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Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order, characterised by long-range translational order. The discovery of quasicrystals, which exhibit rotational symmetries forbidden in crystals and lack periodicity, led to a paradigm shift in solid-state physics. Moving one step forward, it is intriguing to ask whether ordered matter can exist without apparent symmetry breaking. The same question arises considering how ordered amorphous (noncrystalline) solids can be structured. Here, we present the discovery of ideal noncrystals in two dimensions, which are disordered in the conventional sense, lacking Bragg peaks, but exhibit high orderliness based on the steric order, i.e., they are ideally packed. A path-integral-like scheme reveals the underlying long-range structural correlation. We find that these ideal noncrystals are characterised by phononic vibrational modes following the Debye law, fully affine elastic responses, and suppressed density fluctuations at longer wavelengths, reminiscent of hyperuniformity -- all characteristics typically associated with crystals. Therefore, ideal noncrystals represent a peculiar form of matter with a mixed nature -- noncrystalline yet possessing crystal-like properties. Notably, these states are found to be thermodynamically favourable, indicating them as a possible new class of ordered matter without apparent symmetry breaking. Our findings significantly broaden the conceptualization of ordered states of matter and may contribute to a deeper understanding of entropy-driven ordering, particularly in generic amorphous materials.

We present a new software package, "HybridOctree_Hex," for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow regions of the input boundary to identify key surface features and initialize an octree structure. Subsequently, a strongly balanced octree is constructed using the balancing and pairing rules. Inspired by our earlier preliminary hybrid octree-based work, templates are designed to guarantee an all-hexahedral dual mesh generation directly from the strongly balanced octree. With these pre-defined templates, the sophisticated hybrid octree construction step is skipped to achieve an efficient implementation. After that, elements outside and around the boundary are removed to create a core mesh. The boundary points of the core mesh are connected to their corresponding closest points on the surface to fill the buffer zone and build the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes advantage of a delicate optimization-based quality improvement method considering geometric fitting, Jacobian and scaled Jacobian, to achieve a minimum scaled Jacobian that is higher than $0.5$. We empirically verify the robustness and efficiency of our method by running the HybridOctree_Hex software on dozens of complex 3D models without any manual intervention or parameter adjustment. We provide the HybridOctree_Hex source code, along with comprehensive results encompassing the input and output files and statistical data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex.

The genuine entanglement of Dirac fields for an N-partite system is investigated in Schwarzschild spacetime and the analysis is carried out using the single-mode approximation. Due to the Hawking effect, quantum entanglement is divided into two parts physically accessible and inaccessible entanglement. We obtain a general analytic expression of genuine N-partite entanglement that includes all accessible and inaccessible entanglement in a Schwarzschild black hole. Unlike bosonic entanglement, the accessible N-partite entanglement of Dirac fields monotonically decreases to a nonzero value with the Hawking temperature. Interestingly, the inaccessible N-partite entanglement is a monotonic or non-monotonic function of the Hawking temperature, depending on the ratio between accessible and inaccessible modes, in contrast to bipartite or tripartite entanglement that is only a monotonic function of the Hawking temperature. Finally, we obtain two restrictive relationships for the quantum information of the black hole. This conclusion provides a new understanding of Hawking effect of the black hole., Comment: 14 pages, 1 figure

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named ``SRL-assisted AFM" for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using ``policy networks." These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers., Comment: 18 pages, 11 figures, submitted to Journal of Computational Science

The quality of mesh generation has long been considered a vital aspect in providing engineers with reliable simulation results throughout the history of the Finite Element Method (FEM). The element extraction method, which is currently the most robust method, is used in business software. However, in order to speed up extraction, the approach is done by finding the next element that optimizes a target function, which can result in local mesh of bad quality after many time steps. We provide TreeMesh, a method that uses this method in conjunction with reinforcement learning (also possible with supervised learning) and a novel Monte-Carlo tree search (MCTS) (Coulom(2006), Kocsis and Szepesv\'ari(2006), Browne et~al.(2012)). The algorithm is based on a previously proposed approach (Pan et~al.(2021)). After making many improvements on DRL (algorithm, state-action-reward setting) and adding a MCTS, it outperforms the former work on the same boundary. Furthermore, using tree search, our program reveals much preponderance on seed-density-changing boundaries, which is common on thin-film materials., Comment: Didn't publish it

