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The \emph{matching book thickness} $mbt(G)$ of $G$ is the minimum integer $m$ such that an $m$-page matching book embedding exists. A graph $G$ is called \emph{dispersable} if $mbt(G)=\Delta(G)$, \emph{nearly dispersable} if $mbt(G)=\Delta(G)+1$. Recently, the authors determined the nearly dispersability of odd toroidal grids $T_{s,t}$. In this note, we further present a brief proof for this result.

In this paper, the dispersability of the Cartesian graph bundle over two cycles is completely solved. We show the Cartesian graph bundle $G$ over two cycles is dispersable if $G$ is bipartite; otherwise, $G$ is nearly dispersable., Comment: arXiv admin note: text overlap with arXiv:2310.06612

Thermal conductivity $\kappa$ of MgO plays a fundamental role in understanding the thermal evolution and mantle convection in the interior of terrestrial planets. However, previous theoretical calculations deviate from each other and the $\kappa$ of high-pressure B2 phase remains undetermined. Here, by combining molecular dynamics and deep potential trained with first-principles data, we systematically investigate the $\kappa$ of MgO from ambient state to the core-mantle boundary (CMB) of super-Earth with $5M_{\oplus}$. We point out the significance of 4-phonon scatterings and modify the conventional thermal conductivity model of MgO by considering the density-dependent proportion of 3-phonon and 4-phonon scatterings. The $\kappa$ profiles of MgO in Earth and super-Earth are further estimated. For super-Earth, we predict a significant reduction of $\kappa$ at the B1-B2 phase transition area near the CMB. This work provides new insights into thermal transport under extreme conditions and an improved thermal model for terrestrial planets., Comment: 4 figures

The immiscibility of hydrogen-helium mixture under the temperature and pressure conditions of planetary interiors is crucial for understanding the structures of gas giant planets (e.g., Jupiter and Saturn). While the experimental probe at such extreme conditions is challenging, theoretical simulation is heavily relied in an effort to unravel the mixing behavior of hydrogen and helium. Here we develop a method via a machine learning accelerated molecular dynamics simulation to quantify the physical separation of hydrogen and helium under the conditions of planetary interiors. The immiscibility line achieved with the developed method yields substantially higher demixing temperatures at pressure above 1.5 Mbar than earlier theoretical data, but matches better to the experimental estimate. Our results suggest a possibility that H-He demixing takes place in a large fraction of the interior radii of Jupiter and Saturn, i.e., 27.5% in Jupiter and 48.3% in Saturn. This indication of an H-He immiscible layer hints at the formation of helium rain and offers a potential explanation for the decrease of helium in the atmospheres of Jupiter and Saturn., Comment: 3 figures, accepted in Nature Communications

In this paper, we give the classification of circulant graphs $C(\mathbb{Z}_{n},S)$ with $|S|=2$ and completely solve the dispersability of circulant graphs $C(\mathbb{Z}_{n},\{1, k\})$.

Superionic ices with highly mobile protons within the stable oxygen sub-lattice occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the universe. Understanding the thermal transport in superionic ice is vital for the thermal evolution of icy planets. However, it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons, beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics approaches. In this work, by utilizing the deep potential molecular dynamics approach, we investigate the thermal conductivity of ice-VII and superionic ice-VII" along the isobar of $p = 30\ \rm{GPa}$. A non-monotonic trend of thermal conductivity with elevated temperature is observed. Through heat flux decomposition and trajectory-based spectra analysis, we show that the thermally-activated proton diffusion in ice-VII and superionic ice-VII" contribute significantly to heat convection, while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat conduction. The competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in ice. This work unravels the important role of proton diffusion in the thermal transport of high-pressure ice. Our approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials., Comment: 5 figures

The coupling of excited states and ionic dynamics is the basic and challenging point for the materials response at extreme conditions. In laboratory, the intense laser produces transient nature and complexity with highly nonequilibrium states, making it extremely difficult and interesting for both experimental measurements and theoretical methods. With the inclusion of laser-excited states, we extended ab initio method into the direct simulations of whole laser-driven microscopic dynamics from solid to liquid. We constructed the framework of combining the electron-temperaturedependent deep neural network potential energy surface with hybrid atomistic-continuum approach, controlling non-adiabatic energy exchange and atomistic dynamics, which enables consistent interpretation of experimental data. By large scale ab inito simulations, we demonstrate that the nonthermal effects introduced by hot electrons play a dominant role in modulating the lattice dynamics, thermodynamic pathway, and structural transformation. We highlight that the present work provides a path to realistic computational studies of laser-driven processes, thus bridging the gap between experiments and simulations., Comment: 4 figures

