Functional calculus in strong plasma turbulence

1980 ◽  
Vol 24 (3) ◽  
pp. 489-501 ◽  
Author(s):  
Goodarz Ahmadi ◽  
Akira Hirose
Keyword(s):  
Functional Equation ◽  
Plasma Turbulence ◽  
Closure Problem ◽  
Moment Equations ◽  
Characteristic Functional ◽  
Velocity Wave ◽  
Space Characteristic ◽  
The Mean ◽  
Basic Equations ◽  
The Moment

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

scholarly journals Continuum approximations for lattice-free multi-species models of collective cell migration

2017 ◽  
Author(s):  
Oleksii M Matsiaka ◽  
Catherine J Penington ◽  
Ruth E Baker ◽  
Matthew J Simpson
Keyword(s):  
Cell Migration ◽  
Discrete Model ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Collective Cell Migration ◽  
Moment Equations ◽  
The Mean ◽  
Continuum Description ◽  
The Moment ◽  
Adhesive Forces

AbstractCell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.

scholarly journals Helium, [Fe/H] Abundances and the HR (Log TEFF, MBol) Diagram With Hipparcos Data of The Four Nearest Open Clusters: Hyades, Coma Berenices, The Pleiades and Praesepe

1998 ◽  
Vol 11 (1) ◽  
pp. 565-565
Author(s):  
G. Cayrel de Strobel ◽  
R. Cayrel ◽  
Y. Lebreton
Keyword(s):  
Main Sequence ◽  
Open Clusters ◽  
Main Sequence Stars ◽  
Spectroscopic Analyses ◽  
Solar Metallicity ◽  
Metal Abundances ◽  
The Mean ◽  
The Moment ◽  
The One ◽  
Best Fit

After having studied in great detail the observational HR diagram (log Teff, Mbol) composed by 40 main sequence stars of the Hyades (Perryman et al.,1997, A&A., in press), we have tried to apply the same method to the observational main sequences of the three next nearest open clusters: Coma Berenices, the Pleiades, and Praesepe. This method consists in comparing the observational main sequence of the clusters with a grid of theoretical ZAMSs. The stars composing the observational main sequences had to have reliable absolute bolometric magnitudes, coming all from individual Hipparcos parallaxes, precise bolometric corrections, effective temperatures and metal abundances from high resolution detailed spectroscopic analyses. If we assume, following the work by Fernandez et al. (1996, A&A,311,127), that the mixing-lenth parameter is solar, the position of a theoretical ZAMS, in the (log Teff, Mbol) plane, computed with given input physics, only depends on two free parameters: the He content Y by mass, and the metallicity Z by mass. If effective temperature and metallicity of the constituting stars of the 4 clusters are previously known by means of detailed analyses, one can deduce their helium abundances by means of an appropriate grid of theoretical ZAMS’s. The comparison between the empirical (log Teff, Mbol) main sequence of the Hyades and the computed ZAMS corresponding to the observed metallicity Z of the Hyades (Z= 0.0240 ± 0.0085) gives a He abundance for the Hyades, Y= 0.26 ± 0.02. Our interpretation, concerning the observational position of the main sequence of the three nearest clusters after the Hyades, is still under way and appears to be greatly more difficult than for the Hyades. For the moment we can say that: ‒ The 15 dwarfs analysed in detailed in Coma have a solar metallicity: [Fe/H] = -0.05 ± 0.06. However, their observational main sequence fit better with the Hyades ZAMS. ‒ The mean metallicity of 13 Pleiades dwarfs analysed in detail is solar. A metal deficient and He normal ZAMS would fit better. But, a warning for absorption in the Pleiades has to be recalled. ‒ The upper main sequence of Praesepe, (the more distant cluster: 180 pc) composed by 11 stars, analysed in detail, is the one which has the best fit with the Hyades ZAMS. The deduced ‘turnoff age’ of the cluster is slightly higher than that of the Hyades: 0.8 Gyr instead of 0.63 Gyr.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form

1985 ◽  
Vol 107 (2) ◽  
pp. 188-195 ◽  
Author(s):  
S. Okabe ◽  
Y. Kamiya ◽  
K. Tsujikado ◽  
Y. Yokoyama
Keyword(s):  
Experimental Results ◽  
Wave Form ◽  
Velocity Wave ◽  
The Mean ◽  
Straight Lines ◽  
Vibratory Conveyor ◽  
Theoretical Results ◽  
Vibratory Feeding

This paper presents the conveying velocity on a vibratory conveyor whose track is vibrated by nonsinusoidal vibration. The velocity wave form of the vibrating track is approximated by six straight lines, and five distortion factors of the wave form are defined. Considering the modes of motion of the particle, the mean conveying velocity is calculated for various conditions. Referring to these results, the optimum wave form is clarified analytically. The theoretical results show that the mean conveying velocity is considerably larger than that of ordinary feeders if the proper conveying conditions are chosen. The theoretical results are confirmed by experimental results.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals The evaluation of malignant astrocytoma score (MAS)

2013 ◽  
Vol 70 (5) ◽  
pp. 452-456
Author(s):  
Zeljko Kojadinovic ◽  
Petar Vulekovic ◽  
Djordje Jajic ◽  
Tomislav Cigic ◽  
Vladimir Papic ◽  
...  
Keyword(s):  
Performance Status ◽  
Radiation Therapy Oncology Group ◽  
Scoring Systems ◽  
Hospital Treatment ◽  
Malignant Astrocytoma ◽  
Or Groups ◽  
The Mean ◽  
The Moment ◽  
Astrocytoma Grade Iii

