Diatomic Chain Research Articles

Realizations of Su-Schrieffer-Heeger (SSH) edge states in two-dimensional hydrocarbon systems

The Su-Schrieffer-Heeger (SSH) model of one-dimensional (1D) diatomic and four-atom chains, exhibit a topological phase transition characterized by the Zak phase. However, a challenge arises from the inherent difficulty of maintaining strong structural stability in real 1D nanostructures. Here, we show how to realize periodic 1D chains, reminiscent of the SSH model, in a two-dimensional (2D) system. These chains form a quasi-1D chain topological insulator (CTI) where the interchain coupling can be neglected. Based on first-principles calculations, we proposed that such CTIs can be realized in dumbbell (DB) C40H14 and DB C40H12 monolayers. The monolayers are CTIs, with a type of weak topological state, and the topological phase transition can be achieved by unit cell transformation or the application of 2D strain. Furthermore, increasing the number of DB C10H4 rings can enlarge the distance between the chains, corresponding to line defects within the monolayer, providing a possible strategy for experimental synthesis.

The Memory Function of an Impurity in Mass and Hooke Constant in a Diatomic Chain

The memory function of an impurity with different mass and Hooke constant in a classical diatomic chain is studied by means of the recurrence relations method. The Laplace transform of the memory function has two pairs of resonant poles and three branch cuts. The poles contribute a cosine and the cuts contribute acoustic and optic branches, which are expressed as a convolution of a difference of two sines and an expansion of even-order Bessel functions. The expansion coefficients are integrals of Jacobian elliptic function sn(u) along the real axis in a complex u+iv plane for the acoustic branch, and integrals of nd(v) along a contour parallel to the imaginary axis of the plane for the optical branch, respectively. Different special cases are discussed in detail. It shows that a perfect monatomic or diatomic chain and such a chain with a mass impurity share the same memory function except for a constant factor, and that the pole contribution exists only if the impurity has both different mass and Hooke constant.

Single cell dynamics and nitrogen transformations in the chain forming diatom Chaetoceros affinis

Colony formation in phytoplankton is often considered a disadvantage during nutrient limitation in aquatic systems. Using stable isotopic tracers combined with secondary ion mass spectrometry (SIMS), we unravel cell-specific activities of a chain-forming diatom and interactions with attached bacteria. The uptake of 13C-bicarbonate and15N-nitrate or 15N-ammonium was studied in Chaetoceros affinis during the stationary growth phase. Low cell-to-cell variance of 13C-bicarbonate and 15N-nitrate assimilation within diatom chains prevailed during the early stationary phase. Up to 5% of freshly assimilated 13C and 15N was detected in attached bacteria within 12 h and supported bacterial C- and N-growth rates up to 0.026 h−1. During the mid-stationary phase, diatom chain-length decreased and 13C and 15N-nitrate assimilation was significantly higher in solitary cells as compared to that in chain cells. During the late stationary phase, nitrate assimilation ceased and ammonium assimilation balanced C fixation. At this stage, we observed highly active cells neighboring inactive cells within the same chain. In N-limited regimes, bacterial remineralization of N and the short diffusion distance between neighbors in chains may support surviving cells. This combination of “microbial gardening” and nutrient transfer within diatom chains represents a strategy which challenges current paradigms of nutrient fluxes in plankton communities.

High resolution analysis of plankton distributions at the Middle Atlantic Bight shelf-break front

The Middle Atlantic Bight (MAB) is a highly productive ecosystem, supporting several economically important commercial fisheries. Chlorophyll enhancement at the MAB shelf-break front has been observed only intermittently, despite several studies suggesting persistent upwelling at the front. High resolution cross-frontal transects were conducted during three two-week cruises in April 2018, May 2019, and July 2019. Mesoplankton distributions at the front were measured with a Video Plankton Recorder equipped with hydrographic and bio-optical sensors. Zooplankton were also sampled with a Multiple Opening/Closing Net and Environment Sensing System. Each of the three cruises had distinctly different frontal characteristics, with lower variability in frontal position in April 2018 and higher variability in May and July 2019, primarily due to frontal eddies and a Gulf Stream warm core ring, respectively. Eulerian means of all transect crossings within each cruise did not show mean frontal chlorophyll enhancement in April 2018 or July 2019, despite individual crossings showing chlorophyll enhancement in April 2018. Transformation of the April 2018 data into a cross-frontal coordinate system revealed a weak enhancement of chlorophyll and copepods at the front. Mean frontal chlorophyll enhancement was observed in May and was associated with enhancement in the periphery of a frontal eddy rather than the front itself. None of the planktonic categories observed were enhanced at the front in the cross-shelf mean distribution, though diatom chains and copepods were more abundant inshore of the front, particularly in May and July 2019, as well as within the center of a frontal eddy in May. The high variability of the MAB frontal region obscured the impact of ephemeral frontal enhancement in mean observations of April 2018, while frontal eddies contributed to chlorophyll enhancement in mean observations of May 2019. The influence of both argues for the necessity for 3-D models rather than idealized 2-D models to explain frontal behavior and its effects on biological responses.

The swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function.

Many copepods display a swim-and-sink behaviour, which is not energetically efficient but probably aids in perceiving and capturing diatom chains. Here, computational fluid dynamics was employed to calculate the mechanical power required by a negatively buoyant, self-propelled copepod in swim-and-sink versus hovering. The results show that upward swim-and-sink about a fixed depth always demands more power than hovering. Subsequently, high-speed microscale imaging was employed to observe the copepod Centropages sp. in swim-and-sink, specifically its encounter and handling of diatom chains for capture, along with the measured alternating swimming and sinking currents imposed by the swim-and-sink copepod. The findings suggest that during upward swimming, the copepod uses its swimming current to scan the fluid for detecting embedded diatom chains, presumably through chemoreception. Once a diatom chain is perceived, the copepod sinks and uses its sinking current to manipulate the orientation of the diatom chain before swimming upward to capture it. Overall, these results propose a hypothesis that swim-and-sink is an innate behaviour that assists copepods in perceiving and manoeuvring diatom chains for capture. In contrast with near-spherical algae, diatom chains predominately exhibit a horizontal orientation in the ocean, necessitating vertically oriented copepods to possess a handling behaviour that manoeuvres diatom chains for capture.

Mapping topological states with compacted dimensions

With conformal coordinate transformations, compacted dimensions might be realized in photonic systems. Here we show, with a one-dimensional (1D) photonic model system, that the essential topological nature of a two-dimensional (2D) nanoribbon is conserved in a mapping without conformal transformations. We take topological edge states as an example. They exist in physical systems of different dimensions, such as Su-Schrieffer-Heeger (SSH) model in 1D with dimerized polyacetylene, or a Haldane model in a 2D hexagonal lattice with spin-orbit coupling. In addition, the 2D graphene nanoribbon model also hosts topological edge states if the edge is of ``zigzag'' type with nontrivial Zak phase. In this Letter, we introduce a mapping formalism which establishes the correspondence between the momentum space of the nanoribbon and the parameter space of a 1D diatomic chain. It explicitly demonstrates that topological origin of the nanoribbon system can be reduced to the SSH model, which reveals the unification of topological nature across different dimensions. As an example, we reconstruct the 2D graphene nanoribbon band structure, including topological edge states, using 1D optical waveguide arrays. The coupling coefficients between waveguides are directly transformed from nanoribbons' electron momenta. We believe that it is a powerful tool to connect physical phenomena in different dimensions and offers a new experimental methodology based on photonic platforms for condensed-matter research.

Energy harvesting using the edge-state phenomena

Diatomic chain consisting of spring-mass system forms an attenuation bandgap due to the formation of the standing wave when the wavelength matches with the periodicity, known as Bragg-scattering. Edge-state phenomenon can be obtained by breaking the periodicity of the diatomic chain. Owing to this edge state phenomenon, the waves, and in turn the energy, is localized at the point of the asymmetry. In this work, an efficient vibrational energy harvesting technique is proposed exploiting this edge-state energy localization by inserting piezo-electric harvester at the junction of the asymmetry. To illustrate the performance of the proposed harvester under the broad-band noise, voltage-frequency curve for three different diatomic chain configurations, having same mass and stiffness, are analyzed. The performance metric, defined as the area under the voltage-frequency curve, shows 21.5 times higher performance can be obtained just by breaking the symmetry of a conventional diatomic chain. As it is also observed that the attenuation properties of the symmetric and asymmetric chain remain same; thus, the proposed edge-state energy harvester has a significant promise toward simultaneous energy harvesting and vibration control.

