Disturbing Function

The same applies to pathologically-disturbed function. A simulated reduction in coronary blood flow (heart attack) would lead to reduced oxygen supply to the cells in the virtual heart, which would reduce efficiency of cardiac contraction and possibly give rise to heart rhythm disturbances. Ventricular pressure development would be compromised, as would the blood supply to all organs of the body, including the heart. All these implications can be studied in a virtual heart. 

The establishment of quantitative methods for the determination of vitamins in body fluids and tissues by microbiological assay techniques should stimulate the search for the significance of vitamins in disease, not only in nutritional deficiency, but in the much wider field of all metabolic disturbances. Functional vitamin deficiencies are produced by malabsorption, by inhibitors of the vitamin function through products of the body, and particularly through drugs and other toxic substances. Vitamin deficiencies may be relative deficiencies whenever an individual s metabolism is deranged so as to require enhanced quantities of a given vitamin to cure or to counteract certain symptoms as, e.g., in Darier s disease (keratosis follicularis) (P2a). 

Disturbs functions of the immune system by damaging the continuity of mucous membranes and depressing phagocytosis by neutrophils... 

Other models include the olfactory bulbectomy model (Song and Leonard, 2005). Lesions of the olfactory bulb cause behavioral changes, inteipreted to result from disturbed function of the limbic system. These behaviors are reversed by chronic antidepressant administration. 

Therefore, to study the stability problem, we must solve the governing equations, (6-83) and (6-85), with (6-91) as the initial condition, to determine whether h grows or decays in time. The result depends, of course, on the values of the parameters (6-87)-(6-89) and also on the form (and, generally, also the magnitude) of disturbance function. If the disturbance decays so that h - 1 as t - oo, the system is said to be stable to that particular disturbance. 

In this case, we must consider the form of the disturbance in the shape of the film to be arbitrary. Infinitesimal disturbances will be present in any real system at all times, as it is impossible to shield a real system from disturbances that have an arbitrarily small magnitude. At the same time, disturbances of arbitrarily small magnitude will also be present in every conceivable form. However, we shall see that it is not necessary to directly calculate the dynamics of a disturbance with an arbitrary form for the disturbance function h. Because the condition (6 92) is satisfied, when we substitute (6 91) into (6 83) and (6 85) to obtain a governing equation for the dynamics of h, we find that we can linearize the equation by neglecting all terms that involve with rn> 1. Specifically, the governing, linearized equation obtained from (6 83) and (6-85) is... 

The equations (12-20)-( 12-24) are the so-called linear stability equations for this problem in the inviscid fluid limit. We wish to use these equations to investigate whether an arbitrary, infinitesimal perturbation will grow or decay in time. Although the perturbation has an arbitrary form, we expect that it must satisfy the linear stability equations. Thus, once we specify an initial form for one of the variables like the pressure p, we assume that the other variables take a form that is consistent with p by means of Eqs. (12-20)-(12-24). Now the obvious question is this How do we represent a disturbance function of arbitrary form For this, we take advantage of the fact that the governing equations and boundary conditions are now linear, so that we can represent any smooth disturbance function by means of a Fourier series representation. Instead of literally studying a disturbance function of arbitrary form, we study the dynamics of all of the possible Fourier modes. If any mode is found to grow with time, the system is unstable because, with a disturbance of infinitesimal amplitude, every possible mode will always be present. 

A similar equation can also be derived for fluid 2 (with disturbance functions defined just as in (12-61),... 

Hence, incorporating the solution of (12-106) into (12-105), together with the far-field condition that the disturbance functions should decay for large z, we have... 

Because the stability analysis can now be focused exclusively on 2D disturbances, we can again use the stream-function transformation (12-312) to express the linear stability problem in terms of a single equation for the disturbance function [Pg.877]

At last, introducing equation (39) into the expression of the direct part of the disturbing function, and reordering the terms, we get ... 

Since both parts are formally similar, we can unify both expressions and obtain a single series for the disturbing function of the planetary... 

The contents of this paper include, with variable emphasis, the topics of a series of lectures whose main title was Routes to Order Capture into resonance . This was indeed the subject of the last section above. The study of this subject has, however, shown that - unlike the restricted three-body problem - capture into resonance drives the system immediately to stationary solutions known as Apsidal corotations . The whole theory of these solutions was also included in the paper from the beginning - that is, from the formulation of the Hamiltonian equations of the planetary motions and the expansion of the disturbing function in the high-eccentricity planetary three-body problem. The secular theory of non-resonant systems was also given. Motions with aligned or anti-aligned periapses, resonant or not, resulting from non-conservative processes (tidal interactions with the disc) in the early phases of the life of the system, seem to be frequent in extra-solar planetary systems. 

Beauge, C. (1996), On a global expansion of the disturbing function in the planar elliptic three-body problem. Cel. Mech. Dynam,. Astron. 64, 313-349. 

Ferraz-Mello, S. (1994), The convergence domain of the Laplacian expansion of the disturbing function. Cel. Mech. Dynam. Astron. 58, 37-52. 

Kaula, W.M. (1962), Development of the lunar and solar disturbing functions for a... 

With the disturbance function entering the system in the arterial blood and with known steady-state flow characteristics as a function of... 

The leading role in the study of a system for nonintegrahility is played by the expansion term Hi s,p). It is sometimes referred to as the disturbing function. Expand the disturbing function into a multiple Fourier series... 

Disturbed function caused by During float charge Lff 5 A per 100 Ah... 

Repair costs of the component include the costs of access vessels, spare parts and technicians to perform initial inspection, repair or replacement. Moreover, lost production and revenue losses due to the disturbed functionality of the wind turbine(s) are a part of the corrective maintenance costs. 

In addition to its research activities, the Chemical Service Section, from early 1918 until the end of the war, was called on more and more by the Ordnance Department for recommendations on the manufacture of gases at Edgewood Arsenal. Thus, while the purpose behind the Chemical Service Section was to co-ordinate without integrating and without disturbing functions of the statutory bureaus of the War Department, it was becoming evident that the system was developing serious defects. What was needed was... 

Looking several decades forward, these new approaches will likely translate into new strategies for the treatment of neurological diseases that are caused by—or associated with—disturbed functions of neuronal circuits. 

Notice that the variation of the semimajor axis depends on both the radial and the torque, but because the orbit can be taken in the two-body problem as planar, there is no dependence on W. Changes in co and are equivalent to orbital precession. All of these may be periodic or secular, depending on the details of 91. For a given disturbing function, this system of equations can be well explored using numerical methods. 

Symptoms can be caused by the disturbed function of the spinocerebellar co-ordinating complex. Ataxia and dysdiadochokinesis with dysmetria are common findings and can be the first dysfunctions the patient reports. They are often associated with nystagmus and different manifestations of spinal and truncal ataxia. 

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