A First Example: The “Particle in a Box“ and Quantized Translational Motion

2020 ◽  
pp. 59-96
Author(s):  
Jochen Autschbach
Keyword(s):  
Degrees Of Freedom ◽  
Separation Of Variables ◽  
Translational Motion ◽  
Three Dimensional ◽  
Potential Wells ◽  
Quantum Tunnelling ◽  
Atomic Force ◽  
Quantum Behavior ◽  
The One ◽  
Three Degrees Of Freedom

The simple ‘particle in a box’ (Piab) is introduced in this chapter so that the reader can get familiar with applying the quantum recipe and atomic units. The PiaB is introduced in its one, two, and three dimensional variants, which demonstrates the use of the separation of variables technique as a strategy to solve the Schrodinger equation for a particle with two or three degrees of freedom. It is shown that the confinement of the particle causes the energy to be quantized. The one-dimensional PiaB is then applied to treat the electronic spectra of cyanine dyes and their absorption colors. The chapter then introduces more general setups with finite potential wells, in order to introduce the phenomenon of quantum tunnelling and to discuss more generally with the unintuitive ‘quantum behavior’ of particles such as electrons. Scanning tunnelling and atomic force microscopes are also discussed briefly.

The statistical distribution of the length of a rubber molecule

1948 ◽  
Vol 44 (3) ◽  
pp. 342-344 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Statistical Distribution ◽  
Equal Length ◽  
Fixed Angle ◽  
A Chain ◽  
Image Position ◽  
Three Degrees Of Freedom

A rubber molecule containing n + 1 carbon atoms may be represented by a chain of n links of equal length such that successive links are at a fixed angle to each other but are otherwise at random. The statistical distribution of the length of the molecule, that is, the distance between the first and last carbon atoms, has been considered by various authors (Treloar (1) gives references). In particular, if the first atom is kept fixed at the origin of a system of coordinates and the chain is otherwise at random, it has been conjectured that the distribution of the (n + 1)th atom will tend, as n increases, towards a three-dimensional normal distribution of the formwhere σ depends on n. Thus r2 (= x2 + y2 + z2) will be approximately distributed as σ2χ2 with three degrees of freedom.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

Thermogasodynamic Analysis of the Segmented Annular Seal

2020 ◽  
Vol 143 (7) ◽  
Author(s):  
Samia Dahite ◽  
Mihai Arghir
Keyword(s):  
Parametric Study ◽  
Thermal Effects ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Leading Edge ◽  
Test Case ◽  
Isothermal Model ◽  
Pocket Depth ◽  
Annular Seal ◽  
Three Degrees Of Freedom

Abstract The present work deals with the thermogasodynamic analysis of the segmented annular seal provided with Rayleigh pockets. The paper is a continuation of the work presented Arghir, M., and Mariot, A. (2017, “Theoretical Analysis of the Static Characteristics of the Carbon Segmented Seal,” ASME J. Tribol., 139(6), p. 062202.) where an isothermal model of the segmented annular seal was first presented. Each segment had three degrees-of-freedom, and its static position was obtained by solving the nonlinear equations of equilibrium. Thermal effects are now introduced by considering a simplified form of the energy equation in the thin gas film coupled with the three dimensional heat transfer in a segment of the seal and in the rotor. An efficient numerical algorithm is developed. A parametric study was performed for a segmented annular seal with pockets taken from the literature and operating with air. First, a test case proved the necessity of considering three degrees-of-freedom for the segment and not only its radial displacement. The parametric study was then performed for two different pocket depths, two pressure differences, and different rotation speeds. The results showed a non-uniform heating with larger temperatures at the leading edge of the segment where the minimal film thickness occurs. Heating is proportional to the pocket depth that lowers the lift force of the segment and to the pressure difference that closes the seal.

scholarly journals THE FORMATION OF PROFESSIONAL TALENT IN DETERMINATION WITH SEMANTIC ATTITUDE TO INNOVATIONS UNDER THE INFLUENCE OF VARIOUS DEGREES OF FREEDOM IN ACTIVITY

