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Mathematics

Nature.com

A generalization of the standard map and its statistical characterization

From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. Several works on these maps, e.g., the standard map and the web map, have shown that ergodicity breakdown causes the statistical mechanical framework that describes the dynamics of the system to change. In this paper, for a novel generalization of the standard map, which we define by generalizing the periodic function used in its definition, we verify that a q-Gaussian with $$q\simeq 1.935$$ for the probability distribution of sum of the iterates of the system with initial conditions chosen from the nonergodic stability islands is robust. We also show that the probability distributions become more complicated and unexpected limiting behavior occurs for some parameter regimes.
SCIENCE
Nature.com

A new class of bilayer kagome lattice compounds with Dirac nodal lines and pressure-induced superconductivity

Kagome lattice composed of transition-metal ions provides a great opportunity to explore the intertwining between geometry, electronic orders and band topology. The discovery of multiple competing orders that connect intimately with the underlying topological band structure in nonmagnetic kagome metals AV3Sb5 (A"‰="‰K, Rb, Cs) further pushes this topic to the quantum frontier. Here we report a new class of vanadium-based compounds with kagome bilayers, namely AV6Sb6 (A"‰="‰K, Rb, Cs) and V6Sb4, which, together with AV3Sb5, compose a series of kagome compounds with a generic chemical formula (Am-1Sb2m)(V3Sb)n (m"‰="‰1, 2; n"‰="‰1, 2). Theoretical calculations combined with angle-resolved photoemission measurements reveal that these compounds feature Dirac nodal lines in close vicinity to the Fermi level. Pressure-induced superconductivity in AV6Sb6 further suggests promising emergent phenomena in these materials. The establishment of a new family of layered kagome materials paves the way for designer of fascinating kagome systems with diverse topological nontrivialities and collective ground states.
PHYSICS
Nature.com

Efficient world-line-based quantum Monte Carlo method without Hubbard"“Stratonovich transformation

By precisely writing down the matrix element of the local Boltzmann operator ($${\mathrm{e}}^{-\tau h}$$, where $$h$$ is the Hermitian conjugate pairs of off-diagonal operators), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With the current formula, the Hubbard"“Stratonovich transformation is not necessary, accordingly the determinant calculation is not needed, which can improve the computational efficiency. The results show that, the simulation time has the square-law scaling with system sizes, which is comparable with the usual first-principles calculations. The current formula also improves the accuracy of the Suzuki"“Trotter decomposition. As an example, we have studied the one-dimensional half-filled Hubbard model at finite temperature. The obtained results are in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be applied to various studies in future.
COMPUTERS
Nature.com

Theory-guided design of hydrogen-bonded cobaltoporphyrin frameworks for highly selective electrochemical HO production in acid

The pursuit of selective two-electron oxygen reduction reaction to H2O2 in acids is demanding and largely hampered by the lack of efficient non-precious-metal-based electrocatalysts. Metal macrocycles hold promise, but have been relatively underexplored. Efforts are called for to promote their inherent catalytic activities and/or increase the surface exposure of active sites. In this contribution, we perform the high-throughput computational screening of thirty-two different metalloporphyrins by comparing their adsorption free energies towards key reaction intermediates. Cobalt porphyrin is revealed to be the optimal candidate with a theoretical overpotential as small as 40"‰mV. Guided by the computational predictions, we prepare hydrogen-bonded cobaltoporphyrin frameworks in order to promote the solution accessibility of catalytically active sites for H2O2 production in acids. The product features an onset potential at ~0.68"‰V, H2O2 selectivity of >90%, turnover frequency of 10.9"‰sâˆ’1 at 0.55"‰V and stability of ~30"‰h, the combination of which clearly renders it stand out from existing competitors for this challenging reaction.
CHEMISTRY
Nature.com

The visual appearances of disordered optical metasurfaces

Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute the visual appearance of an object, such as the respective weight of specular and diffuse reflectances, object macroscopic shape, illumination and viewing conditions. Here we report the potential of disordered optical metasurfaces to harness visual appearance. We develop a multiscale modelling platform for the predictive rendering of macroscopic objects covered by metasurfaces in realistic settings, and show how nanoscale resonances and mesoscale interferences can be used to spectrally and angularly shape reflected light and thus create unusual visual effects at the macroscale. We validate this property with realistic synthetic images of macroscopic objects and centimetre-scale samples observable with the naked eye. This framework opens new perspectives in many branches of fine and applied visual arts.
SCIENCE
Phys.org