For various engineering and industrial applications it is desirable to realize mechanical systems with broadly adjustable elasticity to respond flexibly to the external environment. Here we discover a topology-correlated transition between affine and non-affine regimes in elasticity in both two- and three-dimensional packing-derived networks. Based on this transition, we numerically design and experimentally realize multifunctional systems with adjustable elasticity. Within one system, we achieve solid-like affine response, liquid-like non-affine response and a continuous tunability in between. Moreover, the system also exhibits a broadly tunable Poisson's ratio from positive to negative values, which is of practical interest for energy absorption and for fracture-resistant materials. Our study reveals a fundamental connection between elasticity and network topology, and demonstrates its practical potential for designing mechanical systems and metamaterials., Comment: 10 pages, 5 figures

Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances inter-particle locking and hence particle-level dynamic correlation length. However, the nonaffine displacement is two orders of magnitude smaller than particle size, indicating that stress is mainly released on the length scale of roughness. The correlation length of non-affine displacements abruptly increases when a quasi-periodic avalanche occurs, suggesting that quasi-periodic avalanches can be interpreted as a spinodal nucleation event in a first-order phase transition., Comment: 22 pages, 7 figures

Using X-ray tomography, we experimentally investigate granular packings subject to mechanical tapping for three types of beads with different friction coefficients. We validate Edwards volume ensemble in these three-dimensional granular systems and establish a granular version of thermodynamic zeroth law. Within Edwards framework, we also explicitly clarify how friction influences granular statistical mechanics as modifying the density of states, which allows us to determine the entropy as a function of packing fraction and friction subsequently. Additionally, we obtain a granular jamming phase diagram based on geometric coordination number and packing fraction., Comment: 20 pages, 7 figures

In marginally jammed solids confined by walls, we calculate the particle and ensemble averaged value of an order parameter, $\left<\Psi(r)\right>$, as a function of the distance to the wall, $r$. Being a microscopic indicator of structural disorder and particle mobility in solids, $\Psi$ is by definition the response of the mean square particle displacement to the increase of temperature in the harmonic approximation and can be directly calculated from the normal modes of vibration of the zero-temperature solids. We find that, in confined jammed solids, $\left<\Psi(r)\right>$ curves at different pressures can collapse onto the same master curve following a scaling function, indicating the criticality of the jamming transition. The scaling collapse suggests a diverging length scale and marginal instability at the jamming transition, which should be accessible to sophisticatedly designed experiments. Moreover, $\left<\Psi(r)\right>$ is found to be significantly suppressed when approaching the wall and anisotropic in directions perpendicular and parallel to the wall. This finding can be applied to understand the $r$-dependence and anisotropy of the structural relaxation in confined supercooled liquids, providing another example of understanding or predicting behaviors of supercooled liquids from the perspective of the zero-temperature amorphous solids.

We develop a single-layer waveguide surface grating structure to vertically couple near infrared (NIR) light at ~1.55 um wavelength from a large area (~100 um length scale) Si waveguide on a Silicon-On-Insulator (SOI) substrates to free-space for high-power laser applications. Our design approach is based on the optimization of local emission angles and the out-coupling intensities. Simulation results show that a focal spot with a 1/e2 width of 3.82 um can be achieved at the desired focal position, with 33% (-4.81 dB) simulated source to free-space focusing efficiency, while initial measurements show an efficiency of 22% (-6.58 dB).

