Diatomic Chain Research Articles

Experimental Study of Strongly Nonlinear Resonances and Anti-Resonances in Granular Dimer Chains

Previous theoretical works considered the intrinsic dynamics of one-dimensional uncompressed granular dimer (diatomic) chains composed of pairs of dissimilar spherical elastic beads in Hertzian interaction. Such ordered granular media exhibit essentially nonlinear acoustics and have been characterized as ‘sonic vacua’ due to the fact that the speed of sound in these media (as defined in classical acoustics) is zero. Yet, depending on the mass ratios of the pairs of dissimilar beads of these dimers, it was proven that they may possess countable infinities of anti-resonances leading to solitary waves (this in spite of their high inhomogeneity), or countable infinities of strongly nonlinear resonances leading to passive strong attenuation of propagating pulses through energy radiation by means of excitation of traveling waves. The aim of this work is to experimentally verify the existence of these strongly nonlinear dynamics through a series of experiments involving granular dimer chains supported by flexures. By carefully designing the supporting flexures so that their dynamics is sufficiently ‘soft’ and thus separate from the ‘stiff’ dynamics governing the bead to bead interactions, we overcome a basic limitation for the experimental realization of such dimer systems, namely the construction of one-dimensional dimer chains with beads of different radii. Our results confirm experimentally the occurrence of nonlinear resonances and anti-resonances in dimer chains, and conclusively prove the capacity of appropriately designed granular dimers for passive strong attenuation of propagating pulses due to nonlinear resonance. Moreover, we validate the theoretical prediction that within the elastic range of bead to bead dynamical interactions the results are fully re-scalable with respect to energy. This work provides the first experimental evidence of strongly nonlinear resonances and anti-resonances in essentially nonlinear ordered granular media.

Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of non-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.

Magnetic property of a one-dimensional FePt atomic chain on a NiAl(110) surface

Through the full potential linearized augmented plane wave (FLAPW) method, the magnetic property of a one-dimensional (1D) FePt diatomic chain has been explored. We find a ferromagnetic (FM) ground state for both free-standing and supported systems on a NiAl(110) surface. In the free-standing state, Fe and Pt atoms have magnetic moments of 3.47 and 0.74 µB, respectively. On a NiAl(110) surface, the magnetic moment of Fe becomes 2.95 µB, and there is no spin polarization in the Pt atom. In contrast, the surface Ni has an induced magnetic moment of 0.2 µB. The direction of magnetization and the strength of magnetic anisotropy energy are found to be substantially affected by the NiAl(110) surface. For instance, the magnetization aligns perpendicular to the chain axis for the free-standing state, and the calculated magnetic anisotropy energy is 18.33 meV/cell, however the magnetization direction of a supported system aligns parallel to the chain axis with an anisotropy energy of 0.568 meV/cell. Overall, we find that the magnetic anisotropy of a 1D FePt atomic chain is substantially influenced by the presence of the NiAl(110) substrate.

Understanding formation mechanism of ZnO diatomic chain and multi-shell structure using physical mechanics: Molecular dynamics and first-principle simulations?

In this paper, the possibility of the monatomic chain (MC) formation for ZnO material was studied by molecular dynamics (MD) simulation. The process of MC formation and the effects of temperature, strain rate and size were studied extensively. The tensile process can be divided to be five stages and the ZnO diatomic chain (DC) can be found. The MD results show that most atoms in MC came from the original surface of ZnO nanowires (NWs). Temperature and strain rate are two important factors affecting the process, and both high temperature and low strain rate in a certain range would be beneficial to the formation of DC. Moreover, the effects of strain rate and temperature could attribute to the Arrhenius model and the energy release mechanism. Furthermore, multi-shell structure was found for the samples under tensile strain and the layer-layer distance was about 3 Å. Our studies based on density functional theory showed that the most stable structure of ZnO DC was confirmed to be linear, and the I–V curve was also got using ATK.

