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Flow studies in control structures require the development of nonlinear differential equations that have no analytical solution but can be approximated by applying the finite volume method in mathematical models such as Fluent. This article presents a comparative analysis between a numerical model and a physical model of water flow in a laboratory channel using ANSYS Fluent. The scope of the study includes the development of a 2D model of the laboratory channel with a control section of a sliding flat rectangular gate and the mathematical development of the Navier-Stokes equations to model a biphasic flow of water and air throughout the computational domain, using appropriate boundary conditions. The methodology employed numerical simulation techniques using ANSYS Fluent, applying the finite volume method to solve the flow equations, and experimental techniques through direct measurements taken in the laboratory. The results demonstrate a 95.46% similarity between the mathematical modeling, direct measurements, and analytical calculations. Variables such as discharge coefficient, flow profiles, velocities at different points in the channel, and pressure distribution remained consistent throughout the computational domain. In conclusion, the advantages of the numerical model over the physical model are highlighted, emphasizing its efficiency and cost-effectiveness by allowing easy and simultaneous modifications in problem configurations, turbulence models, and boundary conditions. Additionally, the importance of the numerical model is highlighted by providing more accurate results than direct measurements made on the physical model, especially in turbulent areas and in the interaction of biphasic flow in the channel and gate. Finally, it is important to include a sensitivity analysis and mesh refinement in the mathematical model in such studies to avoid fluctuations near the gate where the section contracts. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A characterization of the migratory phenomenon is presented, from the macro level with implications for public policies, from its causes, effects, using dynamic systems, non-linear and complex differential equation systems at the macro, institutional, meso-organizational level and as a complete system through level of interaction of individual networks. A mathematical model of differential equations is presented to explain the relationship between migration and organizations, to explain the complex phenomenon of migration, and the complexity of the dynamic system. [ABSTRACT FROM AUTHOR]

The fundamental ideas of the multi-scale analysis of perturbations, also called quasi-stationary method, for soliton-like solutions are exposed. In this approach the perturbed nonlinear differential equations are linearized by expanding the solutions around the undisturbed solutions. Consequently, the auto-functions of the linearized operator are calculated to obtain the disturbances of the solitonic solution. Moreover, the evolution of non-linear structures contained in the non-linear Schrödinger equation and cubic-fifth nonlinear Schrödinger equation with damping is studied. The solutions show the variation of the soliton parameters due to this effect. [ABSTRACT FROM AUTHOR]

One failure of the Black-Scholes valuation model is to assume that the trading activities of agents have no effect on prices, an assumption that it can only be fulfilled in perfectly liquid markets, making the model very restrictive. This element has already been considered in some studies that incorporate the effect of agents' trading activities assuming a continuous process for price dynamics, however, financial markets show that a better description of the price dynamics of Risky assets must incorporate random jumps. The contribution of this document is to consider the problem of the valuation of derivatives in illiquid markets where the price of the underlying asset follows a diffusion process with jumps. The corresponding non-linear partial differential equation of valuation is presented and the trading strategy that minimizes the variance of the hedge is described. [ABSTRACT FROM AUTHOR]

Market models are considered in which a liquidity factor associated with price dynamics and the agents' trading strategies is incorporated. The case is studied in which the liquidity factor is a deterministic function of the price and another in which this factor is stochastic described by a Cox-Ingersoll-Ross process. Different types of trading strategies are considered and the stochastic differential equations for price dynamics as well as the corresponding nonlinear partial differential equations for the valuation of contingent assets are explicitly established. [ABSTRACT FROM AUTHOR]

Copyright of Journal de Ciencia e Ingeniería is the property of Corporacion Universitaria Autonoma del Cauca and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista CienciaUAT is the property of Universidad Autonoma de Tamaulipas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present the fundamentals of option pricing problem in a less restrictive contexts than the one proposed by Black-Scholes using nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator. [ABSTRACT FROM AUTHOR]

In this paper the local segment attractiveness equilibrium that forms on the phenomenon of zip bifurcation for a three-dimensional system of differential equations nonlinear is studied. This work may be regarded as a generalization as a result on Farkas's zip bifurcation in competition models. [ABSTRACT FROM AUTHOR]

Copyright of Revista Tecno Lógicas is the property of Instituto Tecnologico Metropolitano and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)