TOPOLOGICAL MANIFESTATIONS IN CLASSICAL MECHANICS: DISCRETE ALLOWED AND FORBIDDEN STATES OF MOTION

1994 ◽  
Vol 09 (39) ◽  
pp. 3653-3661 ◽  
Author(s):  
RAM K. VARMA
Keyword(s):  
Magnetic Field ◽  
Dynamical System ◽  
Classical Mechanics ◽  
Charged Particles ◽  
Coherent System ◽  
Forbidden States ◽  
Multiply Connected ◽  
Action Integral ◽  
Relationship Of ◽  
The Relationship

Consequences of the topology of the configuration space of a Hamiltonian dynamical system are considered for a coherent system of trajectories. It is shown that when the space is multiply-connected and therefore the action integral is multivalued, the allowed states of motion (labeled by the initial data) are constrained to a discrete set by the requirement that the action be single-valued. One thus obtains a quantum-like discretization of allowed states of motion even in classical mechanics. Such discrete “allowed” and “forbidden” states have indeed been observed in the classical mechanical system of charged particles in a magnetic field. The relationship of this formalism with a Schrödinger-like formalism for the latter problem given earlier is discussed.

Energy levels of charged particles confined in a multiply connected structure in a magnetic field

1993 ◽  
Vol 73 (5) ◽  
pp. 2364-2375 ◽  
Author(s):  
A. Ishibashi ◽  
D. G. Ravenhall ◽  
R. L. Schult ◽  
H. W. Wyld
Keyword(s):  
Magnetic Field ◽  
Energy Levels ◽  
Charged Particles ◽  
Multiply Connected ◽  
Connected Structure

scholarly journals Interhemispheric comparison of average substorm onset locations: evidence for deviation from conjugacy

2007 ◽  
Vol 25 (4) ◽  
pp. 989-999 ◽  
Author(s):  
H. Wang ◽  
H. Lühr ◽  
S. Y. Ma ◽  
H. U. Frey
Keyword(s):  
Magnetic Field ◽  
Significant Influence ◽  
Solar Zenith Angle ◽  
Statistical Study ◽  
Substorm Onset ◽  
Seasonal Effects ◽  
Linear Relationships ◽  
Substorm Onsets ◽  
Relationship Of ◽  
The Relationship

Abstract. Based on 2760 well-defined substorm onsets in the Northern Hemisphere and 1432 in the Southern Hemisphere observed by the FUV Imager on board the IMAGE spacecraft, a detailed statistical study is performed including both auroral regions. This study focuses on the hemispheric comparisons. Southward pointing interplanetary magnetic field (IMF) is favorable for substorm to occur, but still 30% of the events are preceded by northward IMF. The magnetic latitude (MLat) of substorm onset depends mainly on the merging electric field (Em) with a relationship of |dMLat|= −5.2 Em0.5, where dMLat is the deviation from onset MLat. In addition, seasonal effects on onset MLat are also detected, with about 2 degrees higher latitudes during solstices than equinoxes. Both IMF By and solar illumination have a significant influence on the magnetic local time (MLT) of onsets. An average relation, dMLT=0.25 By between IMF By and the deviation from onset MLT, was found. The By dependence varies slightly with the onset latitude. At lower latitudes (higher activity) it is reduced. After removal of the relationship with IMF By a linear relationships remains between the solar zenith angle and onset MLT with dMLT=1 min/deg. Therefore, both solar illumination and IMF By can contribute to hemispheric longitudinal displacements of substorm onset locations from conjugacy. No indications for systematic latitudinal displacements between the hemispheres have been found.

