Energy spreading, equipartition and chaos in lattices with non-central forces

Abstract We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quadratic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quadratic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.

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MODELING AND BIFURCATION BEHAVIOR OF MULTI-PHASE SIMIMO DC–DC SWITCHING REGULATORS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410028021 ◽

2010 ◽

Vol 20 (11) ◽

pp. 3841-3861 ◽

Cited By ~ 1

Author(s):

V. MORENO-FONT ◽

A. EL AROUDI ◽

L. BENADERO

Keyword(s):

Discrete Time ◽

Chaotic Behavior ◽

Piecewise Linear ◽

Dynamical Behavior ◽

Stability Index ◽

Operating Conditions ◽

Continuation Methods ◽

Accurate Information ◽

One Dimensional ◽

Discrete Time Models

In this paper, different discrete-time models in the form of maps are proposed and analyzed in order to describe the dynamics of single inductor multiple-input multiple-output (SIMIMO) switching DC–DC converters. These systems can be used to regulate generally multiple (positive and/or negative) outputs by means of individual switches associated to each of the outputs. These switches are current mode controlled through corresponding channels. The discrete-time approach allows the dynamical behavior of these systems to be accurately predicted as well as to detect possible subharmonic oscillations and chaotic behavior. Under certain operating conditions, for which the system can be modeled by a one-dimensional piecewise constant vector field, a simple one-dimensional and piecewise-linear (PWL) map can be obtained. Some closed form expressions for ensuring stability are derived from this map in terms of a stability index λ, which is, in turn, expressed in terms of system parameters. However, some discrepancies have been found between the switched model and this simpler map, and therefore a full order model is derived to obtain more accurate information about the actual dynamical behavior of these converters. The theoretical results are confirmed by one-dimensional bifurcation diagrams and codimension 1 two-parameter bifurcation curves obtained by standard continuation methods applied to the derived discrete-time models as well as from computer simulations from the switched model.

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Time-dependent properties of interacting active matter: Dynamical behavior of one-dimensional systems of self-propelled particles

Physical Review Research ◽

10.1103/physrevresearch.2.033518 ◽

2020 ◽

Vol 2 (3) ◽

Cited By ~ 4

Author(s):

Lorenzo Caprini ◽

Umberto Marini Bettolo Marconi

Keyword(s):

Dynamical Behavior ◽

Time Dependent ◽

Active Matter ◽

One Dimensional

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Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

Mathematics and Mechanics of Solids ◽

10.1177/10812865211023885 ◽

2021 ◽

pp. 108128652110238

Author(s):

Barış Erbaş ◽

Julius Kaplunov ◽

Isaac Elishakoff

Keyword(s):

Ad Hoc ◽

Moving Load ◽

Low Frequency ◽

Elastic Beam ◽

Winkler Foundation ◽

One Dimensional ◽

Beam Equations ◽

Dimensional Equation ◽

Phase And Group Velocities ◽

Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

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Chemistry Under Shock Conditions

Annual Review of Materials Research ◽

10.1146/annurev-matsci-080819-120123 ◽

2021 ◽

Vol 51 (1) ◽

Author(s):

Brenden W. Hamilton ◽

Michael N. Sakano ◽

Chunyu Li ◽

Alejandro Strachan

Keyword(s):

Materials Science ◽

Low Frequency ◽

Annual Review ◽

Publication Date ◽

Energy Localization ◽

Ambient Conditions ◽

Static Loads ◽

Nonequilibrium Conditions ◽

Life On Earth ◽

Modes Coupling

Shock loading takes materials from ambient conditions to extreme conditions of temperature and nonhydrostatic stress on picosecond timescales. In molecular materials the fast loading results in temporary nonequilibrium conditions with overheated low-frequency modes and relatively cold, high-frequency, intramolecular modes; coupling the shock front with the material's microstructure and defects results in energy localization in hot spots. These processes can conspire to lead to a material response not observed under quasi-static loads. This review focuses on chemical reactions induced by dynamical loading, the understanding of which requires bringing together materials science, shock physics, and condensed matter chemistry. Recent progress in experiments and simulations holds the key to the answer of long-standing grand challenges with implications for the initiation of detonation and life on Earth. Expected final online publication date for the Annual Review of Materials Science, Volume 51 is August 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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MULTIDIMENSIONAL REPRESENTATION OF AUTOMATIC DOSING DEVICE SIGNALS

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2018-4-26-32 ◽

2018 ◽

pp. 26-32

Author(s):

