The Potential Representation Method for Non-spherical Perturbations

2020 ◽  
pp. 139-147
Keyword(s):  
Representation Method ◽  
Potential Representation

scholarly journals POTENTIAL REPRESENTATION METHOD FOR THE SCHRÖDINGER EQUATION

2011 ◽  
Vol 16 (3) ◽  
pp. 442-450 ◽  
Author(s):  
Arvydas Juozapas Janavičius ◽  
Donatas Jurgaitis ◽  
Sigita Turskienė
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Integral Equations ◽  
Schrodinger Equation ◽  
Bound States ◽  
Model Potential ◽  
Variation Of Constants ◽  
Potential Perturbation ◽  
Representation Method ◽  
Potential Representation

A general solution of the Schrödinger equation in the potential representation has been obtained in the form of integral equations. In this representation, the wave function for positive and negative energies or bound states can be expressed as a product of the unperturbed solution for model potential and the function which depends on the additional potential or potential perturbation. Here we have proved that this method is equivalent to the method of variation of constants for negative energies. The linearly independent solutions of Schrödinger equation for harmonic oscillator potential have been obtained for derivation of integral equations, which are used for finding eigenfunctions and eigenvalues for Woods–Saxon potential. Eigenvalues obtained by numerical iterations of these integral equations are in good agreement with results obtained by the discretization method. The kernels of the obtained integral equations are proportional to the perturbation or difference of Woods–Saxon and harmonic oscillator potentials.

Calculations of Polarizabilities and Their Gradients for Electron Energy-Loss Spectroscopy

2008 ◽  
Vol 73 (11) ◽  
pp. 1509-1524 ◽  
Author(s):  
Ivana Paidarová ◽  
Roman Čurík ◽  
Stephan P. A. Sauer
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Theoretical Models ◽  
Basis Set ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Perfect Agreement ◽  
Representation Method ◽  
Response Method ◽  
Electron Energy Loss

We illustrate for a set of small hydrocarbons, CH4, C2H4, C3H6 and C3H8, the important role of the electric dipole polarizability tensor and its geometric derivatives in theoretical models of electron energy-loss spectra (EELS). The coupled cluster linear response method together with Sadlej's polarized valence triple zeta basis set of atomic orbitals were used to calculate the polarizabilities and polarizability gradients. Incorporation of these ab initio data into the discrete momentum representation method (DMR) leads to perfect agreement between theory and collision experiments.

scholarly journals Neuronalis összeköttetések a szomatoszenzoros kérgi área 3b és área 1 kézreprezentációs területén főemlősökben

2016 ◽  
Vol 157 (33) ◽  
pp. 1320-1325
Author(s):  
Emese Pálfi ◽  
Mária Ashaber ◽  
Cory Palmer ◽  
Robert M. Friedman ◽  
Anna W. Roe ◽  
...  
Keyword(s):  
Functional Relationship ◽  
Hand Movement ◽  
Saimiri Sciureus ◽  
Skin Area ◽  
Tract Tracing ◽  
Reciprocal Connections ◽  
Representation Method ◽  
Local Input ◽  
Finger Pad ◽  
Area 3B

Introduction: The close functional relationship between areas 3b and 1 of the somatosensory cortex is based on their reciprocal connections indicating that tactile sensation depends on the interaction of these two areas. Aim: The aim of the authors was to explore this neuronal circuit at the level of the distal finger pad representation. Method: The study was made by bidirectional tract tracing aided by neurophysiological mapping in squirrel monkeys (Saimiri sciureus). Results: Inter-areal connections between the two areas preferred the homologues representations. However, intra-areal connections were formed between the neighboring finger pad representations supporting the physiological observations. Interestingly, the size of the local input area of the injected cortical micro-region, which differed in the two areas, represented the same skin area. Conclusions: The authors propose that intra-areal connections are important in integrating information across fingers, while inter-areal connections are important in maintaining input localization during hand movement. Orv. Hetil., 2016, 157(33), 1320–1325.

scholarly journals Continuous Fusion of Motion Data Using an Axis-Angle Rotation Representation with Uniform B-Spline

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5004
Author(s):  
Haohao Hu ◽  
Johannes Beck ◽  
Martin Lauer ◽  
Christoph Stiller
Keyword(s):  
Forward Direction ◽  
Measurement Unit ◽  
Automated Driving ◽  
Real World Data ◽  
Inertial Measurement ◽  
B Spline ◽  
Motion Data ◽  
Angle Rotation ◽  
Representation Method ◽  
Fusion Approach

The fusion of motion data is key in the fields of robotic and automated driving. Most existing approaches are filter-based or pose-graph-based. By using filter-based approaches, parameters should be set very carefully and the motion data can usually only be fused in a time forward direction. Pose-graph-based approaches can fuse data in time forward and backward directions. However, pre-integration is needed by applying measurements from inertial measurement units. Additionally, both approaches only provide discrete fusion results. In this work, we address this problem and present a uniform B-spline-based continuous fusion approach, which can fuse motion measurements from an inertial measurement unit and pose data from other localization systems robustly, accurately and efficiently. In our continuous fusion approach, an axis-angle is applied as our rotation representation method and uniform B-spline as the back-end optimization base. Evaluation results performed on the real world data show that our approach provides accurate, robust and continuous fusion results, which again supports our continuous fusion concept.

A Smooth Contact Algorithm Using Cubic Spline Surface Interpolation for Rigid and Flexible Bodies

2013 ◽  
Author(s):  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Contact Force ◽  
Cubic Spline ◽  
Surface Representation ◽  
Flexible Bodies ◽  
Contact Algorithm ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Smooth Contact ◽  
Representation Method ◽  
Detailed Search

The contact analysis of multi-flexible-body dynamics (MFBD) has been an important issue in the area of computational dynamics because the realistic dynamic analysis of many mechanical systems includes the contacts among rigid and flexible bodies. But, until now, the contact analysis in the multi-flexible-body dynamics has still remained as a big, challenging area. Especially, the most of contact algorithms have been developed based on the facetted triangles. As a result, the contact force based on the facetted surface was not accurate and smooth because the geometrical error is already included in the contact surface representation stage. This kind of error can be very important in the precise mechanism such as gear contact or cam-valve contact problems. In order to resolve this problem, this study suggests a cubic spline surface representation method and related contact algorithms. The proposed contact algorithms are using the compliant contact force model based on the Hertzian contact theory. In order to evaluate the smooth contact force, the penetration depth and contact normal directions are evaluated by using the cubic spline surface interpolation. Also, for the robust and efficient contact algorithm development, the contact algorithms are divided into four main parts which are a surface representation, a pre-search, a detailed search and a contact force generation. In the surface representation part, we propose a smooth surface representation method which can be used for smooth rigid and flexible bodies. In the pre-search, the algorithm performs collision detection and composes the expected contact pairs for the detailed search. In the detailed search, the penetration depth and contact reference frame are calculated with the cubic spline surface interpolation in order to generate the accurate and smooth contact force. Finally in the contact force generation part, we evaluate the contact force and Jacobian matrix for the implicit time integrator.

Sign in / Sign up

Export Citation Format

Share Document