Study on Silo Pressure by Consider Storage Materials Density Changed along the Height

2012 ◽  
Vol 517 ◽  
pp. 797-800
Author(s):  
Zhi Yong Yang ◽  
Shun Hu Liu ◽  
Song Zhao ◽  
Jun Hu ◽  
Zeng Chan Lu
Keyword(s):  
Differential Equation ◽  
Density Stratification ◽  
Maximum Pressure ◽  
Actual Case ◽  
Storage Materials ◽  
Pressure Calculation ◽  
The Difference

The difference existed between results of silos pressure calculation and the actual case, because the influence of density stratification was not taken into consideration. The aim of this paper was to obtain silo pressure calculating formula by consider of storage materials density stratified. To this end, we assume that the density was continuous changed along the height and differential equation of the storage materials pressure was established. By compared the results calculated from the equation with the results calculated from the code, it is found that the maximum pressure increased. The results showed density stratified is an import factor for silo pressure calculation and the equation obtained in this paper can provide references for the theory of silo pressure calculation.

The Optimum Groove Geometry for Spiral Groove Viscous Pumps

1990 ◽  
Vol 112 (2) ◽  
pp. 409-414 ◽  
Author(s):  
Yuichi Sato ◽  
Kyosuke Ono ◽  
Akihiko Iwama
Keyword(s):  
Differential Equation ◽  
Flow Rate ◽  
Groove Width ◽  
Design Parameters ◽  
Width Ratio ◽  
Maximum Pressure ◽  
Spiral Groove ◽  
Clearance Ratio ◽  
Viscous Pump ◽  
Outflow Rate

The optimum geometries of disk and cylindrical sprial groove viscous pumps to provide the maximum pressure or flow rate are investigated theoretically. The geometrical design parameters, such as the groove angle, groove to ridge clearance ratio, groove width ratio and ridge clearance ratio, are considered as functions of meridional coordinate. Results are obtained from the solution of a differential equation for the smoothed overall pressure distribution of a spiral groove viscous pump. It is found that outflow rate increases with the increase of groove to ridge clearance ratio λ, and that for each value of λ there exist “optimum” values of groove angle and groove width ratio, which give a maximum outflow rate. However, the increase of λ decreases the ridge clearance.

A reduction theory of second order meromorphic differential equations, I

1987 ◽  
Vol 101 (2) ◽  
pp. 323-342
Author(s):  
W. B. Jurkat ◽  
H. J. Zwiesler
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Standard Form ◽  
Reduction Theory ◽  
Fundamental Solution Matrix ◽  
Equivalent Equation ◽  
The Difference ◽  
Solution Matrix ◽  
Meromorphic Differential Equation ◽  
Meromorphic Differential

In this article we investigate the meromorphic differential equation X′(z) = A(z) X(z), often abbreviated by [A], where A(z) is a matrix (all matrices we consider have dimensions 2 × 2) meromorphic at infinity, i.e. holomorphic in a punctured neighbourhood of infinity with at most a pole there. Moreover, X(z) denotes a fundamental solution matrix. Given a matrix T(z) which together with its inverse is meromorphic at infinity (a meromorphic transformation), then the function Y(z) = T−1(z) X(z) solves the differential equation [B] with B = T−1AT − T−1T [1,5]. This introduces an equivalence relation among meromorphic differential equations and leads to the question of finding a simple representative for each equivalence class, which, for example, is of importance for further function-theoretic examinations of the solutions. The first major achievement in this direction is marked by Birkhoff's reduction which shows that it is always possible to obtain an equivalent equation [B] where B(z) is holomorphic in ℂ ¬ {0} (throughout this article A ¬ B denotes the difference of these sets) with at most a singularity of the first kind at 0 [1, 2, 5, 6]. We call this the standard form. The question of how many further simplifications can be made will be answered in the framework of our reduction theory. For this purpose we introduce the notion of a normalized standard equation [A] (NSE) which is defined by the following conditions:(i) , where r ∈ ℕ and Ak are constant matrices, (notation: )(ii) A(z) has trace tr for some c ∈ ℂ,(iii) Ar−1 has different eigenvalues,(iv) the eigenvalues of A−1 are either incongruent modulo 1 or equal,(v) if A−1 = μI, then Ar−1 is diagonal,(vi) Ar−1 and A−1 are triangular in opposite ways,(vii) a12(z) is monic (leading coefficient equals 1) unless a12 ≡ 0; furthermore a21(z) is monic in case that a12 ≡ 0 but a21 ≢ 0.

scholarly journals Finiteness Properties of Affine Difference Algebraic Groups

2020 ◽  
Author(s):  
Michael Wibmer
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Difference Equations ◽  
General Linear Group ◽  
Algebraic Groups ◽  
The Matrix ◽  
Algebraic Difference ◽  
The Difference ◽  
Linear Differential ◽  
Finiteness Properties

Abstract We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the matrix entries can indeed be defined by finitely many such equations. As an application, we show that the difference ideal of all difference algebraic relations among the solutions of a linear differential equation is finitely generated.

scholarly journals Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yunjiao Bai ◽  
Quan Zhang ◽  
Hong Shangguan ◽  
Zhiguo Gui ◽  
Yi Liu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Denoising ◽  
Fourth Order ◽  
Objective Evaluation ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
The Difference ◽  
Adaptively Adjusting ◽  
Difference Curvature