Photo-responsive hydrogel-based re-programmable metamaterials

This paper explores a novel programmable metamaterial using stimuli-responsive hydrogels with a demonstration of bandgap formation and tuning. Specifically, a photo-responsive hydrogel beam that can achieve re-programmable periodicity in geometric and material properties through patterned light irradiation is designed. Hydrogels consist of polymeric networks and water molecules. Many unique properties of hydrogels, including bio-compatibility, stimuli-responsiveness, and low dissipation make them ideal for enabling re-programmable metamaterials for manipulating structural dynamic response and wave propagation characteristics. Bandgap generation and tunability in photo-responsive hydrogel-based metamaterial (in the form of a diatomic phononic chain) as well as the effects of system parameters such as light exposure pattern and photo-sensitive group concentration on the bandgap width and center frequency are systematically studied. In agreement with finite-element model simulations, it is observed that an increase in light exposure region size reduces both the bandgap width and center frequency, while an increase in the concentration of photo-sensitive group increases bandgap width, attenuation and reduces its center frequency. This work unveils the potential of stimuli-response hydrogels as a new class of low-loss soft metamaterials, unlike most other soft materials that are too lossy to sustain and exploit wave phenomena.

The anti-Fermi–Pasta–Ulam–Tsingou problem in one-dimensional diatomic lattices

We study the thermalization dynamics of one-dimensional diatomic lattices (which represents the simplest system possessing multi-branch phonons), exemplified by the famous Fermi–Pasta–Ulam–Tsingou (FPUT)-β and the Toda models. Here we focus on how the system relaxes to the equilibrium state when part of highest-frequency optical modes are initially excited, which is called the anti-FPUT problem comparing with the original FPUT problem (low frequency excitations of the monatomic lattice). It is shown numerically that the final thermalization time T eq of the diatomic FPUT-β chain depends on whether its acoustic modes are thermalized, whereas the T eq of the diatomic Toda chain depends on the optical ones; in addition, the metastable state of both models have different energy distributions and lifetimes. Despite these differences, in the near-integrable region, the T eq of both models still follows the same scaling law, i.e. T eq is inversely proportional to the square of the perturbation strength. Finally, comparisons of the thermalization behavior between different models under various initial conditions are briefly summarized.

Predator Field and Colony Morphology Determine the Defensive Benefit of Colony Formation in Marine Phytoplankton

Colony formation in marine phytoplankton can be modified by the presence of grazers, but the effect of colony size and shape on the feeding behavior of grazers is still relatively unknown. To explore the defensive role of colony formation, we examined the feeding response of three differently sized grazers (copepodites, copepod nauplii, and two heterotrophic dinoflagellates) feeding on colony-forming phytoplankton, using both direct video observations and bottle incubations. We found a dramatic increase in capture clearance rate with colony size for copepodites, up to 140% higher in the largest diatom chains relative to their solitary cells. This was in part facilitated by a mechanism – described here for the first time – by which copepods efficiently detect and capture colonies using the antennules, thereby increasing their capture radius. Prey handling time by copepodites increased with colony size, but did not limit prey ingestion. Larger chains of diatoms were efficiently handled and consumed by the copepodites, whereas larger spherical colonies of Phaeocystis globosa were rejected subsequent to capture. In contrast, colonial phytoplankton were better protected against the microzooplankton and copepod nauplii examined, since these only managed to consume smaller colonies equivalent of a few cells. We find that the defensive value of colony formation depends on the size and foraging behavior of the grazer and the size and shape of the colony. Thus, the defensive benefit is therefore a function of the composition of the grazer community. We argue that bloom formation in chain-forming diatoms is facilitated by the efficient protection against rapidly responding micro-grazers and the lagged numerical response of efficient copepod grazers.

Closed-form existence conditions for bandgap resonances in a finite periodic chain under general boundary conditions.

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free-free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free-free, free-fixed, fixed-free, or fixed-fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free-free boundary conditions. An intriguing case is a free-free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

Non-monotonic thickness dependent and anisotropic in-plane thermal transport in layered titanium trisulphide

Due to the potential applications in many fields such as thermoelectric, transistor, and electrode materials, a novel two-dimensional layered material TiS3 has attracted tremendous attention recently. In this article, the thickness dependent and anisotropic in-plane thermal transport behavior is explored by first-principles calculation with Boltzmann transport equation. The calculation results show that when the thickness is smaller than phonon confinement size (PCS), the phonon confinement effect is dominant and the in-plane thermal conductivity has a negative dependence on thickness due to the increase of phonon–phonon scattering; when the thickness is larger than PCS, the confinement effect is weak and the dependence becomes positive due to the decrease of phonon–boundary scattering. Through further analysis, we find this non-monotonic dependence or phonon confinement phenomenon is mainly caused by the low-frequency phonons. The calculation results also show strong thermal anisotropy within the basal plane. The coupling strength, bond length, phonon group velocity, dispersiveness of optical phonon branches, iso-energy surface and iso-surface of electron density distribution are analyzed to explain the anisotropy. Based on the 1D diatomic chain model, a unit cell having similar atomic mass and strong intracell bond can enhance the dispersiveness of optical phonon branches. Those findings here can give physical insights into the thickness dependent and anisotropic in-plane thermal transport in layered materials.

