A Quasi-Two-Dimensional Method for the Rotordynamic Analysis of Centered Labyrinth Liquid Seals

1999 ◽  
Vol 121 (1) ◽  
pp. 144-152 ◽  
Author(s):  
M. Arghir ◽  
J. Freˆne
Keyword(s):  
Mathematical Model ◽  
Coordinate Transformation ◽  
Present Method ◽  
Dynamic Regime ◽  
Test Case ◽  
Two Dimensional ◽  
First Order ◽  
Simplifying Assumptions ◽  
Theoretical Results ◽  
Dynamic Perturbation

The work presents a method for analyzing the dynamic regime of labyrinth liquid seals. By using the traditional simplifying assumptions for the centered seal (sinusoidal, harmonically varying, first order dynamic perturbation), the approach can be addressed as “quasi” two-dimensional. A numerical coordinate transformation capable to treat displacement perturbations is introduced. The first order mathematical model is then deduced following the same steps as in a previously published work (Arghir and Freˆne, 1997b). From this standpoint, the present method can be regarded as an extension of the above mentioned approach which was able to deal only with stator-grooved seals. The method is validated by comparisons with Nordmann and Dietzen’s (1988) theoretical results for a seal with grooves on both stator and rotor and with the experimental results of Staubli’s (1993) test case concerning a general seal.

scholarly journals A Quasi 2D Method for the Rotordynamic Analysis of Centered Labyrinth Liquid Seals

1998 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Mathematical Model ◽  
Coordinate Transformation ◽  
Present Method ◽  
Dynamic Regime ◽  
Experimental Results ◽  
Test Case ◽  
First Order ◽  
Simplifying Assumptions ◽  
Theoretical Results ◽  
Dynamic Perturbation

The work presents a method for analyzing the dynamic regime of labyrinth liquid seals. By using the traditional simplifying assumptions for the centered seal (sinusoidal, harmonically varying, first order dynamic perturbation), the approach can be addressed as “quasi” 2D. A numerical coordinate transformation capable to treat displacement perturbations is introduced. The first order mathematical model is then deduced following the same steps as in a previously published work (Arghir et Frêne, 1997b). From this standpoint, the present method can be regarded as an extension of the above mentioned approach which was able to deal only with stator-grooved seals. The method is validated by comparisons with Nordmann and Dietzen’s (1988) theoretical results for a seal with grooves on both stator and rotor and with the experimental results of Staubli’s (1993) test case concerning a general seal.

scholarly journals A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

2020 ◽  
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

II. A solution of the integro-differential equation for the slope of the jet

1961 ◽  
Vol 261 (1304) ◽  
pp. 97-118 ◽  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Coordinate Transformation ◽  
Present Author ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Integro Differential Equation ◽  
Mellin Transforms ◽  
Momentum Coefficient ◽  
Slope Function

In an earlier paper with the same general title (Spence 1956, referred to as I), a mathematical model was developed to discuss the flow past a two-dimensional wing at incidence a in a steady incompressible stream, with a jet of momentum coefficient C j emerging from the trailing edge at an angular deflexion r to the chordline. In linearized approximation it was shown that the slope of the jet is given by a certain singular integro-differential equation, and numerical solutions for the equation were obtained by a pivotal points method. A coordinate transformation has now been found (Spence 1959) which makes the equation independent of the jet strength for small values of 14 C j = u, say, yielding a simpler equation solved by Lighthill (1959) using Mellin transforms (and by Stewartson (1959) and the present author by other methods). In this paper the expansion of the slope function is continued in ascending powers of u and In u multiplied by functions of x found by solving, by Lighthill’s method, a series of closely-related inhomogeneous equations. From these, expansions of the lift derivatives with respect to a and r are found as To this order the expressions agree closely with the numerical results found earlier, the discrepancy at u = 1 being less than 4 %.

Quasiperiodicity and Chaos in a Generalized Nosé–Hoover Oscillator

2016 ◽  
Vol 26 (10) ◽  
pp. 1650170 ◽  
Author(s):  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Parameter Space ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
First Order ◽  
Chaotic Region ◽  
Quasiperiodic Structures

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé–Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model.

Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method

2011 ◽  
Vol 328-330 ◽  
pp. 380-383 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Model ◽  
Circle Method ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Two Dimensional ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the minimun circumscribed circle assessment. One example is given to verify the theoretical results presented.

Organization of the Dynamics in a Parameter Plane of a Tumor Growth Mathematical Model

2014 ◽  
Vol 24 (02) ◽  
pp. 1450023 ◽  
Author(s):  
Cristiane Stegemann ◽  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Tumor Growth ◽  
Cross Section ◽  
Periodic Structures ◽  
Focal Point ◽  
Parameter Plane ◽  
Two Dimensional ◽  
First Order ◽  
Self Organized ◽  
Chaotic Region

We report results of a numerical investigation on a two-dimensional cross-section of the parameter-space of a set of three autonomous, eight-parameter, first-order ordinary differential equations, which models tumor growth. The model considers interaction between tumor cells, healthy tissue cells, and activated immune system cells. By using Lyapunov exponents to characterize the dynamics of the model in a particular parameter plane, we show that it presents typical self-organized periodic structures embedded in a chaotic region, that were before detected in other models. We show that these structures organize themselves in two independent ways: (i) as spirals that coil up toward a focal point while undergoing period-adding bifurcations and, (ii) as a sequence with a well-defined law of formation, constituted by two mixed period-adding bifurcation cascades.

Application of coordinate transformation to two-dimensional scattering and diffraction problems

1969 ◽  
Vol 47 (7) ◽  
pp. 795-804 ◽  
Author(s):  
L. Shafai
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Cross Section ◽  
Coordinate Transformation ◽  
Scattered Field ◽  
Arbitrary Cross Section ◽  
Surface Currents ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
First Order

The two-dimensional problem of determining the electromagnetic field scattered by a cylinder of arbitrary cross section is reduced to the solution of first-order, coupled differential equations. The procedure for finding the surface currents, scattered field, and the scattering cross section for a perfectly-conducting cylinder is given in detail. A brief study of the scattering by a polygonal cylinder and n identical strips equally spaced azimuthally around the z axis is used to examine the behavior of the differential equations.

Mathematical Model for Evaluating Roundness Errors by Maximum Inscribed Circle Method

2011 ◽  
Vol 314-316 ◽  
pp. 393-396 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Model ◽  
Circle Method ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Two Dimensional ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model is established for assessing roundness errors by the maximum inscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the maximum inscribed circle assessment. One example is given to verify the theoretical results presented.

scholarly journals A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 376
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State
Sign in / Sign up

Export Citation Format

Share Document