The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

Reply by author to discussion by N. F. Uren

Geophysics ◽  
1970 ◽  
Vol 35 (1) ◽  
pp. 161-161
Author(s):  
M. K. Paul
Keyword(s):  
Differential Equation ◽  
Gravity Field ◽  
The Difference ◽  
Regional Gravity ◽  
Considerable Detail

I thank Mr. N. F. Uren for his interest in my paper. Mr. Uren’s discussion mainly concerns the appropriateness of the difference / differential equation that the regional gravity field, [Formula: see text], has been implied in my paper to satisfy. I think that this point has been discussed in considerable detail in my reply to an earlier discussion on this paper (Geophysics, June 1969, p. 483–485), which can, however, be summarized as follows.

scholarly journals Well-posedness of the difference schemes of the high order of accuracy for elliptic equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Pavel E. Sobolevskiĭ
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Continuous Functions ◽  
High Order ◽  
Difference Schemes ◽  
Well Posedness ◽  
Smooth Functions ◽  
Order Of Accuracy ◽  
High Order Of Accuracy ◽  
The Difference

It is well known the differential equation−u″(t)+Au(t)=f(t)(−∞<t<∞)in a general Banach spaceEwith the positive operatorAis ill-posed in the Banach spaceC(E)=C((−∞,∞),E)of the bounded continuous functionsϕ(t)defined on the whole real line with norm‖ϕ‖C(E)=sup⁡−∞<t<∞‖ϕ(t)‖E. In the present paper we consider the high order of accuracy two-step difference schemes generated by an exact difference scheme or by Taylor's decomposition on three points for the approximate solutions of this differential equation. The well-posedness of these difference schemes in the difference analogy of the smooth functions is obtained. The exact almost coercive inequality for solutions inC(τ,E)of these difference schemes is established.

Lean and Straight Nozzle Vanes in a Variable Geometry Turbine: A Steady and Pulsating Flow Investigation

2008 ◽  
Author(s):  
Srithar Rajoo ◽  
R. F. Martinez-Botas
Keyword(s):  
Pressure Ratio ◽  
Velocity Ratio ◽  
Pulsating Flow ◽  
Maximum Pressure ◽  
Variable Geometry ◽  
Flow Investigation ◽  
Variable Geometry Turbine ◽  
The Difference ◽  
Vane Angle ◽  
Ratio Range

Variable Geometry Turbines (VGT) are widely used to improve engine-turbocharger matching and currently common in diesel engines. VGT has proven to provide air boost for wide engine speed range as well as reduce turbo-lag. This paper presents the design and experimental evaluation of a variable geometry mixed flow turbocharger turbine. The tests have been carried out with a permanent magnet eddy current dynamometer within a velocity ratio range of 0.47 to 1.09. The peak efficiency of the variable geometry turbine corresponds to vane angle settings between 60° and 65°, for both the lean and straight vanes in the region of 80%. The variable geometry turbine was tested under pulsating flow with straight and lean nozzle vanes for different vane angle settings, 40Hz and 60Hz flow. In general, the range of mass flow parameter is higher in the straight nozzle vanes with an average of 66.4% and 69.7% for 40Hz and 60Hz flow respectively. The straight nozzle vanes also shows increasing pressure ratio range compared to the lean nozzle vanes, which is more apparent in the maximum pressure ratio experienced by the turbine in an unsteady cycle. In overall, the cycle averaged efficiency in the straight vane configuration is marginally higher than the lean vane. Furthermore, the difference to the equivalent quasi-steady is better in the straight vane configuration compared to the lean vane.

scholarly journals On the Relation between Pincherle's Polynomials and the Hypergeometric Function

1920 ◽  
Vol 39 ◽  
pp. 58-62 ◽  
Author(s):  
Bevan B. Baker
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Hypergeometric Function ◽  
The Difference ◽  
Image Position

1. The Pincherle polynomials are defined as the coefficients in the expansion of {1 − 3 tx + t3}−½ in ascending powers of t. If the coefficient of tn be denoted by Pn(x), then the polynomials satisfy the difference equationand Pn(x) satisfies the differential equation

scholarly journals Influence on Calculated Blood Pressure of Measurement Posture for the Development of Wearable Vital Sign Sensors

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Shouhei Koyama ◽  
Hiroaki Ishizawa ◽  
Akio Sakaguchi ◽  
Satoshi Hosoya ◽  
Takashi Kawamura
Keyword(s):  
Blood Pressure ◽  
Calibration Curve ◽  
Pressure Measurement ◽  
Pulse Wave ◽  
Blood Pressure Measurement ◽  
Wave Signal ◽  
Fbg Sensor ◽  
Pressure Calculation ◽  
Measurement Height ◽  
The Difference

We studied a wearable blood pressure sensor using a fiber Bragg grating (FBG) sensor, which is a highly accurate strain sensor. This sensor is installed at the pulsation point of the human body to measure the pulse wave signal. A calibration curve is built that calculates the blood pressure by multivariate analysis using the pulse wave signal and a reference blood pressure measurement. However, if the measurement height of the FBG sensor is different from the reference measurement height, an error is included in the reference blood pressure. We verified the accuracy of the blood pressure calculation with respect to the measurement height difference and the posture of the subject. As the difference between the measurement height of the FBG sensor and the reference blood pressure measurement increased, the accuracy of the blood pressure calculation decreased. When the measurement height was identical and only posture was changed, good accuracy was achieved. In addition, when calibration curves were built using data measured in multiple postures, the blood pressure of each posture could be calculated from a single calibration curve. This will allow miniaturization of the necessary electronics of the sensor system, which is important for a wearable sensor.

Sign in / Sign up

Export Citation Format

Share Document