The Out-Rotator of Spin Traveling Wave Pump on Magnetic Fluid

2012 ◽  
Vol 503 ◽  
pp. 3-7
Author(s):  
Meng Zhao ◽  
Ji Bin Zou ◽  
Jing Shang
Keyword(s):  
Magnetic Field ◽  
Magnetic Fluid ◽  
Traveling Wave ◽  
Magnetic Particles ◽  
Theory Method ◽  
The Press ◽  
Relationship Of ◽  
The Relationship ◽  
The Magnetic Field

According to researching the spin traveling wave pump, the relationship of the characteristics of magnetic fluid and the press is investigated under the spin magnetic field by the theory method. The relationship of moving, magnetic field and press is investigated by the decoupled computation between the magnetic field and force. The method is scientificity and rationality by the testing. The distributing shape of magnetic fluid in the pump is affected by the adding magnetic field under the spin magnetic field when the magnetic fluid is filled in the pump. At the same time, the adding magnetic field is affected by magnetic particles of magnetic fluid. The magnetic fluid can be moved by the effect of the adding magnetic field in the pump. The flux of magnetic fluid increases with the magnetic field.

Mixing properties of (α,β)-expansions

2009 ◽  
Vol 29 (4) ◽  
pp. 1119-1140 ◽  
Author(s):  
KARMA DAJANI ◽  
YUSUF HARTONO ◽  
COR KRAAIKAMP
Keyword(s):  
Dynamical System ◽  
Invariant Measure ◽  
Lebesgue Measure ◽  
Natural Extension ◽  
Mixing Properties ◽  
Special Values ◽  
Image Position ◽  
Relationship Of ◽  
The Relationship

AbstractLet 0<α<1 andβ>1. We show that everyx∈[0,1] has an expansion of the formwherehi=hi(x)∈{0,α/β}, andpi=pi(x)∈{0,1}. We study the dynamical system underlying this expansion and give the density of the invariant measure that is equivalent to the Lebesgue measure. We prove that the system is weakly Bernoulli, and we give a version of the natural extension. For special values ofα, we give the relationship of this expansion with the greedyβ-expansion.

scholarly journals INDICATORS OF EVALUATION OF THE VENTURE STRUCTURES DEVELOPMENT

2021 ◽  
Vol 71 (2) ◽  
Author(s):  
Oleh Kuzmin ◽  
Viktoriia Terletska
Keyword(s):  
Rapid Growth ◽  
Integrated Assessment ◽  
Coherent System ◽  
Urgent Task ◽  
Relevant Element ◽  
Group A ◽  
Legislative Support ◽  
Development Evaluation ◽  
Relationship Of ◽  
The Relationship

The article has been examined the problem of formation and evaluation of the development of venture structures (on the example of a venture fund) in terms of intensification of innovation. It has been offered to estimate development of venture structures on element indicators of efficiency of functioning and element indicators of a condition and dynamics of functioning of venture structure. Generalizing is the integrated assessment of the coherence of the development of venture structure, which will help to obtain an adequate assessment of the balance of development of venture structures. Approaches to the development of venture structures by both domestic and foreign scientists have been presented. The system of indicators of estimation of development of venture structures on element indicators of efficiency of functioning and indicators of a condition and dynamics of functioning has been investigated and formed. The complexity and versatility of the concept of development, as well as the ambiguity and variability of the legislative support of venture structures, caused by rapid growth, requires the use of specific approaches to assessing their development. Given the importance of the concept of "development" and taking into account the lack of a normatively established system of indicators for assessing the development of venture structures, there is an urgent task – the formation of a coherent system of indicators for assessing the assessment of development, evaluation of development. The above actualizes the search and construction of a holistic system for assessing the development of venture structures by element indicators. The sequence of calculation of the integrated indicator of the development of venture structures should be carried out in the following sequence: to determine the main elements (indicators) of development of venture structures; to investigate the main groups of indicators and systems of indicators through which the development of venture structures is manifested in accordance with the main elements of the development of venture structures; to determine the importance of each element of the development of the venture structure; to form in accordance with each group a system of indicators of the relevant element of the development of the venture structure; to form a model of the relationship of the system of indicators of each group of the corresponding element of the development of the venture structure for the formation of an integrated assessment of the consistency of the development of the venture structure. Generalizing is the integrated assessment of the coherence of the development of venture structure, which will help to obtain an adequate assessment of the balance of development of venture structures.

