Dense particle packings have served as useful models of the structures of liquid, glassy and crystalline states of matter, granular media, heterogeneous materials and biological systems. Probing the ...symmetries and other mathematical properties of the densest packings is a problem of interest in discrete geometry and number theory. Previous work has focused mainly on spherical particles—very little is known about dense polyhedral packings. Here we formulate the generation of dense packings of polyhedra as an optimization problem, using an adaptive fundamental cell subject to periodic boundary conditions (we term this the ‘adaptive shrinking cell’ scheme). Using a variety of multi-particle initial configurations, we find the densest known packings of the four non-tiling Platonic solids (the tetrahedron, octahedron, dodecahedron and icosahedron) in three-dimensional Euclidean space. The densities are 0.782 , 0.947 , 0.904... and 0.836..., respectively. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other non-tiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. Combining our simulation results with derived rigorous upper bounds and theoretical arguments leads us to the conjecture that the densest packings of the Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This is the analogue of Kepler’s sphere conjecture for these solids.
Abstract In adult cortices, the ratio of excitatory and inhibitory conductances (E/I ratio) is presumably balanced across a wide range of stimulus conditions. However, it is unknown how the E/I ratio ...is postnatally regulated, when the strength of synapses are rapidly changing. Yet, understanding of such a process is critically important, because there are numerous neuropsychological disorders, such as autism, epilepsy and schizophrenia, associated with disturbed E/I balances. Here we directly measured the E/I ratio underlying locally induced synaptic conductances in principal neurons from postnatal day 8 (P8) through 60. We found that (1) within each developmental period, the E/I ratio across four major cortical layers was maintained at a similar value under wide range of stimulation intensities; and (2) there was a rapid developmental decrease in the E/I ratio, which occurred within a sensitive period between P8 to P18 with exception of layer II/III. By comparing the excitatory and inhibitory conductances, as well as key synaptic protein expressions, we found a net increase in the number and strength of inhibitory, but not excitatory synapses, is responsible for the developmental decrease in the E/I ratio in the barrel cortex. The inhibitory markers were intrinsically co-regulated, gave rise to a sharp increase in the inhibitory conductance from P8 to P18. These results suggest that the tightly regulated E/I ratios in adults cortex is a result of drastic changes in relative weight of inhibitory but not excitatory synapses during critical period, and the local inhibitory structural changes are the underpinning of altered E/I ratio across postnatal development.
We study the nonlinear optomechanically induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order ...sidebands, including the transmission rate and the group delay; (ii) for active-passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength and group delay of not only the probe light but also its higher-order sidebands.
Erosion by an Alpine glacier Herman, Frédéric; Beyssac, Olivier; Brughelli, Mattia ...
Science (American Association for the Advancement of Science),
10/2015, Letnik:
350, Številka:
6257
Journal Article
Recenzirano
Assessing the impact of glaciation on Earth's surface requires understanding glacial erosion processes. Developing erosion theories is challenging because of the complex nature of the erosion ...processes and the difficulty of examining the ice/bedrock interface of contemporary glaciers. We demonstrate that the glacial erosion rate is proportional to the ice-sliding velocity squared, by quantifying spatial variations in ice-sliding velocity and the erosion rate of a fast-flowing Alpine glacier. The nonlinear behavior implies a high erosion sensitivity to small variations in topographic slope and precipitation. A nonlinear rate law suggests that abrasion may dominate over other erosion processes in fast-flowing glaciers. It may also explain the wide range of observed glacial erosion rates and, in part, the impact of glaciation on mountainous landscapes during the past few million years.
Two-phase random textures abound in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. Questions surrounding the spatial ...structure of such textures continue to pose many theoretical challenges. For example, can two-point correlation functions be identified that can be manageably measured and yet reflect nontrivial higher-order structural information about the textures? We present a solution to this question by probing the information content of the widest class of different types of two-point functions examined to date using inverse "reconstruction" techniques. This enables us to show that a superior descriptor is the two-point cluster function C₂(r), which is sensitive to topological connectedness information. We demonstrate the utility of C₂(r) by accurately reconstructing textures drawn from materials science, cosmology, and granular media, among other examples. Our work suggests a theoretical pathway to predict the bulk physical properties of random textures and that also has important ramifications for atomic and molecular systems.
An emerging concept is the tight relationship between dysbiosis (microbiota imbalance) and disease. The increase in knowledge about alterations in microbial communities that reside within the host ...has made a strong impact not only on dental science, but also on immunology and microbiology as well as on our understanding of several diseases. Periodontitis is a well-characterized human disease associated with dysbiosis, characterized by the accumulation of multiple bacteria that play individual and critical roles in bone loss around the teeth. Dysbiosis is largely dependent on cooperative and competitive interactions among oral microbes during the formation of the pathogenic biofilm community at gingival sites. Oral pathobionts play different and synergistic roles in periodontitis development, depending on their host-damaging and immunostimulatory activities. Host immune responses to oral pathobionts act as a double-edged sword not only by protecting the host against pathobionts, but also by promoting alveolar bone loss. Recent studies have begun to elucidate the roles of individual oral bacteria, including a new type of pathobionts that possess strong immunostimulatory activity, which is critical for alveolar bone loss. Better understanding of the roles of oral pathobionts is expected to lead to a better understanding of periodontitis disease and to the development of novel preventive and therapeutic approaches for the disease.
Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on ...spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3 , except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823..., 0.836..., 0.904..., and 0.947..., respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the "asphericity" (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be the analog of Kepler's sphere conjecture for these solids.The truncated tetrahedron is the only nonchiral Archimedean solid that is not centrally symmetric corrected, the densest known packing of which is a non-lattice packing with density at least as high as 23/24=0.958 333... . We discuss the validity of our conjecture to packings of superballs, prisms, and antiprisms as well as to high-dimensional analogs of the Platonic solids. In addition, we conjecture that the optimal packing of any convex, congruent polyhedron without central symmetry generally is not a lattice packing. Finally, we discuss the possible applications and generalizations of the ASC scheme in predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra.
We study optomechanically induced transparency (OMIT) in a compound system consisting of coupled optical resonators and a mechanical mode, focusing on the unconventional role of loss. We find that ...optical transparency can emerge at the otherwise strongly absorptive regime in the OMIT spectrum, by using an external nanotip to enhance the optical loss. In particular, loss-induced revival of optical transparency and the associated slow-to-fast light switch can be identified in the vicinity of an exceptional point. These results open up a counterintuitive way to engineer micro-mechanical devices with tunable losses for e.g., coherent optical switch and communications.
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