The accumulation and circulation of carbon-hydrogen dictate the chemical evolution of ice giant planets. Species separation and diamond precipitation have been reported in carbon-hydrogen systems, verified by static and shock-compression experiments. Nevertheless, the dynamic formation processes for the above-mentioned phenomena are still insufficiently understood. Here, combing deep learning model, we demonstrate that diamonds form through a three-step process involving decomposition, species separation and nucleation procedures. Under shock condition of 125 GPa and 4590 K, hydrocarbons are decomposed to give hydrogen and low-molecular-weight alkanes (CH4 and C2H6), which escape from the carbon chains resulting in C/H species separation. The remaining carbon atoms without C-H bonds accumulate and nucleate to form diamond crystals. The process of diamond growth is found to associated with a critical nucleus size where dynamic energy barrier plays a key role. These dynamic processes for diamonds formation are insightful in establishing the model for ice giant planet evolution., Comment: 5 figures

Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model the dramatic change of both electronic structures and ion dynamics during such dynamic processes, the traditional method faces difficulties. Here, we demonstrate the ability of deep neural network (DNN) to capture the atomic local-environment dependence of electronic density of states (DOS) for both multicomponent system under exoplanet thermodynamic condition and nonequilibrium system during super-heated melting process. Large scale and time-resolved diagnosis of DOS can be efficiently achieved within the accuracy of ab initio method. Moreover, the atomic contribution to DOS given by DNN model accurately reveals the information of local neighborhood for selected atom, thus can serve as robust order parameters to identify different phases and intermediate local structures, strongly highlights the efficacy of this DNN model in studying dynamic processes., Comment: 7 Figures, accepted by PRB

Exploring the mechanism of interfacial thermal transport and reducing the interfacial thermal resistance is of great importance for thermal management and modulation. Herein, the interfacial thermal resistance between overlapped graphene nanoribbons is largely reduced by adding bonded carbon chains by performing molecular dynamics simulations. And the analytical model (cross-interface model, CIM) is utilized to analyze and explain the two-dimensional thermal transport mechanism at cross-interface. An order of magnitude reduction in interfacial thermal resistance is found as the graphene nanoribbons are bonded by just one carbon chain. Interestingly, the decreasing rate of interfacial thermal resistance slows down gradually with the increasing of the number of carbon chains, which can be explained by the proposed theoretical relationship based on CIM. Moreover, by the comparison of CIM and traditional simplified model, the accuracy of CIM is verified and demonstrated in overlapped graphene nanoribbons. This work provides a new way to improve the interfacial thermal transport and reveal the essential mechanism for low-dimensional materials applied in thermal management.

Phonon engineering focuses on heat transport modulation on atomic-scale. Different from reported methods, it is shown that electric field can also modulate heat transport in ferroelectric polymers, poly(vinylidene fluoride), by both simulation and measurement. Interestingly, thermal conductivities of poly(vinylidene fluoride) array can be enhanced by a factor of 3.25 along the polarization direction by simulation. The semi-crystalline poly(vinylidene fluoride) film can be also enhanced by a factor of 1.5 which is found by both simulation and measurement. The morphology and phonon property analysis reveal that the enhancement arises from the higher inter-chain lattice order, stronger inter-chain interaction, higher phonon group velocity and suppressed phonon scattering. This study offers a new modulation strategy with quick response and without fillers.

The application of low-dimensional materials for heat dissipation requires a comprehensive understanding of the thermal transport at the cross interface, which widely exists in various composite materials and electronic devices. In this work, we proposed an analytical model, named as cross interface model (CIM), to accurately reveal the essential mechanism of the two-dimensional thermal transport at the cross interface. The applicability of CIM is validated through the comparison of the analytical results with molecular dynamics simulations for a typical cross interface of two overlapped boron nitride nanoribbons. Besides, it is figured out that the factor ({\eta}) has important influence on the thermal transport besides the thermal resistance inside and between the materials, which is found to be determined by two dimensionless parameters from its expression. Our investigations deepen the understanding of the thermal transport at the cross interface and also facilitate to guide the applications of low-dimensional materials in thermal management.