Acoustic bandgaps in polyatomic chains of 3D-printed resonators

Acoustic bandgaps are ranges of frequencies in a medium at which sound cannot propagate. The classical model often used in solid-state physics is that of a 1D chain of masses and springs, the analysis of which can predict the speed of sound in a material, its dispersive nature, and any forbidden sound frequencies. We use a lumped parameter model for the acoustic inertance and compliance of pipes and cavities to create 1D monatomic, diatomic, and triatomic chains that demonstrate these acoustic bandgaps experimentally. The ease of 3D-printing these devices means that this method can be used to explore bandgap engineering in acoustic systems for low-frequency applications and used as a simple platform for creating acoustic analogs of the solid-state physical problem. Furthermore, it allows us to explore novel polyatomic behavior (e.g., tetratomic and pentatomic) and could ultimately find use as filters for experiments requiring miniaturized acoustic isolation.

Hybrid Bandgaps in Mass-coupled Bragg Atomic Chains: Generation and Switching

In this work, without introducing mass-in-mass units or inertial amplification mechanisms, we show that two Bragg atomic chains can form an acoustic metamaterial that possesses different types of bandgaps other than Bragg ones, including local resonance and inertial amplification-like bandgaps. Specifically, by coupling masses of one monatomic chain to the same masses of a diatomic or triatomic chain, hybrid bandgaps can be generated and further be switched through the adjustment of the structural parameters. To provide a tuning guidance for the hybrid bandgaps, we derived an analytical transition parameter (p-value) for the mass-coupled monatomic/diatomic chain and analytical discriminants for the mass-coupled monatomic/triatomic chain. In our proposed mass-coupled monatomic/triatomic chain system, each set of analytical discriminants determines a hybrid bandgap state and a detailed examination reveals 14 different bandgap states. In addition to bandgap switching, the analytical p-value and discriminants can also be used as a guide for designing the coupled-chain acoustic metamaterials. The relations between the mass-coupled monatomic/triatomic chain system and a three-degree-of-freedom (DOF) inertial amplification system further indicate that the band structure of the former is equivalent to that of the latter through coupling masses by negative dynamic stiffness springs.

Manipulation of wave motion in smart nonlinear phononic crystals made of shape memory alloys

Thanks to the functional role of shape memory alloys (SMAs) in controlling the mechanical behavior of structures, researchers have started investigating the possibility of manipulating wave motion in phononic crystals using SMAs. While SMAs were used before to tune the wave propagation in linear phononic crystals, in this work, we aim to extend their utilization to nonlinear lattices. For this purpose, SMA helical springs are used to manipulate the dispersion curves and the location of stop-bands in weakly nonlinear monoatomic and diatomic lattice chains. Using Brinson’s formulation to describe the thermo-mechanical behavior of SMA wires and Lindstedt-Poincaré method to solve the derived governing equations, closed-form nonlinear dispersion relations in monoatomic and diatomic lattice chains are obtained and the effects of temperature-induced phase transformation and stiffness nonlinearity on the wave propagation are investigated. The results reveal that the dispersion curves of a weakly nonlinear monoatomic chain are formed at lower frequencies through the austenite-to-martensite phase transformation. Similarly, both the acoustic and optical branches of a diatomic lattice are moved to lower frequencies during the phase transformation in the cooling process. Therefore, the generated stop-bands in nonlinear diatomic lattices are also moved to lower frequencies. In addition, using auxiliary SMA ground springs, new classes of nonlinear monoatomic and diatomic chains exhibiting additional low-frequency attenuation zones are introduced. These low-frequency stop-bands are tunable and their frequency range can be modulated by exploiting the temperature-induced phase transformation in the SMA springs. The results obtained from analytic formulations are verified by numerical calculations and an excellent agreement is observed. Such tunability and the potential for adding stop-bands in low frequencies reveal that SMAs can be very helpful in designing nonlinear phononic and acoustic devices, such as vibration mitigators and wave filters with pre-defined attenuation zones.