BEHAVIOR OF CHARGED PARTICLE MOTION ALONG A MAGNETIC FIELD AND A RETARDING POTENTIAL-EVIDENCE FOR THE EXISTENCE OF DISCRETE ENERGY STATES IN CLASSICAL MECHANICAL DOMAIN

1993 ◽  
Vol 08 (02) ◽  
pp. 167-176 ◽  
Author(s):  
R.K. VARMA ◽  
A.M. PUNITHAVELU
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Particle Motion ◽  
Classical Mechanics ◽  
Initial Value ◽  
Discrete Energy ◽  
Quantum Numbers ◽  
Energy States ◽  
Charged Particle Motion ◽  
The Relationship

We report here experimental results which point to a rather unexpected, astonishing behavior of charged particle motion in a magnetic field in the presence of a retarding electric potential. An electron beam, when energy scanned with respect to its ‘parallel’ energy using a retarding potential, the response of the transmitted current as a function of the retarding potential is found to be oscillatory as against the monotonic response, expected according to the standard initial value paradigm of classical mechanics. The unexpected ‘peaks’ and ‘dips’ in the transmitted current plots are interpreted as “allowed” and “forbidden” energy states of the system. The peaks (or dips) are found to fit very well with a theoretical relationship which motivated the search for such a behavior; also “quantum numbers” for the peaks have been identified. A very astonishing aspect of the relationship is the dependence of the energies of the allowed states on the length of the box.

Inner Connection of Bainite and Pearlite Transformation in Steels

2014 ◽  
Vol 900 ◽  
pp. 64-67
Author(s):  
Jian Hao Chen ◽  
Xiao Ling· Zhou ◽  
Lan Meng ◽  
Wen Liu
Keyword(s):  
Magnetic Field ◽  
Phase Transformation ◽  
Driving Force ◽  
Spontaneous Magnetization ◽  
Martensite Phase ◽  
Bainite Transformation ◽  
Relationship Of ◽  
The Relationship ◽  
New Phase ◽  
Magnetic Drive

Decomposition of austenite in steels from high to low temperatures is pearlite, bainite and martensite phase transformation. According to studies, magnetic field promotes the three transformations. The phenomenons indicate the three transformations have coherence in magnetics. There is a transformation from paramagnetism (γ) to ferromagnetism (α) among all these three. Magnetic drive ΔGm plays an important role in the phase transition. The bainite transformation was carried out at 300°C during different isothermal time. Combining the results, it studied the relationship of bainite and pearlite transformation from characteristics of the nucleation of BF, microstructures etc. Even without magnetic field, spontaneous magnetization makes contributions to phase transformation driving force. Small deflections cause by spontaneous magnetization may promote the lattice reorganization from FCC to BCC in a certain extent, while promote the formation of the new phase with BCC cube.

scholarly journals Magnetopause stand-off distance in dependence on the magnetosheath and solar wind parameters

1998 ◽  
Vol 16 (4) ◽  
pp. 388-396 ◽  
Author(s):  
M. I. Pudovkin ◽  
B. P. Besser ◽  
S. A. Zaitseva
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Boundary Layers ◽  
Wind Data ◽  
Magnetospheric Physics ◽  
Magnetic Field Penetration ◽  
Solar Wind Parameters ◽  
Relationship Of ◽  
The Relationship ◽  
Field Penetration

Abstract. A model of the magnetosheath structure proposed in a recent paper from the authors is extended to estimate the magnetopause stand-off distance from solar wind data. For this purpose, the relationship of the magnetopause location to the magnetosheath and solar wind parameters is studied. It is shown that magnetopause erosion may be explained in terms of the magnetosheath magnetic field penetration into the magnetosphere. The coefficient of penetration (the ratio of the magnetospheric magnetic field depression to the intensity of the magnetosheath magnetic field Bm⊥z=–Bmsin2Θ/2, is estimated and found approximately to equal 1. It is shown that having combined a magnetosheath model presented in an earlier paper and the magnetosheath field penetration model presented in this paper, it is possible to predict the magnetopause stand-off distance from solar wind parameters.Key words. Magnetospheric physics · Magnetopause · Cusp and boundary layers-Magnetosheath

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