Denis Borisovich Fedosenkov ◽

Anna Alekseevna Simikova ◽

Boris Andreevich Fedosenkov ◽

Stanislav Matveevich Kulakov

Keyword(s):

Fourier Transform ◽

Wigner Distribution ◽

Low Frequency ◽

Stationary Flow ◽

Complex Model ◽

Signal Spectrum ◽

One Dimensional ◽

Time Frequency ◽

Cohen's Class ◽

Discrete Values

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

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Tunable Omnidirectional Band Gap Properties of 1D Plasma Annular Periodic Multilayer Structure Based on an Improved Fibonacci Topological Structure

10.21203/rs.3.rs-181473/v1 ◽

2021 ◽

Author(s):

Hong-Mei Peng ◽

Bao-Fei Wan ◽

Peng-Xiang Wang ◽

Dan Zhang ◽

Hai-Feng Zhang

Keyword(s):

Band Gap ◽

Plasma Frequency ◽

Incident Angle ◽

Low Frequency ◽

Interesting Phenomenon ◽

Azimuthal Mode ◽

One Dimensional ◽

Theoretical Support ◽

Omnidirectional Band Gap ◽

High Reflection

Abstract In this paper, the characteristics of the omnidirectional band gap (OBG) for one-dimensional (1D) plasma cylindrical photonic crystals (PCPCs) are based on an improved Fibonacci topological (IFT) structure are studied. The influences of the azimuthal mode number, incident angle, plasma thickness, and plasma frequency on the OBG are discussed. It is concluded that increasing the azimuth modulus can significantly expand the bandwidth of the OBG, and the OBG can be moved to the low-frequency direction by increasing the plasma frequency. In addition, an interesting phenomenon can be found that when the number of azimuthal modes is equal to 2, the TM wave can produce an extra high reflection zone. It provides a theoretical support for designing the narrowband filters without introducing any physical defect layers in the structure.

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Dimensional tailoring of nitrogen-doped graphene for high performance supercapacitors

RSC Advances ◽

10.1039/c6ra07825g ◽

2016 ◽

Vol 6 (60) ◽

pp. 55577-55583 ◽

Cited By ~ 3

Author(s):

Seung Yong Lee ◽

Chang Hyuck Choi ◽

Min Wook Chung ◽

Jae Hoon Chung ◽

Seong Ihl Woo

Keyword(s):

High Performance ◽

Low Frequency ◽

Frequency Region ◽

Transfer Resistance ◽

One Dimensional ◽

Nitrogen Doped ◽

Efficient Charge ◽

Nitrogen Doped Graphene ◽

Doped Graphene ◽

Low Mass

In supercapacitors, one dimensional graphene ribbons which form net-like porous structure demonstrate low mass transfer resistance at low frequency region and a consequent efficient charge transferability.

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Matter-wave solitons supported by quadrupole–quadrupole interactions and anisotropic discrete lattices

International Journal of Modern Physics B ◽

10.1142/s0217979218501072 ◽

2018 ◽

Vol 32 (09) ◽

pp. 1850107 ◽

Cited By ~ 3

Author(s):

Rong-Xuan Zhong ◽

Nan Huang ◽

Huang-Wu Li ◽

He-Xiang He ◽

Jian-Tao Lü ◽

...

Keyword(s):

Optical Lattices ◽

Chemical Potential ◽

Plane Waves ◽

Einstein Condensate ◽

Matter Wave ◽

Linear Dispersion ◽

One Dimensional ◽

Bose Einstein Condensate ◽

Discrete Lattices ◽

Discrete Solitons

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

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Unique features of the generation–recombination noise in quasi-one-dimensional van der Waals nanoribbons

Nanoscale ◽

10.1039/c8nr06984k ◽

2018 ◽

Vol 10 (42) ◽

pp. 19749-19756 ◽

Cited By ~ 9

Author(s):

Adane K. Geremew ◽

Sergey Rumyantsev ◽

Matthew A. Bloodgood ◽

Tina T. Salguero ◽

Alexander A. Balandin

Keyword(s):

Carrying Capacity ◽

Van Der Waals ◽

Low Frequency ◽

Current Fluctuations ◽

Electronic Noise ◽

High Current ◽

One Dimensional ◽

Frequency Current

We describe the low-frequency current fluctuations, i.e. electronic noise, in quasi-one-dimensional ZrTe3 van der Waals nanoribbons, which have recently attracted attention owing to their extraordinary high current carrying capacity.

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