scholarly journals Derivation of instantaneous unit hydrographs using linear reservoir models

2021 ◽  
Author(s):  
Parjang Monajemi ◽  
Setareh Khaleghi ◽  
Shahrzad Maleki
Keyword(s):  
Linear Function ◽  
Degrees Of Freedom ◽  
Weighting Coefficient ◽  
Reservoir Models ◽  
Proposed Model ◽  
The Difference ◽  
Linear Differential ◽  
Linear Reservoir ◽  
Unit Hydrographs ◽  
Three Degrees Of Freedom

Abstract In this research, a new conceptual model for producing instantaneous unit hydrographs (IUHs) is introduced by a linear combination of the Nash model, which assumes that the discharge from a reservoir is a linear function of its storage, and a model called inter-connected linear reservoir model (ICLRM), which assumes that the discharge from a reservoir is a linear function of the difference of its storage and its adjacent downstream reservoir. By employing these assumptions, a system of first-order linear differential equations with three degrees of freedom (storage coefficient, number of reservoirs, and weighting coefficient) is obtained as the governing equation for the proposed model. This model may be considered as the general form of the two models and is therefore capable of simulating IUHs laying between these two models. To show the capabilities of the model, linear and curvilinear soil conservation service (SCS) hydrographs are simulated using dimensionless hydrographs obtained by this model. Moreover, several real hydrographs were simulated by the proposed model and compared with hydrographs obtained by Nash, ICLRM, and SCS models. The results show that the model yields more accurate results compared to other studied models and may be considered as a new model for simulating IUHs.

Response and Stability of Linear Dynamic Systems With Many Degrees of Freedom Subjected to Nonconservative and Harmonic Forces

1975 ◽  
Vol 42 (2) ◽  
pp. 458-463 ◽  
Author(s):  
F. C. L. Fu ◽  
S. Nemat-Nasser
Keyword(s):  
Asymptotic Solution ◽  
Dynamic Systems ◽  
Autonomous System ◽  
Degrees Of Freedom ◽  
Differential Operators ◽  
Linear Dynamic Systems ◽  
Exciting Frequency ◽  
The Difference ◽  
Linear Differential ◽  
Type Oscillation

Dynamic systems whose response can be characterized by a set of linear differential equations with harmonic coefficients which are proportional to a small parameter ε, are considered. These systems are such that the corresponding autonomous sets of equations which are obtained by setting ε = 0, are defined by nonself-adjoint linear differential operators; i.e., they correspond to dynamic systems subjected to nondissipative nonconservative forces. For these systems, general asymptotic solutions are developed and their stability is examined. An interesting feature of these solutions is that, when the exciting frequency is close to, say, twice of a suitable eigenfrequency, or when it is close to the sum or the difference of two suitable frequencies of the autonomous system, then the asymptotic solution will involve negative fractional powers of ε. Hence, the nonsecular asymptotic solution, in general, may not reduce to the solution of the autonomous system as ε goes to zero. Another interesting feature of the present results is that the addition of small suitable harmonic forces does indeed stabilize an inherently unstable nondissipative nonconservative dynamical system; except when the frequency of the harmonic force resonates with one or several of the frequencies of the autonomous system in either a subharmonic or a combinational-type oscillation.

scholarly journals New Combined Weighting Model Based on Maximizing the Difference in Evaluation Results and Its Application

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Meng ◽  
Guotai Chi
Keyword(s):  
Error Probability ◽  
Programming Model ◽  
Comprehensive Evaluation ◽  
Weight Coefficient ◽  
Weighting Coefficient ◽  
Weighting Method ◽  
Evaluation Scores ◽  
Proposed Model ◽  
The Difference ◽  
Weighting Methods

This paper presents an approach for weighting indices in the comprehensive evaluation. In accordance with the principle that the entire difference of various evaluation objects is to be maximally differentiated, an adjusted weighting coefficient is introduced. Based on the idea of maximizing the difference between the adjusted evaluation scores of each evaluation object and their mean, an objective programming model is established with more obvious differentiation between evaluation scores and the combined weight coefficient determined, thereby avoiding contradictory and less distinguishable evaluation results of single weighting methods. The proposed model is demonstrated using 2,044 observations. The empirical results show that the combined weighting method has the least misjudgment probability, as well as the least error probability, when compared with four single weighting methods, namely, G1, G2, variation coefficient, and deviation methods.

