The Origin of Instability in Airlift Pumps

1973 ◽  
Vol 40 (2) ◽  
pp. 399-404 ◽  
Author(s):  
S. Hjalmars
Keyword(s):  
Differential Equation ◽  
Preliminary Analysis ◽  
Time Lag ◽  
Stationary Flow ◽  
Small Time ◽  
Time Dependent ◽  
High Rise ◽  
Controlling System ◽  
Time Period ◽  
Period Of Oscillation

A preliminary analysis is made of the well-known instability, occurring in airlift pumps, when at sufficiently high rise the ability of the pump as a self-controlling system breaks down, and a rapidly increasing oscillation of the flow sets in. It is shown that the instability is due to the fact that a small time-dependent perturbation of the stationary flow satisfies a difference-differential equation with time lag, of a kind well known from control theory. The theoretically computed values of the critical rise and the time period of oscillation are in satisfactory agreement with observation.

A Study on Sun Shading Reconstruction Design of Residential Buildings in Chongqing City

2014 ◽  
Vol 953-954 ◽  
pp. 1481-1487
Author(s):  
Liu Jin
Keyword(s):  
Energy Saving ◽  
Personal Experience ◽  
Design Pattern ◽  
Simulation Analysis ◽  
Residential Buildings ◽  
Residential Building ◽  
Specific Time ◽  
High Rise ◽  
Time Period ◽  
Chongqing City

Windows energy saving design of residential buildings has increasingly got the attention of people. Through a large number of surveys and analysis of residential buildings in Chongqing and consumers personal experience, the author finds problems and deficiency, and then proposes principles of residential buildings sun shading reconstruction in Chongqing city. Taking the high-rise residential building of one university in Chongqing as reconstruction sample, selecting a specific time period, the author recalculates sun shading coefficient with and without sun shading by using Ecotect software to do simulation analysis. Finally, the reasonable reconstruction design pattern is put forward through cases. Keywords: Buildings Sun Shading, Sun Shading Reconstruction, Energy Saving

Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Transcendental Equation ◽  
Spindle Speed ◽  
Machining Parameters ◽  
Numerical Integration Method ◽  
Stability Diagrams ◽  
Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

Coordinate control of prostaglandin E2 synthesis and uptake by hyperosmolarity in renal medullary interstitial cells

2006 ◽  
Vol 290 (3) ◽  
pp. F641-F649 ◽  
Author(s):  
Michael L. Pucci ◽  
Shinichi Endo ◽  
Teruhisa Nomura ◽  
Run Lu ◽  
Cho Khine ◽  
...  
Keyword(s):  
Cell Surface ◽  
Characteristic Time ◽  
Water Deprivation ◽  
Interstitial Cells ◽  
Time Dependent ◽  
Prostaglandin E ◽  
Coordinate Control ◽  
Time Period ◽  
Cox 2 ◽  
Net Release

During water deprivation, prostaglandin E2 (PGE2), formed by renal medullary interstitial cells (RMICs), feedback inhibits the actions of antidiuretic hormone. Interstitial PGE2 concentrations represent the net of both PGE2 synthesis by cyclooxygenase (COX) and PGE2 uptake by carriers such as PGT. We used cultured RMICs to examine the effects of hyperosmolarity on both PG synthesis and PG uptake in the same RMIC. RMICs expressed endogenous PGT as assessed by mRNA and immunoblotting. RMICs rapidly took up [3H]PGE2 to a level 5- to 10-fold above background and with a characteristic time-dependent “overshoot.” Inhibitory constants ( Ki) for various PGs and PGT inhibitors were similar between RMICs and the cloned rat PGT. Increasing extracellular hyperosmolarity to the range of 335–485 mosM increased the net release of PGE2 by RMICs, an effect that was concentration dependent, maximal by 24 h, reversible, and associated with increased expression of COX-2. Over the same time period, there was decreased cell-surface activity of PGT due to internalization of the transporter. With continued exposure to hyperosmolarity over 7–10 days, PGE2 release remained elevated, COX-2 returned to baseline, and PGT-mediated uptake became markedly reduced. Our findings suggest that hyperosmolarity induces coordinated changes in COX-2-mediated PGE2 synthesis and PGT-mediated PGE2 uptake in RMICs.

scholarly journals Sequential eigenfunction expansion for a problem in combustion theory

