urban area of Rome, between the Ponte Milvio bridge and the Tiber Island. The stratigraphic intervals recognised in the boreholes were parameterised based on their litho-technical characteristics. The new data acquired, and integrated with existing data in the CNR IGAG database, made it possible to produce a three-dimensional model of the lithologies in the study area.The model of the subsoil, simplified for applied reasons, was described in hy-drostratigraphic terms: three different lithotypes were subjected to piezometric levels monitor-ing. Finally, the research generated a numerical hydrological level in a stationary regime. In general, this study demonstrates how a numerical hydrogeological model calibrated by piezo-metric monitoring data can support the construction of a geological model, discarding or con-firming certain hypotheses and suggesting other means of reconstructing sedimentary bodies.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

Analysis for Flow of an Incompressible Brinkman-Type Fluid in Thin Medium with Friction

In this paper, we consider the Brinkman equation in the three-dimensional thin domain ℚ ε ⊂ ℝ 3 . The purpose of this paper is to evaluate the asymptotic convergence of a fluid flow in a stationary regime. Firstly, we expose the variational formulation of the posed problem. Then, we presented the problem in transpose form and prove different inequalities for the solution u ε , p ε independently of the parameter ε . Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.

The oscillatory longwave Marangoni convection in a thin film heated from below

A novel type of Marangoni convection was predicted theoretically a decade ago. The thin liquid film atop a substrate of low thermal conductivity was considered. In the case of heating from below, the Marangoni convection emerges not only in a conventional stationary regime, but also as oscillatory flows. Specifically, the oscillatory Marangoni convection emerges if (1) the heat flux from the free surface is small, and (2) the large-scale deformation of the free surface is allowed. During the past decade, this novel Marangoni convection was detected and investigated in several other theoretical works. The review discusses the recent achievements in studying the oscillatory Marangoni convection in a thin film heated from below. The guiding data for observation of the oscillatory regime are also provided.

On spatial matchings: The first-in-first-match case

We describe a process where two types of particles, marked red and blue, arrive in a domain at a constant rate. When a new particle arrives into the domain, if there are particles of the opposite color present within a distance of 1 from the new particle, then, among these particles, it matches to the one with the earliest arrival time, and both particles are removed. Otherwise, the particle is simply added to the system. Additionally, particles may lose patience and depart at a constant rate. We study the existence of a stationary regime for this process, when the domain is either a compact space or a Euclidean space. In the compact setting, we give a product-form characterization of the stationary distribution, and then prove an FKG-type inequality that establishes certain clustering properties of the particles in the steady state.

The Impact of Arid Climate on the Indoor Thermal Comfort in the South-East of Morocco

The main objective of this work is to study the heat transfer through an administrative building’s envelope in Errachidia City in Morocco. A numerical simulation based on the finite element method was made to describe the effect of introducing several thermal insulators (air, hemp wool, glass wool, rock wool, and extruded polystyrene) of different thicknesses (5 cm, 10 cm, and 15 cm) on the heat transfer through the building’s envelope under different climatic conditions. For the stationary regime, the summer period was chosen on August 7th, 2019, at 17 h, while the winter period was opted on January 1st, 2020, at 7 h. Otherwise, for the transitional regime, the summer period was chosen from August 1st to 8th, 2019, and the winter period from January first to 8th, 2020. The physical model analyzes the temperature variation at the different layers of the wall. It depends on the indoor temperature, the instantaneous climatic conditions of the outdoor air, solar radiations, and the thermal properties of the building’s envelope. The results show that the air gap is a good thermal insulator; it acts as a damper of temperature and heat flux.

Selective Determination of Hydrogen Sulfide Using SnO2–Ag Sensor Working in Non-Stationary Temperature Regime

The application of a non-stationary regime of temperature modulation in metal oxide semiconductor sensor based on SnO2–Ag leads not only to a strongly increased sensor response, but also to a considerably improved sensor selectivity toward hydrogen sulfide. Selectivity with respect to other reducing gases (CO, NH3, H2) is about five orders of magnitude, enabling a correct selective determination of H2S in the presence of interfering gas components.

A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems

Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

Endless elastic beam travelling on a moving rough surface with zones of stick and sliding

We study the planar deformation of a beam that travels across a given control domain supported by a moving rough plane, which is a prototype for various technological processes. A sufficiently small misalignment between the guideways at the ends of the domain results in a stationary regime of motion, which features a zone of sticking contact near the entry to the control domain, followed by infinitely many segments of transverse sliding with alternating directions. Self-similarity of this solution of an essentially nonlinear boundary value problem is the primary novel result of the present contribution. Closed-form analytic results are validated against a finite element simulation of the transient evolution process, which demonstrates stability of the obtained solution and provides insights regarding the characteristic time scales of establishing of subsequent zones of sliding.