Fused-Silica 3D Chiral Metamaterials via Helium-Assisted Microcasting Supporting Topologically Protected Twist Edge Resonances with High Mechanical Quality Factors.

It is predicted theoretically that a 1D diatomic chain of 3D chiral cells can support a topological bandgap that allows for translating a small time-harmonic axial movement at one end of the chain into a resonantly enhanced large rotation of an edge state at the other end. This edge state is topologically protected such that an arbitrary mass of a mirror at the other end does not shift the eigenfrequency out of the bandgap. Herein, this complex 3D laser-beam-scanner microstructure is realized in fused-silica form. A novel microcasting approach is introduced that starts from a hollow polymer cast made by standard 3D laser nanoprinting. The cast is evacuated and filled with helium, such that a highly viscous commercial glass slurry is sucked in. After UV curing and thermal debinding of the polymer, the fused-silica glass is sintered at 1225°C under vacuum. Detailed optical measurements reveal a mechanical quality factor of the twist-edge resonance of 2850 at around 278kHz resonance frequency under ambient conditions. The microcasting approach can likely be translated to many other glasses, to metals and ceramics, and to complex architectures that are not or not yet amenable to direct 3D laser printing.

Bandgap and vibration transfer characteristics of scissor-like periodic metamaterials

A periodic mass-spring-truss chain based on a scissor-like structure and inertial amplification is proposed to seek for low-frequency vibration attenuation. The resonant and anti-resonant frequencies of a basic element are obtained analytically to explain the resonance and anti-resonance of the periodic chain. The formation of bandgaps is explored, revealing that the vertical movements of the vertices take the input kinetic energy away from the horizontal movement energy. The cut-off frequencies of three models are derived analytically to compare the effect of the inertia amplification, which can reach more than three times the classical mass-spring chain with a small angle. Also, the effect of stiffness amplification is presented when the spring mounted vertically, unlike the classical inertial amplification systems. Thus, the optimal configuration for low-frequency attenuation is obtained, that is, the spring mounted horizontally and the masses mounted at the upper and lower vertices. The chain with mass on the upper and lower vertices has the lowest cut-off frequency, which is 17.7% lower than that of the classical mass-spring chain. A diatomic chain is studied to find lower and wider bandgaps, where the central frequency is 25% lower than the classical mass-spring diatomic chain. The central frequency and width of the new bandgap can be tunable accordingly. The result shows that small angles or low stiffness ratios result in lower bandgaps. Meanwhile, the large angles, big differences of masses, or high stiffness ratios lead to wider bandgaps.

Mechanisms for transient localization in a diatomic nonlinear chain

We investigate transient nonlinear localization, namely the self-excitation of energy bursts in an atomic lattice at finite temperature. As a basic model we consider the diatomic Lennard-Jones chain. Numerical simulations suggest that the effect originates from two different mechanisms. One is the thermal excitation of genuine discrete breathers with frequency in the phonon gap. The second is an effect of nonlinear coupling of fast, lighter particles with slow vibrations of the heavier ones. The quadratic term of the force generate an effective potential that can lead to transient grow of local energy on time scales the can be relatively long for small mass ratios. This heuristics is supported by a multiple-scale approximation based on the natural time-scale separation. For illustration, we consider a simplified single-particle model that allows for some insight of the localization dynamics.

Phonon Casimir effect in polyatomic systems

The phonon Casimir effect describes the phonon-mediated interaction between defects in condensed-matter systems. Using the path-integral formalism, we derive a general method for calculating the Helmholtz free energy due to vibrational modes in systems of arbitrary dimensionality and composition. Our results make it possible to extract the defect interaction energy at any temperature for various defect configurations. We demonstrate our approach in action by performing numerical calculations for mono- and diatomic chains, as well as a diatomic molecule, at zero and finite temperatures and validate our results using exact diagonalization.

Robust topological edge states from one-dimensional diatomic chain photonic crystals

The Su–Schrieffer–Heeger (SSH) model can occur in a one-dimensional (1D) diatomic chain photonic crystal (PC) in which a unit cell includes two same slabs (atoms). With different intervals of the two slabs, the two combined 1D PCs can support topological edge states in all photonic boundary bandgaps. These topological edge states come from the inversion of topological phase of the bands through the band folding effect. When the sum of the two atom intervals in the two different 1D PCs equals to the unit cell length, these edge state frequencies keep invariant.