scholarly journals NVU dynamics. III. Simulating molecules at constant potential energy

2012 ◽  
Vol 137 (24) ◽  
pp. 244101 ◽  
Author(s):  
Trond S. Ingebrigtsen ◽  
Jeppe C. Dyre
Keyword(s):  
Potential Energy ◽  
Constant Potential

On zero stiffness

2013 ◽  
Vol 228 (10) ◽  
pp. 1701-1714 ◽  
Author(s):  
Mark Schenk ◽  
Simon D Guest
Keyword(s):  
Potential Energy ◽  
Neutral Stability ◽  
External Work ◽  
Elastic Deformations ◽  
Analysis And Design ◽  
Methods Of Analysis ◽  
Constant Potential ◽  
Working Principle

Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings.

scholarly journals NVUdynamics. I. Geodesic motion on the constant-potential-energy hypersurface

2011 ◽  
Vol 135 (10) ◽  
pp. 104101 ◽  
Author(s):  
Trond S. Ingebrigtsen ◽  
Søren Toxvaerd ◽  
Ole J. Heilmann ◽  
Thomas B. Schrøder ◽  
Jeppe C. Dyre
Keyword(s):  
Potential Energy ◽  
Geodesic Motion ◽  
Constant Potential ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators

2009 ◽  
Author(s):  
Rogier Barents ◽  
Mark Schenk ◽  
Wouter D. van Dorsser ◽  
Boudewijn M. Wisse ◽  
Just L. Herder
Keyword(s):  
Potential Energy ◽  
Adjustment Method ◽  
Free Length ◽  
Regular Extension ◽  
Conceptual Designs ◽  
Constant Potential ◽  
Spring Mechanism

Generally, adjustment of gravity equilibrator to a new payload requires energy, e.g. to increase the pre-load of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.

Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Rogier Barents ◽  
Mark Schenk ◽  
Wouter D. van Dorsser ◽  
Boudewijn M. Wisse ◽  
Just L. Herder
Keyword(s):  
Potential Energy ◽  
Adjustment Method ◽  
Free Length ◽  
Regular Extension ◽  
Conceptual Designs ◽  
Constant Potential ◽  
Spring Mechanism

Generally, adjustment of gravity equilibrators to a new payload requires energy, e.g., to increase the preload of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence, the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and the balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.

Calculations of K absorption edges in some heavy atoms

1953 ◽  
Vol 218 (1134) ◽  
pp. 422-432 ◽  
Keyword(s):  
Binding Energy ◽  
Potential Energy ◽  
Coulomb Field ◽  
The Other ◽  
Nuclear Potential ◽  
Heavy Atoms ◽  
Self Consistent Field ◽  
Constant Potential ◽  
Order Change ◽  
Second Order Change

The binding energy of a K electron in some heavy atoms is calculated to order Zα 2 mc 2 . This energy is considered in three parts: (i) the potential energy of the K electron in the Coulomb field of the nucleus, (ii) the interaction with the other K electron, and (iii) the Coulomb potential energy arising from the other (‘outer’) electrons. Although the potential due to the outer electrons is large, it varies little in the region of the K shell and may be written in the form V = a + b(r) , b (0) = 0, where a is a large constant potential and b(r) a small correction to it. For these the self-consistent field calculations are used. The nuclear potential and α are taken into account exactly and the remaining terms considered as small perturbations. The K electrons are treated relativistically. The change in the wave functions of the outer electrons when a K electron is removed is shown to give only a second-order change in the binding energy of a K electron. The results are found to be in good agreement with experiment.

Can resonances occur in the photodissociation continuum of a diatomic molecule? The role of potential discontinuities

2004 ◽  
Vol 82 (6) ◽  
pp. 826-830 ◽  
Author(s):  
Joel Tellinghuisen
Keyword(s):  
Quantum Mechanics ◽  
Potential Energy ◽  
Resonance Structure ◽  
Piecewise Constant ◽  
Potential Energy Functions ◽  
Molecular Potential ◽  
State Potential ◽  
Constant Potential ◽  
Instructional Literature ◽  
Molecular Potential Energy

Continuum resonances are standard fare in the instructional literature for quantum mechanics, where they arise from the continuity conditions imposed on one-dimensional wavefunctions for piecewise-constant potential energy functions. Such resonance structure weakens progressively as the discontinuity in the potential is smoothed, showing that the structure is specifically attributable to the discontinuity. Since diatomic molecular potential energy curves seldom vary rapidly on the distance scale of the period of the wavefunction, such continuum resonances are not expected in absorption continua. A historically interesting prediction of such structure in the Schumann–Runge continuum (B ← X) of O2 is attributed to the inadvertent incorporation of discontinuity in the B-state potential curve employed in the computations.Key words: quantum mechanics, continuum resonance, diatomic absorption, photodissociation continuum, numerical methods.

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