Hasil untuk "Physics"

Zhiping Mao, Ameya Dilip Jagtap, G. Karniadakis

Abstract In this work we investigate the possibility of using physics-informed neural networks (PINNs) to approximate the Euler equations that model high-speed aerodynamic flows. In particular, we solve both the forward and inverse problems in one-dimensional and two-dimensional domains. For the forward problem, we utilize the Euler equations and the initial/boundary conditions to formulate the loss function, and solve the one-dimensional Euler equations with smooth solutions and with solutions that have a contact discontinuity as well as a two-dimensional oblique shock wave problem. We demonstrate that we can capture the solutions with only a few scattered points clustered randomly around the discontinuities. For the inverse problem, motivated by mimicking the Schlieren photography experimental technique used traditionally in high-speed aerodynamics, we use the data on density gradient ∇ ρ ( x , t ) , the pressure p ( x ∗ , t ) at a specified point x = x ∗ as well as the conservation laws to infer all states of interest (density, velocity and pressure fields). We present illustrative benchmark examples for both the problem with smooth solutions and Riemann problems (Sod and Lax problems) with PINNs, demonstrating that all inferred states are in good agreement with the reference solutions. Moreover, we show that the choice of the position of the point x ∗ plays an important role in the learning process. In particular, for the problem with smooth solutions we can randomly choose the position of the point x ∗ from the computational domain, while for the Sod or Lax problem, we have to choose the position of the point x ∗ from the domain between the initial discontinuous point and the shock position of the final time. We also solve the inverse problem by combining the aforementioned data and the Euler equations in characteristic form, showing that the results obtained by using the Euler equations in characteristic form are better than that obtained by using the Euler equations in conservative form. Furthermore, we consider another type of inverse problem, specifically, we employ PINNs to learn the value of the parameter γ in the equation of state for the parameterized two-dimensional oblique wave problem by using the given data of the density, velocity and the pressure, and we identify the parameter γ accurately. Taken together, our results demonstrate that in the current form, where the conservation laws are imposed at random points, PINNs are not as accurate as traditional numerical methods for forward problems but they are superior for inverse problems that cannot even be solved with standard techniques.

Danijela Marković, A. Mizrahi, D. Querlioz et al.

Neuromorphic computing takes inspiration from the brain to create energy-efficient hardware for information processing, capable of highly sophisticated tasks. Systems built with standard electronics achieve gains in speed and energy by mimicking the distributed topology of the brain. Scaling-up such systems and improving their energy usage, speed and performance by several orders of magnitude requires a revolution in hardware. We discuss how including more physics in the algorithms and nanoscale materials used for data processing could have a major impact in the field of neuromorphic computing. We review striking results that leverage physics to enhance the computing capabilities of artificial neural networks, using resistive switching materials, photonics, spintronics and other technologies. We discuss the paths that could lead these approaches to maturity, towards low-power, miniaturized chips that could infer and learn in real time. Neuromorphic computing takes inspiration from the brain to create energy-efficient hardware for information processing, capable of highly sophisticated tasks. Including more physics in the algorithms and nanoscale materials used for computing could have a major impact in this field.

Ameya Dilip Jagtap, G. Karniadakis

Abstract We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima. Furthermore, the proposed adaptive activation functions are shown to accelerate the minimization process of the loss values in standard deep learning benchmarks using CIFAR-10, CIFAR-100, SVHN, MNIST, KMNIST, Fashion-MNIST, and Semeion datasets with and without data augmentation.

K. Kawabata, Ken Shiozaki, Masahito Ueda et al.

We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, point-like and line-like vacant regions. On the basis of these concepts and K-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons.

M. Raissi, G. Karniadakis

Abstract While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier–Stokes, Schrodinger, Kuramoto–Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

M. Raissi, P. Perdikaris, G. Karniadakis

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models. The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information. In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

M. Perc, Jillian J. Jordan, David G. Rand et al.

Abstract Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is indeed due, to a large degree, to our unparalleled other-regarding abilities. Yet, a comprehensive understanding of human cooperation remains a formidable challenge. Recent research in the social sciences indicates that it is important to focus on the collective behavior that emerges as the result of the interactions among individuals, groups, and even societies. Non-equilibrium statistical physics, in particular Monte Carlo methods and the theory of collective behavior of interacting particles near phase transition points, has proven to be very valuable for understanding counterintuitive evolutionary outcomes. By treating models of human cooperation as classical spin models, a physicist can draw on familiar settings from statistical physics. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among humans often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. The complexity of solutions therefore often surpasses that observed in physical systems. Here we review experimental and theoretical research that advances our understanding of human cooperation, focusing on spatial pattern formation, on the spatiotemporal dynamics of observed solutions, and on self-organization that may either promote or hinder socially favorable states.