2020 ◽  
Vol 17 (4) ◽  
pp. 91-101
Author(s):  
T.N. Soboleva ◽  
Keyword(s):  
Empirical Data ◽  
Degrees Of Freedom ◽  
The Other ◽  
Psychological Analysis ◽  
Other Hand ◽  
Professional Talent ◽  
The One ◽  
The Impact ◽  
Three Degrees Of Freedom

The article is devoted to the poorly studied problem of the formation of talent in the conditions of different degrees of freedom in activity and the impact on that formation of a person’s conservative and innovative semantic attitudes towards the introduction of new equipment. The main objective of the study is to describe how the conditions of different degrees of freedom in the activity are refracted with internal conditions, which are conservative and innovative semantic attitudes and various talent structures. The study was conducted on a sample of 54 qualified railway drivers using a specialized simulator which allows to simulate three degrees of freedom in the activity. The psychological analysis of the activity revealed seven abilities ensuring the implementation of the activity. Based on empirical data, the article shows that low, medium and high degrees of freedom in activity are manifested in different degrees of productivity. Conservative and innovative semantic attitudes to the introduction of new equipment do not have a significant effect on the productivity of the activity in the conditions of different degrees of freedom. Along with this, depending on the conservative and innovative semantic attitudes, different structures of talent in terms of composition and degree of integration under the conditions of different degrees of freedom in the activity are formed. On the one hand, conservative and innovative semantic attitudes act as internal determinants; on the other hand, low, medium and high degrees of freedom in the activity act as external determinants of the formation of various talent structures.

scholarly journals Contact Force Control of Three-Dimensional Flexible Manipulator

2020 ◽  
Author(s):  
Minoru Sasaki ◽  
Shunta Ito ◽  
Daiki Maeno ◽  
Waweru Njeri ◽  
Muguro Josephh ◽  
...  
Keyword(s):  
Contact Force ◽  
Force Control ◽  
Degrees Of Freedom ◽  
Force Feedback ◽  
Three Dimensional ◽  
Flexible Manipulator ◽  
Force Tracking ◽  
Feedback Method ◽  
Three Degrees Of Freedom ◽  
Contact Force Control

This paper proposes a contact force controller for a constrained flexible manipulator in three-dimensional motion. This controller used the conversion formula obtained empirically and experimental results showed the effectiveness of the proposed contact force controller. First, the manipulator was operated with the tip of the second link restrained, then, time response of the root strain, joint angles and contact force were used to derive the relational between the three quantities. The effectiveness of the relational expression was verified by conducting a target contact force tracking experiment by inputting the angle from the relational expression. The contact force control using the strain feedback method was proposed with the strain amount estimated from the target contact force as the target value, and its effectiveness was verified by experiments. From the results obtained, controller using the strain feedback method was designed for the purpose of controlling the contact force at the tip of a flexible manipulator with two links and three degrees of freedom that performs three-dimensional spatial motion, and its effectiveness was shown by comparison with the contact force feedback method.

Static and Vibration Analyses of a Three-Dimensional Snake-Like Micropositioning Stage

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Nicola Scuor ◽  
Paolo Gallina ◽  
Marco Giovagnoni
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Dynamic Tests ◽  
Lumped Mass ◽  
Simulation Data ◽  
End Effector ◽  
Three Degrees Of Freedom

This paper presets three degrees of freedom (DOF) piezoelectric micropositioning stage. The stage is composed of a stack of piezodisk bender actuators actuated in such a way to prevent the end-effector from rotating; this way the end-effector can only translate along the x, y, and z axes. Thanks to its snake-like configuration, the system is capable of large displacements (of the order of 50 μm) with low driving voltages (of the order of 100 V). Several lumped-mass static and dynamic models of the device have been implemented. Static experimental results, which are in agreement with simulation data, confirmed the performances of the device. A dynamic model showed the natural frequencies of the mechanism. Also dynamic tests have been conducted in order to validate the dynamic model.