scholarly journals Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

2021 ◽  
Vol 10 (4) ◽  
pp. 0-0
Keyword(s):  
Degrees Of Freedom ◽  
Design Parameters ◽  
Bernoulli’S Equation ◽  
Proposed Model ◽  
Frequency Domains ◽  
Mass Flowrate ◽  
Air Cushion ◽  
Base Radius ◽  
Air Cushion Vehicles ◽  
Three Degrees Of Freedom

In this study, three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli's equation and the thermodynamics nonlinear isentropic relations along with the Newton’s second law of translation and rotation. In this study, the dynamical investigation was based on numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model is provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flowrate entering the cushion volume (m ̇_in), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

scholarly journals Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

2021 ◽  
Vol 26 (2) ◽  
pp. 219-234
Author(s):  
A.S. Sowayan
Keyword(s):  
Degrees Of Freedom ◽  
Control Design ◽  
Design Parameters ◽  
Bernoulli’S Equation ◽  
Proposed Model ◽  
Frequency Domains ◽  
Air Cushion ◽  
Base Radius ◽  
Air Cushion Vehicles ◽  
Three Degrees Of Freedom

Abstract In this study, a three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli’s equation and the thermodynamics nonlinear isentropic relations along with the Newton second law of translation and rotation. In this study, the dynamical investigation was based on a numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model are provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flow rate entering the cushion volume (ṁin ), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

Analysis of a 3-DOF Micro-Positioning Stage

2014 ◽  
Vol 620 ◽  
pp. 234-239 ◽  
Author(s):  
De De Zhai ◽  
Shi Xun Fan ◽  
Da Peng Fan
Keyword(s):  
Theoretical Basis ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Theory Analysis ◽  
Stage Design ◽  
Flexure Hinges ◽  
Positioning Stage ◽  
Effect Curve ◽  
The Difference ◽  
Three Degrees Of Freedom

Firstly a three degrees of freedom micro-positioning stage constructed by flexure hinges is designed, and the simplified model of the stage is established. Secondly, the stiffness of the stage along X, Y direction or around Z direction is deduced by structural mechanics. The difference between finite element method and theory value is less than 7%, so it shows the theory analysis is feasible, further more, stress of the moving stage is analyzed, and the effect curve of the key parameters to the stiffness and stress is obtained. It can be concluded that the stiffness and stress mainly related with the flexure hinge length L and width t, thus it provide a theoretical basis for three-dimensional micro-positioning stage design.

scholarly journals Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

2021 ◽  
Vol 10 (4) ◽  
pp. 1-27
Author(s):  
Ahmed Sowayan
Keyword(s):  
Degrees Of Freedom ◽  
Design Parameters ◽  
Bernoulli’S Equation ◽  
Proposed Model ◽  
Frequency Domains ◽  
Mass Flowrate ◽  
Air Cushion ◽  
Base Radius ◽  
Air Cushion Vehicles ◽  
Three Degrees Of Freedom

In this study, three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli's equation and the thermodynamics nonlinear isentropic relations along with the Newton’s second law of translation and rotation. In this study, the dynamical investigation was based on numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model is provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flowrate entering the cushion volume (m ̇_in), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

scholarly journals Factors controlling the sequence of asperity failures in a fault model

2018 ◽  
Author(s):  
Emanuele Lorenzano ◽  
Michele Dragoni
Keyword(s):  
Degrees Of Freedom ◽  
Seismic Event ◽  
Frictional Resistance ◽  
Fault Model ◽  
Seismic Events ◽  
Viscoelastic Relaxation ◽  
Viscoelastic Deformation ◽  
Tectonic Loading ◽  
The Difference ◽  
Three Degrees Of Freedom

Abstract. We consider a fault with two asperities embedded in a shear zone subject to a uniform strain rate owing to tectonic loading. The static stress field generated by seismic events undergoes viscoelastic relaxation as a consequence of the rheological properties of the asthenosphere. We treat the fault as a dynamical system whose basic elements are the asperities. The system has three degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The dynamics of the system can be described in terms of one sticking mode and three slipping modes, for which we provide analytical solutions. We discuss how the stress state at the beginning of the interseismic interval preceding a seismic event controls the sequence of slipping modes during the event. We focus on the events associated with the separate (consecutive) slips of the asperities and investigate how they are affected by the seismic efficiency of the fault, by the difference in frictional resistance of the asperities and by the intensity of coupling between the asperities.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

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