scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

scholarly journals Ground-state energy of a Richardson-Gaudin integrable BCS model

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links
Keyword(s):  
Integral Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Continuum Limit ◽  
State Energy ◽  
Mean Field ◽  
Bcs Model ◽  
Energy Expression ◽  
The Continuum

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

Cooperative Broadcast in Large-Scale Wireless Networks

2012 ◽  
pp. 604-623
Author(s):  
Birsen Sirkeci-Mergen ◽  
Anna Scaglione ◽  
Michael Gastpar
Keyword(s):  
Wireless Networks ◽  
Power Efficiency ◽  
Large Scale ◽  
Continuum Limit ◽  
Single Node ◽  
Large Scale Network ◽  
Scale Network ◽  
Multiple Groups ◽  
The Continuum

This chapter studies the cooperative broadcasting in wireless networks. We especially focus on multistage cooperative broadcasting in which the message from a source node is relayed by multiple groups of cooperating nodes. Interestingly, group transmissions become beneficial in the case of broadcasting as opposed to the case in traditional networks where receptions from different transmitters are considered as collision and disregarded. Different aspects of multistage cooperative broadcasting are analyzed in the chapter: (i) coverage behavior; (ii) power efficiency; (ii) error propagation; (iv) maximum communication rate. Whenever possible, performance is compared with multihop broadcasting where transmissions are relayed by a single node at each hop. We consider a large-scale network with many nodes distributed randomly in a given area. In order to analyze such networks, an important methodology, the continuum limit, is introduced. In the continuum limit, random networks are approximated by their dense limits under sum relay power constraint. This method allows us to obtain analytical results for the analysis of cooperative multistage broadcasting.

THZ-FREQUENCY SPECTROSCOPIC SENSING OF DNA AND RELATED BIOLOGICAL MATERIALS

2003 ◽  
Vol 13 (04) ◽  
pp. 903-936 ◽  
Author(s):  
T. GLOBUS ◽  
D. WOOLARD ◽  
M. BYKHOVSKAIA ◽  
B. GELMONT ◽  
L. WERBOS ◽  
...  
Keyword(s):  
Absorption Spectra ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Low Frequency ◽  
Biological Materials ◽  
Mode Analysis ◽  
Resonance Structure ◽  
Terahertz Frequency ◽  
Dna Molecules ◽  
Phonon Modes

The terahertz frequency absorption spectra of DNA molecules reflect low-frequency internal helical vibrations involving rigidly bound subgroups that are connected by the weakest bonds, including the hydrogen bonds of the DNA base pairs, and/or non-bonded interactions. Although numerous difficulties make the direct identification of terahertz phonon modes in biological materials very challenging, recent studies have shown that such measurements are both possible and useful. Spectra of different DNA samples reveal a large number of modes and a reasonable level of sequence-specific uniqueness. This chapter utilizes computational methods for normal mode analysis and theoretical spectroscopy to predict the low-frequency vibrational absorption spectra of short artificial DNA and RNA. Here the experimental technique is described in detail, including the procedure for sample preparation. Careful attention was paid to the possibility of interference or etalon effects in the samples, and phenomena were clearly differentiated from the actual phonon modes. The results from Fourier-transform infrared spectroscopy of DNA macromolecules and related biological materials in the terahertz frequency range are presented. In addition, a strong anisotropy of terahertz characteristics is demonstrated. Detailed tests of the ability of normal mode analysis to reproduce RNA vibrational spectra are also conducted. A direct comparison demonstrates a correlation between calculated and experimentally observed spectra of the RNA polymers, thus confirming that the fundamental physical nature of the observed resonance structure is caused by the internal vibration modes in the macromolecules. Application of artificial neural network analysis for recognition and discrimination between different DNA molecules is discussed.

Raman Investigation of Heavily Al Doped 4H-SiC Layers Grown by CVD

2014 ◽  
Vol 806 ◽  
pp. 51-55 ◽  
Author(s):  
Pawel Kwasnicki ◽  
Roxana Arvinte ◽  
Hervé Peyre ◽  
Marcin Zielinski ◽  
Leszek Konczewicz ◽  
...  
Keyword(s):  
Carrier Concentration ◽  
Raman Spectra ◽  
Secondary Ion Mass Spectrometry ◽  
Low Frequency ◽  
Electrical Measurement ◽  
Longitudinal Optical ◽  
Electronic Transitions ◽  
Longitudinal Optical Phonon ◽  
Phonon Modes ◽  
The Continuum

In this work, we focus on heavily aluminum (Al) doped 4H-SiC samples. We compare the effect of the Al concentration and Hall carrier concentration on the Raman spectra in a large frequency range. The Al concentration measured by Secondary Ion Mass Spectrometry ranged from 2×1016to 8.4×1019cm-3while the electrical measurement give a carrier concentration up to 5×1019Al×cm-3. On the Raman spectra, three different frequency domains have been analysed: i) at high frequency where we consider the change in longitudinal optical phonon-plasmon coupled mode; ii°) at low frequency where we consider the continuum of electronic transitions and iii°) finally, considering the Fano interference effect between the continuum of electronic transitions and the Folded Transverse Acoustic phonon modes. This analysis is applied to comment a Raman spectra mapping collected on a 4H-SiC 2 inch wafer.

scholarly journals On the helicity characteristics and induced emf of magnetic-Coriolis wave packets

