Search results for "Balance equation"

Closed-form solutions of the energy balance equation for drip laterals under the Darcy-Weisbach resistance formula

2018

Many studies have investigated easy methods to design drip laterals, as well as the best resistance equation to use, which is fundamental to accurately account for friction losses. This paper addresses both the features of lateral design relationships and the influence of the friction-loss equation on the design variables. First, simple closed-form solutions of the energy balance equation for both sloped and horizontal drip laterals are derived with the simplified Darcy-Weisbach resistance formula by assuming the Darcy friction factor as invariant versus the Reynolds number. Second, an error analysis is performed assuming the friction factor as constant in the design, which is compared to u…

The distribution of velocities in an ensemble of accelerated particles on a surface

2016

An ensemble of particles diffusing with acceleration on a surface is considered as a 2D billiard system. The process of the finite-time diffusion of particles is studied using the balance equation. The probability distribution functions of the velocity and lifetime of particles are obtained analytically and by means of numerical simulations. A thermodynamic interpretation of the process is discussed. The effective temperature and entropy obey the relationship for an ideal gas.

An intelligent Proportional controller of a Seeded Batch Crystallizer

2020

Crystallization process is used in a very wide range of industrial applications. However, highly nonlinear comportment of such process and the difficulties of characterizing several phenomenological effects makes difficult to find suitable operational procedures for producing required products. In this article, we use a model-free control (MFC) for controlling the mean size of crystals produced by seeded batch cooling crystallization. The MFC method is distinguished notably in terms of the modeling strategy. Rather than developing a crystallization model within the classic population balance equation (PBE) together with the mass balance and the energy balance, as is usually done, we use a l…

Balance equations-based properties of the Rabi Hamiltonian

2014

A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.

The pianigiani-yorke measure for topological markov chains

1997

We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.

Nonlinear nonviscous hydrodynamical models for charge transport in the framework of extended thermodynamic methods

2002

This paper develops a procedure, based on methods of extended thermodynamics, to design nonlinear hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. Models obtained in this way allow the study of the motion of electric charges in the presence of arbitrary external electric fields and may be useful when one wishes to study phenomena in a neighborhood of a stationary nonequilibrium process: indeed, the drift velocity of the charge gas with respect to the crystal lattice is not regarded as a small parameter.

The barotropic model

2003

Convergence of Markov Chains

2020

We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.

TRANSIENT SEMICONDUCTOR DEVICE SIMULATION INCLUDING ENERGY BALANCE EQUATION

1992

An efficient numerical method for the solution of hot‐carrier transport equations describing transient processes in submicrometer semiconductor devices is proposed. The calculations of transient processes in submicrometer MOS transistor were carried out and compared with the results obtained by conventional drift‐diffusion model.

Estimation of the mean crystal size and the moments of the crystal size distribution in batch crystallization processes

2016

International audience; A cascade high gain observer is designed to estimate the first four leading moments of the crystal size distribution (CSD) and the mean crystal size in batch crystallization processes. The proposed observer is based on a well-known transformation of the partial differential equation describing the CSD to a set of ordinary differential equations (the method of moments). Due to numerical difficulties resulting from the important differences in the magnitudes of the moments, a set of new variables is computed to allow a good estimation of the moments and thus the mean crystal size. In this work, only solute concentration and crystallizer temperature are used to estimate…