scholarly journals Excitation Spectrum of the Néel Ensemble of Antiferromagnetic Nanoparticles as Revealed in Mössbauer Spectroscopy

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Mikhail A. Chuev
Keyword(s):  
Absorption Spectra ◽  
Excitation Spectrum ◽  
Magnetic Moment ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Quantum Mechanical ◽  
Solution Of Equations ◽  
Regular Precession ◽  
Macroscopic Quantum Effects ◽  
Quantum Mechanical Representation

The excitation spectrum of the Néel ensemble of antiferromagnetic nanoparticles with uncompensated magnetic moment is deduced in the two-sublattice approximation following the exact solution of equations of motion for magnetizations of sublattices. This excitation spectrum represents four excitation branches corresponding to the normal modes of self-consistent regular precession of magnetizations of sublattices and the continuous spectrum of nutations of magnetizations accompanying these normal modes. Nontrivial shape of the excitation spectrum as a function of the value of uncompensated magnetic moment corresponds completely to the quantum-mechanical calculations earlier performed. This approach allows one to describe also Mössbauer absorption spectra of slowly relaxing antiferromagnetic and ferrimagnetic nanoparticles and, in particular, to give a phenomenological interpretation of macroscopic quantum effects observed earlier in experimental absorption spectra and described within the quantum-mechanical representation.

scholarly journals Magnetic reversal dynamics of a quantum system on a picosecond timescale

2015 ◽  
Vol 6 ◽  
pp. 1946-1956 ◽  
Author(s):  
Nikolay V Klenov ◽  
Alexey V Kuznetsov ◽  
Igor I Soloviev ◽  
Sergey V Bakurskiy ◽  
Olga V Tikhonova
Keyword(s):  
Magnetic Moment ◽  
Magnetization Reversal ◽  
Quantum Mechanical ◽  
Magnetic Reversal ◽  
Level System ◽  
Macroscopic Theory ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
Classical Behavior ◽  
Flux Qubit

We present our approach for a consistent, fully quantum mechanical description of the magnetization reversal process in natural and artificial atomic systems by means of short magnetic pulses. In terms of the simplest model of a two-level system with a magnetic moment, we analyze the possibility of a fast magnetization reversal on the picosecond timescale induced by oscillating or short unipolar magnetic pulses. We demonstrate the possibility of selective magnetization reversal of a superconducting flux qubit using a single flux quantum-based pulse and suggest a promising, rapid Λ-scheme for resonant implementation of this process. In addition, the magnetization reversal treatment is fulfilled within the framework of the macroscopic theory of the magnetic moment, which allows for the comparison and explanation of the quantum and classical behavior.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method

1997 ◽  
Vol 11 (06) ◽  
pp. 245-258 ◽  
Author(s):  
J. Seke ◽  
A. V. Soldatov ◽  
N. N. Bogolubov
Keyword(s):  
Projection Operator ◽  
Equations Of Motion ◽  
Operator Method ◽  
Approximation Order ◽  
Quantum Mechanical ◽  
Approximation Technique ◽  
Operator Structure ◽  
Projection Operator Method ◽  
Self Consistent ◽  
Effective Hamiltonians

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes

1999 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre ◽  
S. W. Shaw
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Single Equation ◽  
Rotating Beam ◽  
Model Size ◽  
Nonlinear Normal

Abstract Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.

An Emerging O(N) Model and Algorithm for Virtual Prototyping of Dynamics of Molecular Conformation

2008 ◽  
Author(s):  
Andrew Ries ◽  
Shanzhong Shawn Duan
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Conformation ◽  
Molecular System ◽  
Equations Of Motion ◽  
Integration Step ◽  
Computational Costs ◽  
System A ◽  
Hard Constraints ◽  
Solution Of Equations ◽  
Computationally Intensive

Molecular dynamics is effective for nano-scale phenomenon analysis. There are two major computational steps associated with computer simulation of dynamics of molecular conformation and they are the calculation of the interatomic forces and the formation and solution of the equations of motion. Currently, these two computational steps are treated separately, but in this paper an O(N) (order N) procedure is presented for an integration between these computational steps. For computational costs associated with calculating the interatomic forces, an internal coordinate method (ICM) approach is used for determining potentials due to both the bonding and non-bonding interactions. Thus, the potential gradients can be expressed as a combination of the potential in absolute and relative coordinates. For computational costs associated with the formation and solution of the equations of motion for the system, a constraint method that is used in computational multibody dynamics is utilized. This frees some degrees of freedom so that Kane’s method can be applied for the recursive formation and solution of equations of motion for the atomistic molecular system. Because the inclusion of lightly excited high frequency degrees of freedom, such as inter-atomic oscillations and rotation about double bonds would force the use of very small integration step sizes, holonomic constraints are introduced to freeze these “uninteresting” degrees of freedom. By introducing these hard constraints the time scale can be appropriately sized for to provide a less computationally intensive dynamic simulation of molecular conformation. The algorithm developed improves computational speed significantly when compared with any traditional O(N3) procedure.

scholarly journals Simulating Absorption Spectra of Flavonoids in Aqueous Solution: A Polarizable QM/MM Study

Molecules ◽  
2020 ◽  
Vol 25 (24) ◽  
pp. 5853
Author(s):  
Sulejman Skoko ◽  
Matteo Ambrosetti ◽  
Tommaso Giovannini ◽  
Chiara Cappelli
Keyword(s):  
Molecular Dynamics ◽  
Aqueous Solution ◽  
Hydrogen Bonding ◽  
Force Field ◽  
Absorption Spectra ◽  
Computational Study ◽  
Md Simulations ◽  
Quantum Mechanical ◽  
Hydrogen Bonding Interactions

We present a detailed computational study of the UV/Vis spectra of four relevant flavonoids in aqueous solution, namely luteolin, kaempferol, quercetin, and myricetin. The absorption spectra are simulated by exploiting a fully polarizable quantum mechanical (QM)/molecular mechanics (MM) model, based on the fluctuating charge (FQ) force field. Such a model is coupled with configurational sampling obtained by performing classical molecular dynamics (MD) simulations. The calculated QM/FQ spectra are compared with the experiments. We show that an accurate reproduction of the UV/Vis spectra of the selected flavonoids can be obtained by appropriately taking into account the role of configurational sampling, polarization, and hydrogen bonding interactions.

The Use of Normal Modes in Problems of Forced Vibration and Impact

1957 ◽  
Vol 61 (560) ◽  
pp. 552-559
Author(s):  
R. P. N. Jones
Keyword(s):  
Forced Vibration ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Very High Frequency ◽  
Linear Elastic ◽  
Modes Of Vibration ◽  
Fundamental Equations ◽  
Very High ◽  
Simple Exposition

SummaryA simple exposition, using d'Alembert's principle and methods of virtual work, is given of the properties and applications of the normal modes of vibration of a linear elastic system. The use of the normal modes in problems of free and forced vibration and dynamic loading is discussed with the aid of simple examples, and it is shown that by these methods dynamical problems for any linear system may be solved without the use of the fundamental equations of motion, provided the natural frequencies and modes of the system are known. In most problems the solutions converge rapidly, so that only the first few modes of vibration need be considered, and in these cases the solution may be modified to give further improvement in convergence. Unsatisfactory convergence may be obtained, however, in problems where there is an exciting force of very high frequency, or an impact of short duration. An approximate allowance may be made for damping, provided this is small.

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