2003 ◽  
Vol 45 (1) ◽  
pp. 35-48 ◽  
Author(s):  
M. Al-Refai ◽  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Eigenfunction Expansion ◽  
Time Dependent ◽  
Linear Parabolic Equation ◽  
System Of Equations ◽  
Multiple Steady State ◽  
Definitive Answer ◽  
Combustion Theory ◽  
The Galerkin Method ◽  
Steady State Solutions

AbstractA method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

scholarly journals Dynamic Analysis on RCC and Composite Structure for Uniform and Optimized Section

2021 ◽  
Vol 9 (12) ◽  
pp. 1114-1127
Author(s):  
Ankit Kumar
Keyword(s):  
Dynamic Analysis ◽  
Composite Structure ◽  
Composite Structures ◽  
Response Spectrum ◽  
Steel Structures ◽  
Seismic Zone ◽  
Dead Weight ◽  
Conventional Concrete ◽  
High Rise ◽  
Time Period

Abstract: This study examines the composite structure that is increasing commonly in developing countries. For medium-rise to high-rise building construction, RCC structures is no longer economical due to heavy dead weight, limited span, low natural frequency and hazardous formwork. The majority of commercial buildings are designed and constructed with reinforced concrete, which largely depends on the existence of the constituent materials as well as the quality of the necessary construction skills, and including the usefulness of design standards. Conventional RCC structure is not preferred nowadays for high rise structure. However, composite construction, is a recent development in the construction industry. Concrete-steel composite structures are now very popular due to some outstanding advantages over conventional concrete and steel structures. In the present work, RCC and steel-concrete composite structure are being considered for a Dynamic analysis of a G+25-storey commercial building of uniform and optimized section, located at in seismic zone IV. Response Spectrum analysis method is used to analyze RCC and composite structure, CSI ETABS v19 software is used and various results are compared such as time period, maximum storey displacement, maximum storey stiffness. Maximum storey shear and maximum stoey overturning moment. Keywords: RCC Structure, Composite Structure, Uniform Section, Optimized Section, Shear Connector, Time Period, Storey Displacement, Storey Shear, Storey Stiffness, Response Spectrum method, ETABS

On the Control of Chaos in Extended Structures

1997 ◽  
Vol 119 (4) ◽  
pp. 551-556 ◽  
Author(s):  
C. Barratt
Keyword(s):  
Nearest Neighbor ◽  
Duffing Oscillator ◽  
Vertical Plane ◽  
Small Time ◽  
Time Dependent ◽  
External Forcing ◽  
Control Of Chaos ◽  
Chaotic Vibrations ◽  
Order Of Magnitude ◽  
The Individual

A mechanism is proposed for synchronizing the chaotic vibrations of an externally forced array of oscillators with nearest-neighbor viscoelastic coupling. The proposed mechanism involves the application of small time-dependent perturbations to the individual oscillators. The perturbations required to preserve the coherence are of the order of magnitude of any noise present. The mechanism works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.

Clocking the buildup dynamics of light-induced states through attosecond transient absorption spectrum

2021 ◽  
Author(s):  
Xiaoxia Wu ◽  
Shaofeng Zhang ◽  
Difa Ye
Keyword(s):  
Floquet Theory ◽  
Transient Absorption ◽  
Scaling Law ◽  
Time Lag ◽  
Time Dependent ◽  
Transient Absorption Spectroscopy ◽  
Transient Absorption Spectrum ◽  
Wide Range ◽  
Maximal Shift ◽  
Buildup Time

Abstract The buildup processes of the light-induced states (LISs) in attosecond transient absorption spectroscopy are studied by solving the time-dependent Schrödinger equation and compared with the quasistatic Floquet theory, revealing a time lag of the maximal shift and strongest absorbance of the LIS with respect to the zero delay that is referred to as the buildup time. We analytically derive a scaling law for the buildup time that confirms the numerical results over a wide range of detunings. Our theory verifies the commonly accepted scenario of nearly instantaneous response of matter to light if the pump field is blue-detuned, but some differences are found in the near-resonant and red-detuning cases. Implications of the buildup time in petahertz optoelectronics are discussed.

Numerical analysis of time-dependent stagnation point flow of Oldroyd-B fluid subject to modified Fourier’s law

2021 ◽  
pp. 2150187
Author(s):  
Foukeea Qasim ◽  
Tian-Chuan Sun ◽  
S. Z. Abbas ◽  
W. A. Khan ◽  
M. Y. Malik
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equation ◽  
Thermal Relaxation ◽  
Stagnation Point Flow ◽  
Time Dependent ◽  
Parameter Values

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

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