Stochastic Motion in a Central Field with a Weak Non—Rotating Bar Perturbation

1995 ◽  
pp. 537-543 ◽  
Author(s):  
Pablo M. Cincotta ◽  
Josué A. Núñez ◽  
Juan C. Muzzio
Keyword(s):  
Central Field ◽  
Stochastic Motion

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations

1988 ◽  
Vol 53 (6) ◽  
pp. 1181-1197
Author(s):  
Vladimír Kudrna
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Parabolic Type ◽  
Diffusion Equations ◽  
Stochastic Motion ◽  
Energy Component ◽  
Classic Form

The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.

Erratum: Perturbation theory for a Dirac particle in a central field

1981 ◽  
Vol 23 (3) ◽  
pp. 1561-1561
Author(s):  
C. K. Au ◽  
G. W. Rogers
Keyword(s):  
Perturbation Theory ◽  
Dirac Particle ◽  
Central Field

Azimuthal sensitivity of neurons in primary auditory cortex of cats. II. Organization along frequency-band strips

1990 ◽  
Vol 64 (3) ◽  
pp. 888-902 ◽  
Author(s):  
R. Rajan ◽  
L. M. Aitkin ◽  
D. R. Irvine
Keyword(s):  
Spatial Distribution ◽  
Auditory Cortex ◽  
Frequency Band ◽  
Primary Auditory Cortex ◽  
Companion Paper ◽  
Significant Feature ◽  
Central Field ◽  
Cortical Surface ◽  
Peak Response ◽  
The Individual

1. The organization of azimuthal sensitivity of units across the dorsoventral extent of primary auditory cortex (AI) was studied in electrode penetrations made along frequency-band strips of AI. Azimuthal sensitivity for each unit was represented by a mean azimuth function (MF) calculated from all azimuth functions obtained to characteristic frequency (CF) stimuli at intensities 20 dB or more greater than threshold. MFs were classified as contrafield, ipsi-field, central-field, omnidirectional, or multipeaked, according to the criteria established in the companion paper (Rajan et al. 1990). 2. The spatial distribution of three types of MFs was not random across frequency-band strips: for contra-field, ipsi-field, and central-field MFs there was a significant tendency for clustering of functions of the same type in sequentially encountered units. Occasionally, repeated clusters of a particular MF type could be found along a frequency-band strip. In contrast, the spatial distribution of omnidirectional MFs along frequency-band strips appeared to be random. 3. Apart from the clustering of MF types, there were also regions along a frequency-band strip in which there were rapid changes in the type of MF encountered in units isolated over short distances. Most often such changes took the form of irregular, rapid juxtapositions of MF types. Less frequently such changes appeared to show more systematic changes from one type of MF to another type. In contrast to these changes in azimuthal sensitivity seen in electrode penetrations oblique to the cortical surface, much less change in azimuthal sensitivity was seen in the form of azimuthal sensitivity displayed by successively isolated units in penetrations made normal to the cortical surface. 4. To determine whether some significant feature or features of azimuthal sensitivity shifted in a more continuous and/or systematic manner along frequency-band strips, azimuthal sensitivity was quantified in terms of the peak-response azimuth (PRA) of the MFs of successive units and of the azimuthal range over which the peaks occurred in the individual azimuth functions contributing to each MF (the peak-response range). In different experiments shifts in these measures of the peaks in successively isolated units along a frequency-band strip were found generally to fall into one of four categories: 1) shifts across the entire frontal hemifield; 2) clustering in the contralateral quadrant; 3) clustering in the ipsilateral quadrant; and 4) clustering about the midline. In two cases more than one of these four patterns were found along a frequency-band strip.(ABSTRACT TRUNCATED AT 400 WORDS)

Assessing and visualizing uncertainty of 3D geological surfaces using level sets with stochastic motion

2019 ◽  
Vol 122 ◽  
pp. 54-67 ◽  
Author(s):  
Liang Yang ◽  
David Hyde ◽  
Ognjen Grujic ◽  
Celine Scheidt ◽  
Jef Caers
Keyword(s):  
Level Sets ◽  
Stochastic Motion

On planar oscillations of a body with a variable mass distribution in an elliptic orbit

2011 ◽  
Vol 225 (10) ◽  
pp. 2288-2295 ◽  
Author(s):  
A Burov ◽  
I Kosenko
Keyword(s):  
Mass Distribution ◽  
Large Scale ◽  
Variable Mass ◽  
Relative Equilibria ◽  
The Body ◽  
Global Dynamics ◽  
Central Field ◽  
Attitude Dynamics ◽  
Orbital Eccentricity ◽  
Space Elevators

