Step Responses of Liquid Lines With Frequency-Dependent Effects of Viscosity

1965 ◽  
Vol 87 (2) ◽  
pp. 504-510 ◽  
Author(s):  
F. T. Brown ◽  
S. E. Nelson
Keyword(s):  
Laminar Flow ◽  
Frequency Response ◽  
Characteristic Impedance ◽  
Step Response ◽  
Curve Complex ◽  
Principle Of Superposition ◽  
Analytic Expressions ◽  
Analytical Expressions ◽  
Theoretical Considerations ◽  
Step Responses

Universal step-response plots are given from theoretical considerations for rigid cylindrical lines containing a compressible Newtonian laminar-flow liquid. The pressure and flow step inputs and pressure and flow outputs for semi-infinite lines can, with the principle of superposition, be used to estimate the responses of a network of lines, terminations, and so on, for any transient input. Where possible, analytic expressions were found for these step responses, but in a certain region of each curve complex numerical routines based on the analytic frequency response were necessary. Analytical expressions are based on propagation and characteristic impedance operators published earlier by one of the authors.

Strip yield model for multiple straight cracks with coalesced yield zones: A theoretical study

2021 ◽  
pp. 1-15
Author(s):  
S. Hasan ◽  
N. Akhtar ◽  
S. Shekhar
Keyword(s):  
Numerical Study ◽  
Multiple Cracks ◽  
Principle Of Superposition ◽  
Yield Model ◽  
Zone Length ◽  
Yield Zone ◽  
Strip Yield Model ◽  
Opening And Closing ◽  
The Impact ◽  
Analytical Expressions

The paper presents a complicated case of coalescence of yield zones between two internal cracks out of four collinear straight cracks weakened an infinite isotropic plate. Two solutions are presented for the case of opening and closing of multiple cracks under general yielding conditions. Using these two solutions and the principle of superposition, we found the analytical expressions for load-bearing capacity of the plate using complex variable method. A numerical study has been carried out to investigate the behavior of yield zone length concerning remotely applied stresses at the boundary of the plate and the impact of two outer cracks on the propagation of inner cracks due to coalesced yield zones. Results obtained are reported graphically.

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

Abstract 104: Dynamic Autoregulation of Glomerular Capillary Pressure

Hypertension ◽  
2016 ◽  
Vol 68 (suppl_1) ◽  
Author(s):  
Scott C Thomson
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Blood Flow ◽  
Capillary Pressure ◽  
Tubuloglomerular Feedback ◽  
Step Response ◽  
Glomerular Capillary ◽  
Arterial Blood ◽  
Glomerular Capillary Pressure ◽  
Step Responses

It is generally accepted that renal blood flow (RBF) autoregulation is mediated by myogenic and tubuloglomerular feedback responses acting on the pre-glomerular resistance. If this is so, then autoregulation of RBF and glomerular capillary pressure (PGC) should change in the same direction throughout an autoregulatory step response. We computed autoregulatory step responses from time series recordings of arterial blood pressure (BP) and RBF (Transonics) blood flow or tubular stop-flow pressure (micropuncture), which is a surrogate for PGC in Wistar-Froemter rats fed for one week on low or high salt diets (n=6-10 ). Autoregulatory step responses were generated from time series by an algorithm that treats BP as a leading indicator of RBF or PGC and uses the projection theorem to solve for the impulse response which is integrated to obtain the step response. Step responses shown in the figure represent the uncompensated changes in RBF and PGC (mean + SEM) following a 1 mmHg BP step. The data clearly reveal that the time courses of RBF and PGC differ such that changes in RBF cannot predict changes in PGC. This implies that the renal hemodynamic response to a blood pressure disturbance is not confined to the pre-glomerular resistance. Furthermore, the participation of post-glomerular resistance in the autoregulatory response is sensitive to dietary salt such that PGC is more sensitive to BP on low salt diet.

