We perform path integral molecular dynamics (PIMD) simulations of a monatomic liquid that exhibits a liquid–liquid phase transition and liquid–liquid critical point. PIMD simulations are performed using different values of Planck’s constant h, allowing us to study the behavior of the liquid as nuclear quantum effects (NQE, i.e., atoms delocalization) are introduced, from the classical liquid ( h = 0) to increasingly quantum liquids ( h > 0). By combining the PIMD simulations with the ring-polymer molecular dynamics method, we also explore the dynamics of the classical and quantum liquids. We find that (i) the glass transition temperature of the low-density liquid (LDL) is anomalous, i.e., [Formula: see text] decreases upon compression. Instead, (ii) the glass transition temperature of the high-density liquid (HDL) is normal, i.e., [Formula: see text] increases upon compression. (iii) NQE shift both [Formula: see text] and [Formula: see text] toward lower temperatures, but NQE are more pronounced on HDL. We also study the glass behavior of the ring-polymer systems associated with the quantum liquids studied (via the path-integral formulation of statistical mechanics). There are two glass states in all the systems studied, low-density amorphous ice (LDA) and high-density amorphous ice (HDA), which are the glass counterparts of LDL and HDL. In all cases, the pressure-induced LDA–HDA transformation is sharp, reminiscent of a first-order phase transition. In the low-quantum regime, the LDA–HDA transformation is reversible, with identical LDA forms before compression and after decompression. However, in the high-quantum regime, the atoms become more delocalized in the final LDA than in the initial LDA, raising questions on the reversibility of the LDA–HDA transformation.
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On the structure of limiting flocks in hydrodynamic Euler Alignment models
The goal of this paper is to study limiting behavior of a self-organized continuous flock evolving according to the 1D hydrodynamic Euler Alignment model. We provide a series of quantitative estimates that show how far the density of the limiting flock is from a uniform distribution. The key quantity that controls density distortion is the entropy [Formula: see text], and the measure of deviation from uniformity is given by a well-known conserved quantity [Formula: see text], where [Formula: see text] is velocity and [Formula: see text] is the communication operator with kernel [Formula: see text]. The cases of Lipschitz, singular geometric, and topological kernels are covered in the study.
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- Award ID(s):
- 1813351
- NSF-PAR ID:
- 10358271
- Date Published:
- Journal Name:
- Mathematical Models and Methods in Applied Sciences
- Volume:
- 29
- Issue:
- 13
- ISSN:
- 0218-2025
- Page Range / eLocation ID:
- 2419 to 2431
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Helium atom scattering and density-functional theory (DFT) are used to characterize the phonon band structure of the (3 × 1)-O surface reconstruction of Nb(100). Innovative DFT calculations comparing surface phonons of bare Nb(100) to those of the oxide surface show increased resonances for the oxide, especially at higher energies. Calculated dispersion curves align well with experimental results and yield atomic displacements to characterize polarizations. Inelastic helium time-of-flight measurements show phonons with mixed longitudinal and shear-vertical displacements along both the ⟨[Formula: see text]⟩, [Formula: see text] and ⟨[Formula: see text]⟩, [Formula: see text] symmetry axes over the entire first surface Brillouin zone. Force constants calculated for bulk Nb, Nb(100), and the (3 × 1)-O Nb(100) reconstruction indicate much stronger responses from the oxide surface, particularly for the top few layers of niobium and oxygen atoms. Many of the strengthened bonds at the surface create the characteristic ladder structure, which passivates and stabilizes the surface. These results represent, to our knowledge, the first phonon dispersion data for the oxide surface and the first ab initio calculation of the oxide’s surface phonons. This study supplies critical information for the further development of advanced materials for superconducting radiofrequency cavities.
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null (Ed.)Urban parks and green spaces provide a wide range of ecosystem services, including social interaction and stress reduction. When COVID-19 closed schools and businesses and restricted social gatherings, parks became one of the few places that urban residents were permitted to visit outside their homes. With a focus on Philadelphia, PA and New York City, NY, this paper presents a snapshot of the park usage during the early phases of the pandemic. Forty-three Civic Scientists were employed by the research team to observe usage in 22 different parks selected to represent low and high social vulnerability, and low, medium, and high population density. Despite speculation that parks could contribute to the spread of COVID-19, no strong correlation was found between the number of confirmed COVID-19 cases in adjacent zip codes and the number of park users. High social vulnerability neighborhoods were associated with a significantly higher number of COVID-19 cases ([Formula: see text]). In addition, no significant difference in the number of park users was detected between parks in high and low vulnerability neighborhoods. The number of park users did significantly increase with population density in both cities ([Formula: see text]), though usage varied greatly by park. Males were more frequently observed than females in parks in both high vulnerability and high-density neighborhoods. Although high vulnerability neighborhoods reported higher COVID-19 cases, residents of Philadelphia and New York City appear to have been undeterred from visiting parks during this phase of the pandemic. This snapshot study provides no evidence to support closing parks during the pandemic. To the contrary, people continued to visit parks throughout the study, underscoring their evident value as respite for urban residents during the early phases of the pandemic.more » « less
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Gyroid structure, a nature inspired cellular architecture, is under extensive exploration recently due to its structure continuity, uniform stress distribution under compression, and stable collapse mechanism during deformation. However, when combining with a functional gradient, the Gyroid structure can perform much different mechanical behavior from its homogeneous counterpart. Herein, bottom-up computational modeling is performed to investigate the mechanics of functional gradient nano-gyroid structure made of copper (Cu). Our work reveals that its mechanical properties degrade with a density that is much slower than those of homogeneous gyroid structure. The scaling of yield strength [Formula: see text] to the relative density [Formula: see text] for the functional gradient gyroid structure is in the factor of 1.5. Moreover, the layer-by-layer collapsing mechanism yields significantly better mechanical energy absorption ability. This study not only leads to insightful understanding of the deformation mechanisms in nonuniform gyroid structures but also promotes the development of the functional gradient cellular materials.more » « less
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A model is developed that accounts for the effects of thermal disorder (both static and dynamic) in predicting the thermoelectric (TE) performance of weakly bonded semiconductors. With dynamic disorder included, the model is found to fit well with experimental results found in the literature for the density-of-states and the energy-dependent carrier mobility, which are key for assessing TE properties. The model is then used to analyze the concentration-dependent TE properties of the prototypical small molecular semiconductor rubrene. At low (e.g., intrinsic) carrier concentrations, where Fermi level pinning occurs, dynamic disorder is found to reduce electrical conductivity ([Formula: see text]), Seebeck coefficient ([Formula: see text]), and thermoelectric power factor ([Formula: see text]) to values that are much lower than those traditionally predicted by static disorder models. As carrier concentration ([Formula: see text]) increases, [Formula: see text] exhibits nonlinear behavior, increasing well above the conventional [Formula: see text] vs [Formula: see text] relationship before reaching a peak value ([Formula: see text]). A critical carrier concentration ([Formula: see text] molar ratio) is observed near [Formula: see text] at which thermoelectric transport transitions from trap-limited behavior at low concentrations to conventional band behavior at high concentrations. Above this value, [Formula: see text] and [Formula: see text] are reduced compared to the perfect crystal and static-only conditions, causing a drop in the maximum [Formula: see text] by factors of 3 and 2.3, respectively. This [Formula: see text] reduction, while not as large as the [Formula: see text] reduction that occurs for low carrier concentration, is found to occur in a high concentration regime ([Formula: see text]) that contains the [Formula: see text] maximum and has remained inaccessible to experimentalists due to dopant limitations that are worsened in the presence of dynamic disorder.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0218202519500507