Planar motion of an orbiting body having a variable mass distribution in a central field of gravity is under analysis. Within the so-called ‘satellite approximation’ planar attitude dynamics is reduced to the 3/2-degrees of freedom description by one ODE of second order. The law of the mass distribution variations implying an existence of the special relative equilibria, such that the body is oriented pointing to the attracting centre by the same axis for any value of the orbit eccentricity is indicated. For particular example of an orbiting dumb-bell equipped by a massive cabin, wandering between the ends of the dumb-bell. For this example stability of the equilibria such that the dumb-bell ‘points to’ the attracting centre by one of its ends is studied. The chaoticity of global dynamics is investigated. Two important examples of a vibrating dumb-bell and of a dumb-bell equipped by a cabin wandering between its endpoints are considered. The dynamics of space objects, including moving elements, has been investigated by many authors. These studies usually have been connected with the necessity to estimate the influence of relative motions of moving parts, for example, crew motions [ 1 , 2 ], circulation of liquids [ 3 ], etc. on the attitude dynamics of a spacecraft. The development of projects of large-scale space systems with mobile elements, in particular, of satellite systems with tethered elements and space elevators, has posed problems related to their dynamics. Various aspects of the role of mass distribution even for the simplest orbiting systems, like dumb-bell systems are known since the publications [ 4 – 7 ], etc. The possibility of the sudden loss of stability because of the mass redistribution has been pointed out in reference [ 8 ] (see also references [ 9 – 13 ]). The considered system belongs to the mentioned class of systems and represents by itself one of the simplest systems allowing both analytical and numerical treatment, without supplementary simplifying assumptions such as smallness of the orbital eccentricity. Another set of applied problems is related to orientation keeping of the system for deployment and retrieval of tethered subsatellites as well as for relative cabin motions of space elevators. In particular, the problem of the stabilization/destabilization possibility for the given state of motion due to rapid oscillations of the cabin exists. This could be the subject of another additional investigation.

scholarly journals Notes upon late Anatolian Art

1898 ◽  
Vol 4 ◽  
pp. 79-94
Author(s):  
J. W. Crowfoot
Keyword(s):  
Central Field ◽  
Considerable Size

Phrygia is remarkable for the variety (and number) of its funeral monuments: in one place the sarcophagus, in another the altar, in a third the stele. The last named was fashionable in the land of the Praipenissians, whose ancient centre was Soa in the neighbourhood of Altyn Tash. The Phrygian stele was often of considerable size, six feet or more in height, and fixed upright in the ground or in a socket by a wedge-like tongue, which still remains in some cases.The central field is filled sometimes by figures of the deceased, often more than life-size, never by ridiculous little dolls such as are found further east. The place of the figures is sometimes taken by a door: in this case the busts of the departed are occasionally sculptured in an arch-shaped pediment above (cf. Texier, Description de I'Asie Mineure, Pls. 38, 51). Otherwise the pediment is filled by various symbolic or decorative subjects—two lions with a prostrate bull or merely its head between them, an eagle with wings “displayed,” dolphins with small fishes in their mouths, and in one case Herakles and Cerberus.

ROBUSTNESS, STABILITY AND EFFICIENCY OF PHAGE λ GENETIC SWITCH: DYNAMICAL STRUCTURE ANALYSIS

2004 ◽  
Vol 02 (04) ◽  
pp. 785-817 ◽  
Author(s):  
X.-M. ZHU ◽  
L. YIN ◽  
L. HOOD ◽  
P. AO
Keyword(s):  
Saddle Points ◽  
Life Cycles ◽  
Transverse Force ◽  
Structure Theory ◽  
Exponential Dependence ◽  
Mathematical Framework ◽  
Dynamical Structure ◽  
Stochastic Fluctuation ◽  
Stochastic Motion ◽  
Genetic Switch

Based on the dynamical structure theory for complex networks recently developed by one of us and on the physical-chemical models for gene regulation, developed by Shea and Ackers in the 1980's, we formulate a direct and concise mathematical framework for the genetic switch controlling phage λ life cycles, which naturally includes the stochastic effect. The dynamical structure theory states that the dynamics of a complex network is determined by its four elementary components: The dissipation (analogous to degradation), the stochastic force, the driving force determined by a potential, and the transverse force. The potential may be interpreted as a landscape for the phage development in terms of attractive basins, saddle points, peaks and valleys. The dissipation gives rise to the adaptivity of the phage in the landscape defined by the potential: The phage always has the tendency to approach the bottom of the nearby attractive basin. The transverse force tends to keep the network on the equal-potential contour of the landscape. The stochastic fluctuation gives the phage the ability to search around the potential landscape by passing through saddle points.With molecular parameters in our model fixed primarily by the experimental data on wild-type phage and supplemented by data on one mutant, our calculated results on mutants agree quantitatively with the available experimental observations on other mutants for protein number, lysogenization frequency, and a lysis frequency in lysogen culture. The calculation reproduces the observed robustness of the phage λ genetic switch. This is the first mathematical description that successfully represents such a wide variety of major experimental phenomena. Specifically, we find: (1) The explanation for both the stability and the efficiency of phage λ genetic switch is the exponential dependence of saddle point crossing rate on potential barrier height, a result of the stochastic motion in a landscape; and (2) The positive feedback of cI repressor gene transcription, enhanced by the CI dimer cooperative binding, is the key to the robustness of the phage λ genetic switch against mutations and fluctuations in kinetic parameter values.

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