Cerebral blood flow velocity response to induced and spontaneous sudden changes in arterial blood pressure

2001 ◽  
Vol 280 (5) ◽  
pp. H2162-H2174 ◽  
Author(s):  
Ronney B. Panerai ◽  
Suzanne L. Dawson ◽  
Penelope J. Eames ◽  
John F. Potter
Keyword(s):  
Blood Pressure ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Flow Velocity ◽  
Arterial Blood Pressure ◽  
Blood Flow Velocity ◽  
Cerebral Blood Flow Velocity ◽  
Step Response ◽  
Arterial Blood ◽  
Step Responses

The influence of different types of maneuvers that can induce sudden changes of arterial blood pressure (ABP) on the cerebral blood flow velocity (CBFV) response was studied in 56 normal subjects (mean age 62 yr, range 23–80). ABP was recorded in the finger with a Finapres device, and bilateral recordings of CBFV were performed with Doppler ultrasound of the middle cerebral arteries. Recordings were performed at rest (baseline) and during the thigh cuff test, lower body negative pressure, cold pressor test, hand grip, and Valsalva maneuver. From baseline recordings, positive and negative spontaneous transients were also selected. Stability of Pco 2 was monitored with transcutaneous measurements. Dynamic autoregulatory index (ARI), impulse, and step responses were obtained for 1-min segments of data for the eight conditions by fitting a mathematical model to the ABP-CBFV baseline and transient data (Aaslid's model) and by the Wiener-Laguerre moving-average method. Impulse responses were similar for the right- and left-side recordings, and their temporal pattern was not influenced by type of maneuver. Step responses showed a sudden rise at time 0 and then started to fall back to their original level, indicating an active autoregulation. ARI was also independent of the type of maneuver, giving an overall mean of 4.7 ± 2.9 ( n = 602 recordings). Amplitudes of the impulse and step responses, however, were significantly influenced by type of maneuver and were highly correlated with the resistance-area product before the sudden change in ABP ( r = −0.93, P < 0.0004). These results suggest that amplitude of the CBFV step response is sensitive to the point of operation of the instantaneous ABP-CBFV relationship, which can be shifted by different maneuvers. Various degrees of sympathetic nervous system activation resulting from different ABP-stimulating maneuvers were not reflected by CBFV dynamic autoregulatory responses within the physiological range of ABP.

scholarly journals A New Design Method for Ultrawideband Microstrip-to-Suspended Stripline Transitions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Young-Gon Kim ◽  
Kang Wook Kim
Keyword(s):  
Conformal Mapping ◽  
Insertion Loss ◽  
Design Method ◽  
Impedance Matching ◽  
Characteristic Impedance ◽  
Ultra Wideband ◽  
Efficient Design ◽  
Em Simulation ◽  
Simulation Results ◽  
Analytical Expressions

A clear and efficient design method for ultra-wideband microstrip-to-suspended stripline transition, which is based on the analytical expressions of the whole transitional structure, is presented. The conformal mapping is applied to obtain the characteristic impedance of the transitional structure within 2.85% accuracy as compared with the EM-simulation results. The transition is designed to provide broadband impedance matching and smooth field conversion. The implemented transition performs less than 0.6 dB insertion loss per transition for frequencies up to 30 GHz.

A Dynamic Model of Electrostrictive Unimorph Actuators for Haptic Devices

2016 ◽  
Author(s):  
Tahzib Safwat ◽  
Ryan Tosto ◽  
Michael D. Grissom ◽  
Christopher D. Rahn
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Time Domain ◽  
Haptic Feedback ◽  
High Strain ◽  
Piezoelectric Materials ◽  
Domain Model ◽  
Electroactive Polymer ◽  
Step Response ◽  
Compliant Actuators

Piezoelectric materials are commonly found in many devices, but their usage is limited by the low strain and high stiffness of the material. This prevents their use in “soft” applications, such as compliant actuators for haptic feedback devices and wearable technology. The actuation dynamics of a ferro-electric relaxor terpolymer, a type of soft and high strain electroactive polymer (EAP), are examined. This paper studies the unimorph actuator via a linearized time-domain model and experiments to validate the model include step response and frequency response of tip displacement.

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