scholarly journals Ears on the Hand: Reaching Three-Dimensional Targets With an Audio-Motor Device

2020 ◽  
Vol 33 (4-5) ◽  
pp. 433-455 ◽  
Author(s):  
Sylvain Hanneton ◽  
Thomas Hoellinger ◽  
Vincent Forma ◽  
Agnes Roby-Brami ◽  
Malika Auvray
Keyword(s):  
Degrees Of Freedom ◽  
Body Movement ◽  
Three Dimensional ◽  
Sensory Substitution ◽  
Dominant Hand ◽  
Coupling Condition ◽  
Electromagnetic System ◽  
3D Audio ◽  
Auditory Experience ◽  
The One

Abstract Understanding the processes underlying sensorimotor coupling with the environment is crucial for sensorimotor rehabilitation and sensory substitution. In doing so, devices which provide novel sensory feedback consequent to body movement may be optimized in order to enhance motor performance for particular tasks. The aim of the study reported here was to investigate audio-motor coupling when the auditory experience is linked to movements of the head or the hands. The participants had to localize and reach a virtual source with the dominant hand in response to sounds. An electromagnetic system recorded the position and orientation of the participants’ head and hands. This system was connected to a 3D audio system that provided binaural auditory feedback on the position of the virtual listener located on the participants’ body. The listener’s position was computed either from the hands or from the head. For the hand condition, the virtual listener was placed on the dominant hand (the one used to reach the target) in Experiment 1 and on the non-dominant hand, which was constrained in order to have similar amplitude and degrees of freedom as that of the head, in Experiment 2. The results revealed that, in the two experiments, the participants were able to localize a source within the 3D auditory environment. Performance varied as a function of the effector’s degrees of freedom and the spatial coincidence between sensor and effector. The results also allowed characterizing the kinematics of the hand and head and how they change with audio-motor coupling condition and practice.

The Qualitative Synthesis of Parallel Manipulators

2004 ◽  
Vol 126 (4) ◽  
pp. 617-624 ◽  
Author(s):  
Jorge Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Qualitative Reasoning ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Qualitative Synthesis ◽  
Motion Representation ◽  
Six Degrees Of Freedom ◽  
Three Degrees Of Freedom

As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.

A Low-Cost, Automated Wafer Loading System With Submicron Alignment Accuracy for Nanomanufacturing and Nanometrology Applications

2016 ◽  
Vol 4 (4) ◽  
Author(s):  
Andrew Duenner ◽  
Tsung-Fu Yao ◽  
Bruno De Hoyos ◽  
Marianna Gonzales ◽  
Nathan Riojas ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Low Cost ◽  
Atomic Force ◽  
Total Capital ◽  
Alignment System ◽  
Loading System ◽  
Nanoscale Metrology ◽  
The Voice ◽  
Metrology System ◽  
Three Degrees Of Freedom

This paper introduces a low-cost, automated wafer alignment system capable of submicron wafer positioning repeatability. Accurate wafer alignment is critical in a number of nanomanufacturing and nanometrology applications where it is necessary to be able to overlay patterns between fabrication steps or measure the same spot on a wafer over and over again throughout the manufacturing process. The system presented in this paper was designed to support high-throughput nanoscale metrology where the goal is to be able to rapidly and consistently measure the same features on all the wafers in a wafer carrier without the need for slow and expensive vision-based alignment systems to find and measure the desired features. The wafer alignment system demonstrated in this paper consists of a three-pin passive wafer alignment stage, a voice coil actuated nesting force applicator, a three degrees-of-freedom (DOFs) wafer handling robot, and a wafer cassette. In this system, the wafer handling robot takes a wafer from the wafer cassette and loads it on to the wafer alignment stage. The voice coil actuator is then used to load the wafer against the three pins in the wafer alignment system and align the wafer to an atomic force microscope (AFM)-based metrology system. This simple system is able to achieve a throughput of 60 wafers/h with a positional alignment repeatability of 283 nm in the x-direction, 530 nm in the y-direction, and 398 nm in the z-direction for a total capital cost of less than $1800.

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