scholarly journals X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

2020 ◽  
Vol 15 ◽  
pp. 157
Author(s):  
D. Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. A. Terziev ◽  
I. Yiyitoglou
Keyword(s):  
Experimental Data ◽  
Critical Point ◽  
Degrees Of Freedom ◽  
Separation Of Variables ◽  
Point Symmetry ◽  
Transition Rates ◽  
Scale Factors ◽  
Exact Separation ◽  
Three Degrees Of Freedom ◽  
Good Agreement

A γ-rigid version (with γ = 0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter free (up to overall scale factors) predictions for spectra and B(E2) transition rates, which are in good agreement with existing experimental data for 172Os and 186Pt. An unexpected similarity of the β1-bands of the X(5) nuclei 150Nd, 152Sm, 154Gd, and 156Dy to the X(3) predictions is observed.

scholarly journals Z(5): Critical Point Symmetry for the Prolate to Oblate Nuclear Shape Phase Transition

2020 ◽  
Vol 13 ◽  
pp. 73
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. A. Terziev
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Critical Point ◽  
Point Symmetry ◽  
Transition Rates ◽  
Oblate Shape ◽  
Scale Factors ◽  
Shape Phase Transition ◽  
Nuclear Shape Phase Transition ◽  
Good Agreement

A critical point symmetry for the prolate to oblate shape phase transition is intro­ duced, starting from the Bohr Hamiltonian and approximately separating variables for γ=30°. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours (192Pt, 196Pt).

scholarly journals γ-rigid solution of the Bohr Hamiltonian compared to the E(5) critical point symmetry

2019 ◽  
Vol 14 ◽  
pp. 71
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. Terziev ◽  
I. Yigitoglu
Keyword(s):  
Critical Point ◽  
Ground State ◽  
Close Agreement ◽  
Point Symmetry ◽  
Transition Rates ◽  
Ground State Band ◽  
Scale Factors ◽  
State Band ◽  
Euclidean Algebra ◽  
Rigid Solution

A γ-rigid solution of the Bohr Hamiltonian for 7 = 30° is derived, its ground state band being related to the second order Casimir operator of the Euclidean algebra E(4). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are in close agreement to the E (5) critical point symmetry, as well as to experimental data in the Xe region around A = 130.

A theoretical study of energy spectra and transition probabilities of 200–204Hg isotopes in transitional region of IBM

2014 ◽  
Vol 23 (10) ◽  
pp. 1450056 ◽  
Author(s):  
H. Sabri
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Transition Probabilities ◽  
Energy Spectra ◽  
Interacting Boson Model ◽  
Transitional Region ◽  
Transition Rates ◽  
Scale Factors ◽  
Boson Model ◽  
Good Agreement

In this paper, by using the SO(6) representation of eigenstates and transitional Interacting Boson Model (IBM) Hamiltonian, the evolution from prolate to oblate shapes along the chain of Hg isotopes is studied. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 200–204 Hg isotopes which are supported to be located in this transitional region.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

scholarly journals Response of a Warped Flexible Rotor with a Fluid Bearing

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Jim Meagher ◽  
Xi Wu ◽  
Chris Lencioni
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Equation Of Motion ◽  
Diagnostic Information ◽  
Flexible Rotor ◽  
Vibration Data ◽  
Rotor Model ◽  
Good Agreement

A two-complex-degrees-of-freedom model is developed and compared to experimental data for various amounts of rotor bow and its orientation to mass imbalance of the rotor. The equation of motion is developed by adding constant forces that rotate with the rotor to a Bently-Muszynska two-mode isotropic rotor model with a plane journal bearing. Diagnostic information discernable from probes at the bearing is explored and compared to midspan response, where previous research has concentrated. The model presented also extends earlier work by representing the effect of a nonrigid bearing. Good agreement between the analytical model and experiment demonstrates that the analysis presented can be useful to diagnose and balance residual shaft bow from probes located at the bearings, where vibration data are typically more available than midspan probes.

POWER AND EFFICIENCY OF F1-ATPase MOLECULAR MOTOR

2012 ◽  
Vol 11 (01) ◽  
pp. 1240003
Author(s):  
J. M. SANCHO ◽  
RUBEN PEREZ-CARRASCO
Keyword(s):  
Experimental Data ◽  
Angular Velocity ◽  
Molecular Motor ◽  
Transition Rates ◽  
Motor Power ◽  
F1 Atpase ◽  
Flashing Ratchet ◽  
Model Predictions ◽  
Good Agreement ◽  
Ratchet Potential

We present the study of the energetics of the F1-ATPase rotatory molecular motor. The dynamics of this machine are described by a overdamped Langevin equation with a dichotomous flashing ratchet potential whose transition rates are controlled by an analysis of the chemical and physical steps. The model predictions on the observable angular velocity are in good agreement with the experimental data. Inspired by these results we extend our approach to study the energetics of this motor. Power and efficiency are analyzed for different experimental situations which can be tested in experiments.

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.

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

scholarly journals Generalized Ehrenfest's equations and phase transition in black holes

2015 ◽  
Vol 24 (03) ◽  
pp. 1550029 ◽  
Author(s):  
Mohammad Bagher Jahani Poshteh ◽  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Critical Point ◽  
Order Phase Transition ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Second Order ◽  
First Law Of Thermodynamics ◽  
Three Degrees Of Freedom ◽  
Second Order Phase Transition

In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is [Formula: see text] equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.

Limit Points Behavior in Electrostatically Actuated Initially Curved Micro Plate

2016 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Load ◽  
Electrostatic Force ◽  
Equilibrium Path ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Base Functions ◽  
Three Degrees Of Freedom ◽  
Good Agreement

The axisymmetric snap-through of an initially curved circular micro plate, subjected to a transversal distributed electrostatic force is studied. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition, with buckling modes of a flat plate used as the base functions. In order to check the validity of the RO model, the corresponding problem for a displacement-independent (“mechanical”) load is solved, and a comparison between the RO model and those obtained using finite elements (FE) analysis is carried out. It is shown, that the two are in good agreement, indicating that the RO model can be used for a plate undergoing electrostatic loading. However, the study shows that at least three degrees of freedom (DOF) are required for an accurate prediction of the equilibrium path and bistability. The coupled electromechanical analysis shows that due to the nonlinearity of the electrostatic load, the snap-through occurs at a lower displacement than in the case of the “mechanical” load. Moreover, the study concludes that actuation of plates of realistic dimensions can be achieved by reasonably low voltages.

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