Ab initio study of the vibrational properties of single-walled silicon nanotubes

We investigate the vibrational properties of pentagonal and hexagonal single walled silicon nanotubes by using DFT and the frozen phonons method. The phononic band structure and the vibrational density of states are reported. The stability of each structure is discussed based on these results. We investigate the influence of isotopic substitutions upon the vibrational density of states for the two types of nanotubes. Finally, we show that the model of vibrational Hamiltonian in a diatomic chain can be used to give a qualitative description of the relation between the amount of isotopically substituted layers in the nanotube and their influence upon the vibrational density of states.

Dynamic properties of integrated nanostructure on metallic surface

We investigated the vibration properties of integrated nanostructure on crystalline surface. The embedded chain of molecules is parallel to y-axis and takes three different positions: top, hollow, and bridge. The vibrational dynamics of the structure is considered within the harmonic approximation framework. The evanescent and propagating vibrational field of the perfect lattice is determined and interpreted. The presence of the diatomic molecule chain breakdown the translation symmetry in one direction, and gives rise to localized states on its neighborhood. Our study is based on the matching method and the Green functions, the spectral and state densities associated to localized modes are determined and calculated numerically. Our results show that the presence of the inhomogeneity contribute to the creation of new branches of localized vibrational modes, and their number and feature depend strongly on structural parameters of the system and the position of the diatomic chain.

A vibrational dynamics of molecule chain on metallic surface

We investigate the vibration properties of adsorbed nanostructure on the infinite square crystalline surface. The surface is considered as an infinite slab of one atomic layer, and the nanostructure as an isolated diatomic molecule chain on the surface of a cubic lattice which is parallel to y-axis, and takes three different positions: top, hollow and bridge. The vibrational dynamics of the structure is considered within the harmonic approximation framework. The evanescent and propagating vibrational field of the perfect lattice is determined and discussed. The presence of the molecule chain breaks down the translation symmetry in one direction and gives rise to localized states on its neighborhood. The mathematical framework of the matching method is used to analyze the localization phenomena at the nanostructure boundaries. Typical dispersion curves for modes of energies along the inhomogeneity are given with their polarizations. The fine structure of the spectrum and its origins are clearly identifiable, which gives a new insight into the localization problem. Furthermore, the existence and nature of the localized phonons like modes associated with an isolated defect are derived, and the importance of the contribution of these modes to the spectral and states densities is exhibited clearly.

Study of wave propagation in strongly nonlinear periodic lattices using a harmonic balance approach

This paper presents a general harmonic balance method for studying plane wave propagation in strongly nonlinear periodic media. The proposed approach starts by assuming a multi-wavenumber and frequency solution for the unit cell degrees of freedom. A Galerkin projection then transforms the nonlinear differential equations of motion into a set of nonlinear algebraic equations, which are subsequently solved numerically through a Newton-like iteration scheme. These solutions reveal amplitude-dependent dispersion behavior and group velocities. Specific example systems studied include one-dimensional chains and two-dimensional lattices, both formed by a periodic arrangement of spheres interacting under a Hertzian contact law. Amplitude-dependent dispersion is noted in monatomic and diatomic chains, and in hexagonally close-packed two-dimensional lattices. The validity of the presented technique is assessed through direct numerical simulation of the equations governing finite-extent lattices. Strong agreement is documented for results calculated using the harmonic balance approach and the direct numerical simulations.