Single layer molybdenum disulfide (SLMoS2), a semiconductor possesses intrinsic bandgap and high electron mobility, has attracted great attention due to its unique electronic, optical, mechanical and thermal properties. Although thermal conductivity of SLMoS2 has been widely investigated recently, less studies focus on molybdenum disulfide nanotube (MoS2NT). Here, the comprehensive temperature, size and strain effect on thermal conductivity of MoS2NT are investigated. A chirality-dependent strain effect is identified in thermal conductivity of zigzag nanotube, in which the phonon group velocity can be significantly reduced by strain. Besides, results show that thermal conductivity has a ~T-1 and a ~L\b{eta} relation with temperature from 200 to 400 K and length from 10 to 320 nm, respectively. This work not only provides feasible strategies to modulate the thermal conductivity of MoS2NT, but also offers useful insights into the fundamental mechanisms that govern the thermal conductivity, which can be used for the thermal management of low dimensional materials in optical, electronic and thermoelectrical devices. Introduction.

Understanding thermal transport through nanoscale van der Waals interfaces is vital for addressing thermal management challenges in nanoelectronic devices. In this work, the interfacial thermal conductance (GCA) between copper phthalocyanine (CuPc) nanoribbons is reported to be on the order of 10^5 Wm-2K-1 at 300 K, which is over two orders of magnitude lower than the value predicted by molecular dynamics (MD) simulations for a perfectly smooth interface between two parallelly aligned CuPc nanoribbons. Further MD simulations and contact mechanics analysis reveal that surface roughness can significantly reduce the adhesion energy and effective contact area between CuPc nanoribbons, and thus result in an ultralow GCA. In addition, the adhesion energy at the interface also depends on the stacking configuration of two CuPc nanoribbons, which may also contribute to the observed ultralow GCA., Comment: Main manuscript: 21 pages, 3 figures. Supplementary material: 13 pages, 5 figures and 1 table

The van der Waals (vdW) interactions exist in reality universally and play an important role in physics. Here, we show the study on the mechanism of vdW interactions on phonon transport in atomic scale, which would boost developments in heat management and energy conversion. Commonly, the vdW interactions are regarded as a hindrance in phonon transport. Here, we propose that the vdW confinement will enhance phonon transport. Through molecular dynamics simulations, it shows that the vdW confinement makes more than two-fold enhancement on thermal conductivity of both polyethylene single chain and graphene nanoribbon. The quantitative analyses of morphology, local vdW potential energy and dynamical properties are carried out to reveal the underlying physical mechanism. It is found that the confined vdW potential barriers reduce the atomic thermal displacement magnitudes, thus lead to less phonon scattering and facilitate thermal transport. Our study offers a new strategy to modulate the heat transport.

Solid-state lithium-ion batteries (SSLIBs) are considered to be the new generation of devices for energy storage due to better performance and safety. Poly (ethylene oxide) (PEO) based material becomes one of the best candidate of solid electrolytes, while its thermal conductivity is crucial to heat dissipation inside batteries. In this work, we study the thermal conductivity of PEO by molecular dynamics simulation. By enhancing the structure order, thermal conductivity of aligned crystalline PEO is obtained as high as 60 W/m-K at room temperature, which is two orders higher than the value (0.37 W/m-K) of amorphous structure. Interestingly, thermal conductivity of ordered structure shows a significant stepwise negative temperature dependence, which is attributed to the temperature-induced morphology change. Our study offers useful insights into the fundamental mechanisms that govern the thermal conductivity of PEO but not hinder the ionic transport, which can be used for the thermal management and further optimization of high-performance SSLIBs.

The ultra-low thermal conductivity (~0.3 Wm-1K-1) of amorphous epoxy resins significantly limits their applications in electronics. Conventional top-down methods e.g. electrospinning usually result in aligned structure for linear polymers thus satisfactory enhancement on thermal conductivity, but they are deficient for epoxy resin polymerized by monomers and curing agent due to completely different cross-linked network structure. Here, we proposed a bottom-up strategy, namely parallel-linking method, to increase the intrinsic thermal conductivity of bulk epoxy resin. Through equilibrium molecular dynamics simulations, we reported on a high thermal conductivity value of parallel-linked epoxy resin (PLER) as 0.80 Wm-1K-1, more than twofold higher than that of amorphous structure. Furthermore, by applying uniaxial tensile strains along the intra-chain direction, a further enhancement in thermal conductivity was obtained, reaching 6.45 Wm-1K-1. Interestingly, we also observed that the inter-chain thermal conductivities decrease with increasing strain. The single chain of epoxy resin was also investigated and, surprisingly, its thermal conductivity was boosted by 30 times through tensile strain, as high as 33.8 Wm-1K-1. Our study may provide a new insight on the design and fabrication of epoxy resins with high thermal conductivity.