By using long-range interacting polygons, we experimentally probe the coupling between particle shape and long-range interaction. For two typical space-filling polygons, square and triangle, we find two types of coupling modes that predominantly control the structure formation. Specifically, the rotational ordering of squares brings a lattice deformation that produces a hexagonal-to-rhombic transition in the high-density regime, whereas the alignment of triangles introduces a large geometric frustration that causes an order-to-disorder transition. Moreover, the two coupling modes lead to small and large "internal roughness" of the two systems, and thus predominantly control their structure relaxations. Our study thus provides a physical picture to the coupling between long-range interaction effect and short-range shape effect in the high-density regime unexplored before.

Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical stability and entropy, with the latter's effect increasing with friction. We show that a parameter-free maximum-entropy argument alone predicts an exponential cell order distribution, with excellent agreement with the experimental observation. We show that friction only tunes the mean cell order and, consequently, the exponential decay rate and the packing fraction. We further show that cells, which can be very large in such systems, are short-lived, implying that our systems are liquid-like rather than glassy.

It is a persistent problem in condensed matter physics that glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses at the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. It is well known that phonons in crystals couple through phonon-phonon interactions, an extremely efficient mechanism for anharmonic decay that is also important in glasses. Here, however, we show that an additional anharmonic channel of different origin emerges in the case of glasses, which induces intermittent rearrangements of particles. We have found that thermal vibrations in glasses trigger transitions among numerous different local minima of the energy landscape, which, however, are located within the same wide (meta)basin. These processes generate motions that are different from both diffusive and out-of-equilibrium aging dynamics. We suggest that the intermittent rearrangements accompanying thermal fluctuations are crucial features distinguishing glasses from crystals., Comment: 13 pages, 9 figures, 1 table

General relativity reproduces main current cosmological observations, assuming the validity of cosmic distance duality relation (CDDR) at all scales and epochs. However, CDDR is poorly tested in the redshift interval between the farthest observed Type Ia supernovae (SN Ia) and that of the Cosmic Microwave background (CMB). We present a new idea of testing the validity of CDDR, through the multiple measurements of high-redshift quasars. Luminosity distances are derived from the relation between the UV and X-ray luminosities of quasars, while angular diameter distances are obtained from the compact structure in radio quasars. This will create a valuable opportunity where two different cosmological distances from the same kind of objects at high redshifts are compared. Our constraints are more stringent than other currently available results based on different observational data and show no evidence for the deviation from CDDR at $z\sim 3$. Such accurate model-independent test of fundamental cosmological principles can become a milestone in precision cosmology., Comment: 8 pages, 6 figures, 1 table, Accepted for publication in ApJ

We rejuvenate well-aged quasi-2D binary colloidal glasses by thermal cycling, and systematically measure both the statistical responses and particle-level structural evolutions during rejuvenation. While the moduli and boson peak are continuously rejuvenated with increasing number of cycles, the mean square displacement (MSD) fluctuates significantly between different groups of thermal cycles. The decoupling between the thermodynamical and dynamical evolutions suggests different microscopic origins for different bulk properties of glasses. We find that a small fraction of structural rearrangements triggered by thermal cycling could alter the whole elastic continuum and lead to the significant thermodynamic rejuvenation, while localized defects could be activated and deactivated at the positions close to the rearrangements with significantly high mobility change and hence result in the fluctuated dynamics even with only about 10% of particles as fast regions. Our results offer a comprehensive picture for the microscopic mechanisms underlying bulk glass rejuvenation, which could be readily used to refine glass properties or to formulate further statistical theories in glassy systems., Comment: 14 pages, 6 figures

When randomly displacing the nodes of a crystalline and unstressed spring network, we find that the Possion's ratio decreases with the increase of structural disorder and even becomes negative. Employing our finding that longer springs tend to contribute more to the shear modulus but less to the bulk modulus, we are able to achieve negative Poisson's ratio with lower structural disorder by attributing each spring a length dependent stiffness. Even with perfect crystalline structure, the network can have negative Possion's ratio, if the stiffness of each spring is set by its virtual length after a virtual network distortion. We also reveal that the nonaffine contribution arising from the structural or spring constant disorder produced in some cooperative way by network distortion is essential to the emergence of negative Poisson's ratio., Comment: 5 pages, 4 figures