Stability of discrete breathers in diatomic nonlinear oscillator chains

Stability of discrete breathers in diatomic nonlinear oscillator chains

Monte Carlo Simulation of Multiferroic Magnetic Order in Ca3Co2-xMnxO6 System

Ca3Co2-xMnxO6 (x≈1, CCMO) is a typical magnetic multiferroic material. The spins of Co2+ and Mn4+ have strong magnetic anisotropy, which are similar to Ising spins. Moreover, at low temperatures, CCMO forms a particular up-up-town-town (↑↑↓↓) spin order, the so-called E-type antiferromagnetic state. In this paper, a diatomic Ising chain model for CCMO system, with the nearest-neighbour exchange frustration, has been studied by Monte Carlo simulation. The zero-temperature phase diagram is calculated by the variational method, which contains the E-type antiferromagnetic phase. Monte Carlo simulations confirm the existence of E-type antiferromagnet. Based on the results of specific heat and spin structure factor, two phase transition temperatures have been revealed, which may correspond to two phase transitions in real CCMO. By continuously adjusting the intensity of nearest-neighbour exchange interaction in Monte Carlo simulations, the phase transition boundary between the G-type and E-type antiferromagnetic states shows critical phenomena. Near the phase boundary, the spin modulation period becomes incommensurate. The instability of E-type antiferromagnetic order in real CCMO with x=1, may just due to the low dimensional features of the 1D Ising spin chain and the exchange frustration.

Bacterial attachment to phytoplankton in the pelagic marine environment

Direct interactions between phytoplankton and bacteria are hypothesized to impact bloom dynamics, community succession, and primary productivity. Such impacts may be depen- dent upon bacterial attachment to phytoplankton, but few studies have quantified this relation- ship in natural marine waters and little is known regarding factors regulating attachment. During a study of thin layer dynamics in Monterey Bay, California, USA, we collected over 18 000 phyto- plankton cells and analyzed them for attached bacteria. We focused our statistical analysis on abundant diatoms and dinoflagellates often associated with thin layers and surface slicks. More than 90% of phytoplankton cells analyzed did not harbor attached bacteria. When colonization had occurred, a single attached bacterium was the most common occurrence and few cells had multiple attached bacteria. Visually healthy phytoplankton were rarely colonized, but those col- lected outside of dense thin layers and surface slicks had higher incidences of colonization and were more likely to harbor multiple bacteria. Longer diatom chains had a higher probability of being colonized and of bacteria being selectively attached to specific regions within the chains. These results strongly suggest that phytoplankton abundance, health, and morphology regulate colonization by bacteria in the natural marine environment.

Dynamics of Phase Transitions in a Piecewise Linear Diatomic Chain

We consider a diatomic chain with nearest neighbors connected by phase-transforming springs. Assuming a piecewise linear interaction force, we use the Fourier transform to construct exact traveling wave solutions representing a moving phase-transition front and examine their stability through numerical experiments. We find that the identified traveling wave solutions may be stable in some velocity intervals. We show that the kinetic relation between the driving force on the phase boundary and its velocity is significantly affected by the ratio of the two masses. When the ratio is small enough, the relation may become multivalued at some velocities, with the two solutions corresponding to the different orders in which the two springs in a dimer cell change phase. The model bears additional interesting waveforms such as the so-called twinkling phase, which is also briefly discussed and compared to its monatomic analog.

FlowCAM: Sizing cells and understanding the impact of size distributions on biovolume of ­planktonic community structure

Instruments for in vivo identification and quantification of marine organisms are becoming more common, and the interpretation of data from these instruments is still evolving. In the present study, we compare the sizing performance of 3 instruments: (1) a black and white (B/W) FlowCAM II; (2) a BeckmanCoulter Multisizer III (MIII); and (3) an inverted microscope. We applied 3 different particle sizing algorithms available from the FlowCAM to suspensions of 5 dif- ferent particle morphotypes (4 different phytoplankton species and a spherical NIST calibration bead). The FlowCAM generated size distributions similar to those reported by the MIII for the spherical calibration beads. However, differences in reported sizes emerged among FlowCAM algorithms as well as among instruments when applied to morphologically more complex parti- cles, such as diatom chains. There was an immediate and substantial loss of cell counts when live cells were fixed in Lugol's solution, but only minor differences in cell size distributions among the different FlowCAM algorithms. The difference in sizing performance of the FlowCAM algorithms affects biovolume estimates of the natural plankton samples analysed. Species diversity was apparently higher in samples analysed by microscopy than with the FlowCAM, but the cell size distribution from the microscope was extremely narrow compared to FlowCAM and MIII. The present study demonstrates that the particle sizing algorithm has severe impact on the character- istics of the particle size distribution and on the total community biomass estimate.