Organic thermoelectric (TE) materials create a brand new perspective to search for high-efficiency TE materials, due to their small thermal conductivity. The overlap of pz orbitals, commonly existing in organic {\pi}-stacking semiconductors, can potentially result in high electronic mobility comparable to inorganic electronics. Here we propose a strategy to utilize the overlap of pz orbitals to increase the TE efficiency of layered polymeric carbon nitride (PCN). Through first-principles calculations and classical molecular dynamics simulations, we find that A-A stacked PCN has unexpectedly high cross-plane ZT up to 0.52 at 300 K, which can contribute to n-type TE groups. The high ZT originates from its one-dimensional charge transport and small thermal conductivity. The thermal contribution of the overlap of pz orbitals is investigated, which noticeably enhances the thermal transport when compared with the thermal conductivity without considering the overlap effect. For a better understanding of its TE advantages, we find that the low-dimensional charge transport results from strong pz-overlap interactions and the in-plane electronic confinement, by comparing {\pi}-stacking carbon nitride derivatives and graphite. This study can provide a guidance to search for high cross-plane TE performance in layered materials., Comment: 22 pages and 4 figures

The design of graphene-based composite with high thermal conductivity requires a comprehensive understanding of phonon coupling in graphene. We extended the two-temperature model to coupled groups of phonon. The study give new physical quantities, the phonon-phonon coupling factor and length, to characterize the couplings quantitatively. Besides, our proposed coupling length has an obvious dependence on system size. Our studies can not only observe the nonequilibrium between different groups of phonon, but explain theoretically the thermal resistance inside graphene., Comment: 4figures

We proposed a new way, adding intertube atoms, to enhance interfacial thermal conductance (ITC) between SiC-carbon nanotube (CNT) array structure. Non-equilibrium molecular dynamics method was used to study the ITC. The results show that the intertube atoms can significantly enhance the ITC. The dependence of ITC on both the temperature and the number of intertube atoms are shown. The mechanism is analyzed by calculating probability distributions of atomic forces and vibrational density of states. Our study may provide some guidance on enhancing the ITC of CNT-based composites.

Recently, some reports show that the ultra-low thermal conductivity of bulk polymers can be enhanced along one direction, which limits its applications. Here, we proposed paved crosswise laminate methods which can enhance the thermal conductivity of bulk polyethylene (PE) along two directions. We find that the thermal conductivity of paved crosswise polyethylene laminate (PPEL) reaches as high as 181 W/m-K along two in-plane directions, which is three orders of magnitude larger than bulk amorphous polyethylene and even more than two times larger than PE single chain (54 W/m-K). The analyses of mechanism indicated that PPEL is a much more crystal-like structure due to the inter-chain van der Waals interactions. Our study may provide guides on the design and fabrication of polymer structures with high thermal conductivity., Comment: 21 pages

Low-dimensional electronic and glassy phononic transport are two important ingredients of highly-efficient thermoelectric material, from which two branches of the thermoelectric research emerge. One focuses on controlling electronic transport in the low dimension, while the other on multiscale phonon engineering in the bulk. Recent work has benefited much from combining these two approaches, e.g., phonon engineering in low-dimensional materials. Here, we propose to employ the low-dimensional electronic structure in bulk phonon-glass crystal as an alternative way to increase the thermoelectric efficiency. Through first-principles electronic structure calculation and classical molecular dynamics simulation, we show that the $\pi$-$\pi$ stacking Bis-Dithienothiophene molecular crystal is a natural candidate for such an approach. This is determined by the nature of its chemical bonding. Without any optimization of the material parameter, we obtain a maximum room-temperature figure of merit, $ZT$, of $1.48$ at optimal doping, thus validating our idea., Comment: Nano Lett.2015