Background/Aim. At the moment there are few scoring systems for malignant astrocytoma but they are not widely accepted. The aim of this study was to evaluate malignant astrocytoma score (MAS) on a new group of patients with malignant astrocytoma, to compare MAS with other prognostic tools and to describe the use of MAS in everyday practice in neurooncology. Methods. The study was performed on 124 patients with supratentorial malignant astrocytoma grade III or IV. They were operated on and subsequently irradiated with 50-60 Gy. Results. The mean age of the patients was 57.3 years. The mean Karnofski performance status (KPS) of the functional inpairment was 54. The removal of the tumor > 90% was done in 59.7% of patients. The mean survival was 9.1 months, and 27.4% of patients had a 12-month survival. The area under receiver operating characteristic (ROC) curve (AUC) of the MAS for predicting 6-, 12- and 18-month survival was 0.754, 0.783 and 0.882, respectively. We compared the MAS with the two mostly cited scoring systems. The AUC for the same prediction for medical research council (MRC) was 0.601, 0.693, 0.772 respectively. For the Radiation Therapy Oncology Group (RTOG) the AUC was 0.732, 0.765, 0.827, respectively. Conclusion. MAS represents a useful scoring system for determining illness severity and prognosis in patients with malignant supratentorial astrocytoma. It can be helpful in comparing single patients or groups of patients, as well as results of different treatments and in controlling the quality of hospital treatment and so on.

The moment equations for three-group systems

1981 ◽  
Vol 43 (1) ◽  
pp. 40-48
Author(s):  
P.L Corio ◽  
M.L Trover
Keyword(s):  
Moment Equations ◽  
The Moment

scholarly journals ANALYSIS OF CHANGES IN HOMOCYSTEIN USED AS A MARKER OF METABOLIC SYNDROME IN PATIENTS WITH INCREASED BODY MASS INDEX WHO HAVE MULTIPLE TRAUMA

2018 ◽  
Vol 18 (4) ◽  
pp. 30-33
Author(s):  
V. V. Kucheryavchenko
Keyword(s):  
Metabolic Syndrome ◽  
Body Mass Index ◽  
Body Mass ◽  
Apache Ii ◽  
Anthropometric Parameters ◽  
Mean Values ◽  
Initial Values ◽  
The Mean ◽  
The Moment ◽  
Combined Injuries

In recent years, the concept of "metabolic syndrome" has become more spreading, and in parallel with disorders of carbohydrate and lipid metabolism, endothelial dysfunction is no less significant. The aim of our work was to analyze changes in homocysteine (HC) as a marker of metabolic syndrome in patients with an increased body mass index (IBMI) in polytrauma. The study involved 224 patients with polytrauma, who had different initial values of body mass index (BMI) and were treated at the polytrauma department and the intensive care unit for patients with combined injuries for a period from 1 day to 1 year since the moment of injury. All the patients were subjected to identifying the level of serum HC. The patients had the same severity according to the APACHE II scale, 14 ± 5.8, at the admission to the hospital, and were divided into 3 stratified clinical groups depending on the initial values of anthropometric parameters and BMI. The study was conducted on the 1, 3, 7, 14, 30 and 360 days from the date of polytrauma. Assessment of blood serum HC was performed by ELISA. It was found that the overweight patients with BMI ≤ 29.9 demonstrated an increase in the mean values of blood HC on the 7th and 14th days of the treatment, with a further decrease on the 15th day since the date of injury. For the patients with BMI within the range of 30.0 - 39.9, the persistence of the HC index during the first month of the treatment at baseline with an increase on the 360th day was found out. The patients with BMI ˃ 40.0 showed an increase in the level of blood HC through the year since the date of polytrauma. It was revealed that the level of HС directly affects the course of traumatic disease in patients with increased BMI, its severity in terms of uniformity of injuries received and the same range of severity according to the APACHE II scale depends on BMI at the admission to the hospital.

scholarly journals Doppler Shift of Radio Signals Transmitted between Orbiting Satellites

1982 ◽  
Vol 35 (2) ◽  
pp. 155 ◽  
Author(s):  
PL Dyson ◽  
JA Bennett
Keyword(s):  
Electron Concentration ◽  
Doppler Shift ◽  
Rate Of Change ◽  
Line Of Sight ◽  
Concentration Gradients ◽  
Mean Velocity ◽  
Radio Signals ◽  
The Mean ◽  
The Moment ◽  
The Individual

A general expression, applicable at VHF and above, is derived for the Doppler shift of radio signals transmitted between two satellites embedded in the ionosphere. The Doppler shift is made up of several contributions which depend on (a) the rate of change of the free space path between the satellites, (b) the components, perpendicular to the line of sight between the satellites, of both the mean velocity of the satellites and the electron concentration gradients, (c) the moment of the perpendicular electron concentration gradients and the deviations from the mean of the individual satellite perpendicular velocities, (d) the velocity components along the line of sight between the satellites, and the electron concentration values at each satellite, and (e) changes occurring in the ionosphere with time.

Sign in / Sign up

Export Citation Format

Share Document