A new mathematical model of cellular movement

A mathematical model that describes how cells change their shape during movement suggests that the movement is mainly driven by the contraction of the skeletal proteins, called "myosin." The new model developed at Penn State can help researchers to better understand the various biological processes where cellular movement plays a key role and also could inform the development of artificial systems that mimic biological processes.
SCIENCE
Nature.com

Quasi-symmetry-protected topology in a semi-metal

The crystal symmetry of a material dictates the type of topological band structure it may host, and therefore, symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has exact symmetry at a lower order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine tuning as they enforce that sources of large Berry curvature occur at arbitrary chemical potentials. We demonstrate that quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2"‰meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.
PHYSICS

Hey Ray: Water magic

PITTSBURGH (KDKA) — We have shown you several experiments dealing with air pressure, and we want to show you how to perform an air pressure experiment that looks like magic.Our atmosphere is always pushing on us in all directions. Containers that seem empty are filled with air. Even when you turn that container upside down, it is full of air.  Even when a container is full of something else, like water, air is still pushing on it.  Also, this could get messy, so make sure you are doing this experiment in a place that is OK to get wet.Physics creates...
PHYSICS
Nature.com

Representing logic gates over Euclidean space via heaviside step function

Theoretical concepts asserted by Alan Turing are the basis of the computation and hence of machine intelligence. Turing Machine, the fundamental computational model, has been proven to be reducible to a logic circuit and, at the same time, portable into a computer program that can be expressed through a combination of fundamental programming language control structures. This work proposes a mathematical framework that analytically models logic gates employing Heaviside Step Function. The existence of a correspondence between a generic finite-time algorithm and the proposed mathematical formulation is proven. The proposed interpretation is given through a well-defined logical circuit analytical expression. Relevant geometrical applications, related to polygon processing, having wide implications in engineering branches are presented together with a new Penalty Method for constrained optimization problems handling. A detailed simulation campaign is conducted to assess the effectiveness of the applications derived from the proposed mathematical framework.
Nature.com

Spatial-dependent quantum dot-photon entanglement via tunneling effect

Utilizing the vortex beams, we investigate the entanglement between the triple-quantum dot molecule and its spontaneous emission field. We present the spatially dependent quantum dot-photon entanglement created by Laguerre-Gaussian (LG) fields. The degree of position-dependent entanglement (DEM) is controlled by the angular momentum of the LG light and the quantum tunneling effect created by the gate voltage. Various spatial-dependent entanglement distribution is reached just by the magnitude and the sign of the orbital angular momentum (OAM) of the optical vortex beam.
PHYSICS
Nature.com

Accelerated identification of equilibrium structures of multicomponent inorganic crystals using machine learning potentials

The discovery of multicomponent inorganic compounds can provide direct solutions to scientific and engineering challenges, yet the vast uncharted material space dwarfs synthesis throughput. While the crystal structure prediction (CSP) may mitigate this frustration, the exponential complexity of CSP and expensive density functional theory (DFT) calculations prohibit material exploration at scale. Herein, we introduce SPINNER, a structure-prediction framework based on random and evolutionary searches. Harnessing speed and accuracy of neural network potentials (NNPs), the program navigates configurational spaces 102"“103 times faster than DFT-based methods. Furthermore, SPINNER incorporates algorithms tuned for NNPs, achieving performances exceeding conventional algorithms. In blind tests on 60 ternary compositions, SPINNER identifies experimental (or theoretically more stable) phases for ~80% of materials. When benchmarked against data-mining or DFT-based evolutionary predictions, SPINNER identifies more stable phases in many cases. By developing a reliable and fast structure-prediction framework, this work paves the way to large-scale, open exploration of undiscovered inorganic crystals.
CHEMISTRY
Nature.com

The difference between semi-continuum model and Richards' equation for unsaturated porous media flow

Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a hyperbolic-parabolic partial differential equation with a hysteresis operator of Prandl's type. This limit differs from the standard Richards' equation, which is a parabolic equation and is not able to describe finger-like flow.
SCIENCE