2020 ◽  
Vol 223 (2) ◽  
pp. 1398-1411
Author(s):  
B R McDermott ◽  
P A Davidson
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Rotation Axis ◽  
Wave Packets ◽  
Mean Field Theory ◽  
Mean Field ◽  
Low Frequency ◽  
Dynamo Model ◽  
Small Scale ◽  
Inertial Wave

SUMMARY In a rapidly rotating Boussinesq fluid, buoyant anomalies radiate low-frequency inertial wave packets that disperse along the rotation axis. The wave packets lead to axially elongated vortices, which propagate negative (positive) kinetic helicity upwards (downwards) with respect to the rotation vector. The kinetic helicity carried by the inertial wave packets is near-maximal relative to the velocity and vorticity fields. In classical mean-field theory, kinetic helicity is often associated with the α-effect, which is thought to be an important ingredient for planetary dynamos. The modification of inertial wave packets in the presence of a transverse uniform magnetic field is investigated here, motivated by small-scale dynamics in planetary cores, where a large-scale magnetic field affects fluid motions. We study numerically the dispersion of wave packets from an isolated buoyant source and from a random layer of buoyant anomalies, while varying the Lehnert number Le—the ratio of the frequencies of Alfvén and inertial waves. We find that for Le < 0.1, the vortices are columnar and continue to segregate kinetic helicity so that it is negative (positive) above (below) the buoyant source. Importantly, the wave packets induce an α-effect, which remains strong and coherent for Earth-like values of the Lehnert number (Le < 0.1). The interaction of wave packets emitted by multiple neighbouring buoyant sources results in an α-effect that is stronger than the α-effect induced by wave packets launched from an isolated buoyant source, and we provide an analytical explanation for this. The coherence of the α-effect induced by the wave packets, for Earth-like values of the Lehnert number, lends support to the α2 dynamo model driven by helical waves.

scholarly journals Inhomogeneous Phases in the Chirally Imbalanced 2+1-Dimensional Gross-Neveu Model and Their Absence in the Continuum Limit

2021 ◽  
Author(s):  
Laurin Pannullo ◽  
Marc Wagner ◽  
Marc Winstel
Keyword(s):  
Continuum Limit ◽  
Chemical Potential ◽  
Finite Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Inhomogeneous Phase ◽  
T Phase ◽  
The Continuum ◽  
Gross Neveu Model

We study the μ-μ45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where μ denotes the ordinary chemical potential, μ45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.

Cooperative Broadcast in Large-Scale Wireless Networks

2010 ◽  
pp. 497-520
Author(s):  
Birsen Sirkeci-Mergen ◽  
Anna Scaglione ◽  
Michael Gastpar
Keyword(s):  
Wireless Networks ◽  
Power Efficiency ◽  
Large Scale ◽  
Continuum Limit ◽  
Single Node ◽  
Large Scale Network ◽  
Scale Network ◽  
Multiple Groups ◽  
The Continuum

This chapter studies the cooperative broadcasting in wireless networks. We especially focus on multistage cooperative broadcasting in which the message from a source node is relayed by multiple groups of cooperating nodes. Interestingly, group transmissions become beneficial in the case of broadcasting as opposed to the case in traditional networks where receptions from different transmitters are considered as collision and disregarded. Different aspects of multistage cooperative broadcasting are analyzed in the chapter: (i) coverage behavior; (ii) power efficiency; (ii) error propagation; (iv) maximum communication rate. Whenever possible, performance is compared with multihop broadcasting where transmissions are relayed by a single node at each hop. We consider a large-scale network with many nodes distributed randomly in a given area. In order to analyze such networks, an important methodology, the continuum limit, is introduced. In the continuum limit, random networks are approximated by their dense limits under sum relay power constraint. This method allows us to obtain analytical results for the analysis of cooperative multistage broadcasting.

LOCALIZED LOW-FREQUENCY VIBRATIONAL MODES IN A SIMPLE MODEL GLASS

1991 ◽  
Vol 05 (11) ◽  
pp. 735-739 ◽  
Author(s):  
H.R. SCHOBER ◽  
BRIAN B. LAIRD
Keyword(s):  
Normal Mode Analysis ◽  
Low Frequency ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Zero Temperature ◽  
Localized Modes ◽  
Low Frequencies ◽  
Effective Masses ◽  
Model Glass ◽  
Soft Spheres

By molecular dynamics we produce a glass of soft spheres quenched to zero temperature. Normal mode analysis of the vibrational spectrum shows the existence of (quasi)localized modes at low frequencies. The structure of the glass around the centers of these modes deviates significantly from the average. The effective masses of these soft modes range upward from about 10 atomic masses.

scholarly journals Dynamical Scaling and Phase Coexistence in Topologically-Constrained DNA Melting

2017 ◽  
Author(s):  
Y. A. G. Fosado ◽  
D. Michieletto ◽  
D. Marenduzzo
Keyword(s):  
Field Theory ◽  
Single Molecule ◽  
Brownian Dynamics ◽  
Large Scale ◽  
Scaling Law ◽  
Mean Field Theory ◽  
Mean Field ◽  
Phase Coexistence ◽  
Single Molecule Level ◽  
Dynamical Scaling

There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular-closed plasmids, is less abrupt than that of linear molecules. This finding points to an important role of topology in the physics of DNA denaturation, which is however poorly understood. Here, we shed light on this issue by combining large-scale Brownian Dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the single molecule level. This coexistence occurs in a wide temperature range, thereby accounting for the broadening of the transition. Finally, our simulations show an intriguing topology-dependent scaling law governing the growth of denaturation bubbles in supercoiled plasmids, which can be understood within the proposed mean field theory.

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