Critical points for finite Fibonacci chains of point delta-interactions and orthogonal polynomials

For a one-dimensional Schrödinger operator with a finite number n of point delta-interactions with a common intensity, the parameters are the intensity, the n − 1 intercenter distances and the mass. Critical points are points in the parameters space of the Hamiltonian where one bound state appears or disappears. The study of critical points for Hamiltonians with point delta-interactions arranged along a Fibonacci chain is shown to be closely related to the study of the so-called Fibonacci operator, a discrete one-dimensional Schrödinger-type operator, which occurs in the context of tight binding Hamiltonians. These critical points are the zeros of orthogonal polynomials previously studied in the context of special diatomic linear chains with elastic nearest-neighbor interaction. Properties of the zeros (location, asymptotic behavior, gaps, …) are investigated. The perturbation series from the solvable periodic case is determined. The measure which yields orthogonality is investigated numerically from the zeros. It is shown that the transmission coefficient at zero energy can be expressed in terms of the orthogonal polynomials and their associated polynomials. In particular, it is shown that when the number of point delta-interactions is equal to a Fibonacci number minus 1, i.e. when the intervals between point delta-interactions form a palindrome, all the Fibonacci chains at critical points are completely transparent at zero energy.

Heat conduction of the hard point chain at zero pressure

Equilibrium and nonequilibrium studies of a hard point chain are performed under thecondition of a vanishing external pressure. If all particles have the same mass, the dynamicsis integrable, but the evolution is highly nontrivial. Numerical simulations in fact revealthat the particle velocities (which are integrals of motion) subdiffuse at equilibrium, whilethey superdiffuse in steady nonequilibrium regimes. This latter behaviour induces ananomalous thermal conductivity similar to that seen in standard ergodic models. Thecomplexity of the dynamics can be traced back to a peculiar property of the hard pointchain which acts as a velocity-dependent filter. Finally, an accurate study of a diatomic(ergodic) chain is performed, which reveals that the thermal conductivity diverges asN2/5 with thenumber N of particles. This analysis confirms the conjecture that one-dimensional systems belong to adifferent universality class when the thermodynamic pressure vanishes.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Optical response of resonator induced plasmon filters: Nanometric diatomic structures

We investigate the optical response of plasmon filters, which are composed of a diatomic chain of metallic nanoclusters along which a resonator, composed of one or two metallic nanoclusters, is coupled vertically. Taking into account the resonator, we show that the transmission amplitude T of the electromagnetic radiation may display dips when the geometrical parameters are chosen properly. The presence of a resonator composed of one metallic nanocluster yields a dip at the cluster resonance frequency. When the resonator is composed of two nanoclusters, then if the nanoclusters are of the same material, two dips emerge as a consequence of the splitting of the dip of the one-nanocluster resonator. If the resonator is of two different materials, then we obtain two dips near the resonance frequencies of the nanoclusters. These dips appear when the separations between nanoclusters are properly adjusted. Such a device may be used to transfer directionally the electromagnetic radiation. In the limit of equal atomic nanoclusters we reproduce the monoatomic chain results.

Nonlinear waves in disordered diatomic granular chains

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

Matching boundary conditions for diatomic chains

We propose a class of efficient matching boundary conditions to suppress spurious reflection for multiscale computations of one dimensional diatomic chains. This provides the first local effective treatment of both acoustic and optical phonons. Adopting the extended zone scheme of the dispersion relation, we design a class of force boundary conditions by enforcing perfect absorption at certain selected wave numbers. Reflection suppression is improved by involving more neighboring atoms in the condition. The effectiveness of the proposed matching boundary conditions is demonstrated by reflection coefficient analysis, numerical tests, and comparisons with the time history treatment.

The effect of cubic potentials on discrete breathers in a mixed Klein–Gordon/Fermi–Pasta–Ulam chain

Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein–Gordon/Fermi–Pasta–Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.