scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

scholarly journals Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

2007 ◽  
Vol 2007 ◽  
pp. 1-25
Author(s):  
M. P. Markakis
Keyword(s):  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Nonlinear Odes ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Strongly Nonlinear ◽  
Parameter Values

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration.

Analysis and Synthesis of Dynamic Response of a Flexibly Coupled Rotor Assembly

1997 ◽  
Author(s):  
Valdas Chaika
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Response ◽  
Wide Range ◽  
Analysis And Synthesis ◽  
Coupling Parameters ◽  
Elastic Couplings ◽  
Rotor Assembly

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.

Improved Parker-Sochacki Approach for Closed Form Solution of Enzyme Catalyzed Reaction Model

2017 ◽  
Vol 8 (1-2) ◽  
pp. 90
Author(s):  
Babatunde Sunday Ogundare ◽  
Saheed O Akindeinde ◽  
Adebayo O Adewumi ◽  
Adebayo A Aderogba
Keyword(s):  
Closed Form ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Processing Technique ◽  
Reaction Model ◽  
Form Solution ◽  
Post Processing ◽  
Analytical Technique ◽  
Comparison Of The Results

In this article, a new analytical technique called Improved Parker-Sochacki Method (IPSM) for solving nonlinear Michaelis-Menten enzyme catalyzed reaction model is proposed. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations.  The proposed method showed a significant improvement  over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions elucidated the simplicity and accuracy of the proposed method.

scholarly journals Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

2016 ◽  
Vol 113 (40) ◽  
pp. 11220-11225 ◽  
Author(s):  
Ramu Anandakrishnan ◽  
Zining Zhang ◽  
Rory Donovan-Maiye ◽  
Daniel M. Zuckerman
Keyword(s):  
Closed Form Solution ◽  
Atp Synthesis ◽  
Form Solution ◽  
Energy Conditions ◽  
Rotary Machine ◽  
Wide Range ◽  
Steady State Rate ◽  
Systematic Enumeration ◽  
Kinetic Effects ◽  
Chemical Cycle

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated “kinetic equivalence” of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Estimation of Stress Intensity Factor for Circumferential Through-Wall Cracked Elbows Subjected to In-Plane Bending

2015 ◽  
Author(s):  
Han-Bum Surh ◽  
Jong Wook Kim ◽  
Min Kyu Kim ◽  
Min-Gu Won ◽  
Moon Ki Kim ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Form Solution ◽  
Accurate Estimation ◽  
Wide Range ◽  
Plane Bending ◽  
Geometric Variables

The stress intensity factor (SIF) is the major fracture mechanics parameter in LEFM concept. Since the SIF can be used for not only calculation of J-integral based on the GE/EPRI and reference stress method but also evaluation of fatigue crack growth, an accurate estimation of the SIF is an important issue for the piping in nuclear power plant. Recently, there is a need to develop the SIF solution which can cover wide geometric variables since there are on-going efforts that are developing next generation reactors in Korea, which is designed to thin-walled structures. For the through-wall cracked straight pipes, many researchers have proposed the SIF solutions which can cover wide range of wall thickness. However, since only limited solutions have been proposed yet for the through-wall cracked elbows, a research related to the SIF estimation for the elbows with wide geometric variables should be performed. In this study, the extended SIF solution for circumferential through-wall cracked elbows subjected to in-plane bending is proposed as the tabulated form through the finite element (FE) analyses. Wide elbow geometries are selected to range between 5 and 50 of Rm/t and range between 2∼20 of Rb/Rm. The existing solutions are then reviewed by comparing with the FE results. Furthermore, effects of geometric variables on the SIF are addressed through systematic investigation of FE based SIF results. These investigated results are expected to contribute to the development of closed form solution for the circumferential through-wall cracked elbows subjected to in-plane bending.

scholarly journals An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1086
Author(s):  
Ravi P. Agarwal ◽  
Fatemah Mofarreh ◽  
Rasool Shah ◽  
Waewta Luangboon ◽  
Kamsing Nonlaopon
Keyword(s):  
Closed Form ◽  
Fractional Order ◽  
Parabolic Equations ◽  
Closed Form Solution ◽  
Adomian Decomposition Method ◽  
Form Solution ◽  
Order Problem ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Adomian Decomposition

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.

NEUROFUZZY MODELING OF NATURAL FREQUENCIES OF CYLINDRICAL SHELLS APPLIED TO EVOLUTIONARY BASED OPTIMAL DESIGN OF SR MOTORS

2006 ◽  
Vol 03 (03) ◽  
pp. 263-277 ◽  
Author(s):  
HOSSEIN ROUHANI ◽  
MANSOUR NIKKHAH BAHRAMI ◽  
BABAK NADJAR ARAABI ◽  
CARO LUCAS
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Closed Form ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Problems ◽  
Special Cases ◽  
Wide Range

A thorough analysis of cylindrical shells' dynamical behavior is essential in many different industrial design problems, and particularly in electric motor design. Shell vibration equations form a set of partial differential equations of order eight, where their closed form solution is only known for few special cases with a few known boundary conditions along with many not necessarily realistic assumptions. On the other hand, finite element based numerical solutions does not yield a lumped model that can be regarded as a general solution for natural frequencies of cylindrical shells. In this paper, a neurofuzzy model for natural frequencies of cylindrical shells is developed. At first, natural frequencies are calculated for a wide range of cylindrical shells' dimensions, using either closed form solution or finite element method. Gathered data is exploited for training of a Locally Linear Neurofuzzy Network, which yields a general model for calculation of natural frequencies of cylindrical shells. While the developed neurofuzzy model may be used in different design problems that deals with cylindrical shells, as a case study, the proposed model along with an evolutionary algorithm are utilized in the optimal design of a Switched Reluctance motor.

scholarly journals A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation

2012 ◽  
Vol 19 (6) ◽  
pp. 1415-1426 ◽  
Author(s):  
A. Barari ◽  
A. Kimiaeifar ◽  
M.G. Nejad ◽  
M. Motevalli ◽  
M.G. Sfahani
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Nonlinear Oscillators ◽  
Form Solution ◽  
Closed Form Expression ◽  
System Response ◽  
Classical Dynamics ◽  
Analytical Technique

Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF) approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM) and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.

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