P. Battaglia, Razvan Pascanu, M. Lai et al.

Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact, supporting dynamical predictions, as well as inferences about the abstract properties of the system. Our model takes graphs as input, performs object- and relation-centric reasoning in a way that is analogous to a simulation, and is implemented using deep neural networks. We evaluate its ability to reason about several challenging physical domains: n-body problems, rigid-body collision, and non-rigid dynamics. Our results show it can be trained to accurately simulate the physical trajectories of dozens of objects over thousands of time steps, estimate abstract quantities such as energy, and generalize automatically to systems with different numbers and configurations of objects and relations. Our interaction network implementation is the first general-purpose, learnable physics engine, and a powerful general framework for reasoning about object and relations in a wide variety of complex real-world domains.

Houtong Chen, A. Taylor, N. Yu

Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam–Berry phase and Huygens’ metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.

F. Battiston, E. Amico, A. Barrat et al.

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems. Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.

R. Courant, K. Friedrichs, H. Lewy

J. Langer

M. Jusup, Petter Holme, Kiyoshi Kanazawa et al.

Recent decades have seen a rise in the use of physics methods to study different societal phenomena. This development has been due to physicists venturing outside of their traditional domains of interest, but also due to scientists from other disciplines taking from physics the methods that have proven so successful throughout the 19th and the 20th century. Here we dub this field 'social physics' and pay our respect to intellectual mavericks who nurtured it to maturity. We do so by reviewing the current state of the art. Starting with a set of topics that are at the heart of modern human societies, we review research dedicated to urban development and traffic, the functioning of financial markets, cooperation as the basis for our evolutionary success, the structure of social networks, and the integration of intelligent machines into these networks. We then shift our attention to a set of topics that explore potential threats to society. These include criminal behaviour, large-scale migrations, epidemics, environmental challenges, and climate change. We end the coverage of each topic with promising directions for future research. Based on this, we conclude that the future for social physics is bright. Physicists studying societal phenomena are no longer a curiosity, but rather a force to be reckoned with. Notwithstanding, it remains of the utmost importance that we continue to foster constructive dialogue and mutual respect at the interfaces of different scientific disciplines.

V. Rakov, M. Uman

Andrei Linde

With the invention of unified theories of strong, weak, electromagnetic and gravitational interactions, elementaryparticle physics has entered a very interesting and unusual stage of its development. The end of the 1960s saw the introduction of the Glashow‐Weinberg‐Salam unification of the weak and electromagnetic interactions. In 1974 came the grand unified theories of the strong, weak and electromagnetic interactions. Two years later we had supergravity, giving us the first hope of unifying all fundamental interactions, including gravitation. The beginning of the 1980s witnessed a renewal of interest in the Kaluza‐Klein theories and supergravity in higher‐dimensional space‐time. Nowadays superstring theory is the leading candidate for the role of “theory of everything.”

N. Cartwright

R. Haag, M. E. Mayer

L. Chomaz, I. Ferrier-Barbut, F. Ferlaino et al.

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole–dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Jonathan L. Feng, F. Kling, M. Reno et al.

High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe standard model (SM) processes and search for physics beyond the standard model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF’s physics potential.

M. Achasov, X. Ai, R. Aliberti et al.

The super τ-charm facility (STCF) is an electron–positron collider proposed by the Chinese particle physics community. It is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of 0.5 × 1035 cm−2·s−1 or higher. The STCF will produce a data sample about a factor of 100 larger than that of the present τ-charm factory — the BEPCII, providing a unique platform for exploring the asymmetry of matter-antimatter (charge-parity violation), in-depth studies of the internal structure of hadrons and the nature of non-perturbative strong interactions, as well as searching for exotic hadrons and physics beyond the Standard Model. The STCF project in China is under development with an extensive R&D program. This document presents the physics opportunities at the STCF, describes conceptual designs of the STCF detector system, and discusses future plans for detector R&D and physics case studies.