Abstract

We use direct numerical simulations to study a steady bathtub vortex in a cylindrical tank with a central drain-hole, a flat stress-free surface and velocity prescribed at the inlet. We find that the qualitative structure of the meridional flow does not depend on the radial Reynolds number, whereas we observe a weak overall rotation at a low radial Reynolds number and a concentrated vortex above the drain-hole at a high radial Reynolds number. We introduce a simple analytically integrable model that ...

Abstract

The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [ Cavalleri and Tonni Phys. Rev. E 57 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of ...

Abstract

Cooperation is beneficial for the species as a whole, but, at the level of an individual, defection pays off. Natural selection is then expected to favor defectors and eliminate cooperation. This prediction is in stark contrast with the abundance of cooperation at all levels of biological systems: from cells cooperating to form a biofilm or an organism to ecosystems and human societies. Several explanations have been proposed to resolve this paradox, including direct reciprocity, kin, and group selection. However, our work builds upon an observation that selection on ...

Abstract

Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if ...

Abstract

Recent advances in fields ranging from cosmology to computer science have hinted at a possible deep connection between intelligence and entropy maximization, but no formal physical relationship between them has yet been established. Here, we explicitly propose a first step toward such a relationship in the form of a causal generalization of entropic forces that we find can cause two defining behaviors of the human “cognitive niche”—tool use and social cooperation—to spontaneously emerge in simple physical systems. Our results suggest a ...

Abstract

This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains. ...

Abstract

The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with remarkable efficiency; but propagating in time is more physical and gives correctly behaved reflections and scattering without effort. Which should be chosen in a given situation, and what compromises might have to be made? Here the natural behaviors of each choice of propagation are compared and contrasted for an ordinary second ...

Abstract

We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to the design of multimode waveguide bends (realized experimentally in a previous paper) and mode squeezers, in which all modes are transported equally without scattering. In addition to the optimization, a key point is the identification of the correct boundary conditions ...

Abstract

Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider programming a dispersive filter near atomic resonance in rare earth ion doped crystals, which leads to unprecedented high values of dispersive power. This filter is used in an approximate imaging scheme, combining a single time lens and a single dispersive section and operating as a time reversing device. This scheme is closely related to three-pulse photon echo ...

Abstract

In 1973, Le Bellac and Levy-Leblond (Nuovo Cimento B 14, 217-234) discovered that Maxwell's equations possess two non-relativistic Galilei-covariant limits, corresponding to E >> cB (electric limit) or E << cB (magnetic limit). Here, we provide a systematic, yet simple, derivation of these two limits based on a dimensionless form of Maxwell's equations and an expansion of the electric and magnetic fields in a power series of some small parameters. Using this procedure, all previously known results are recovered in a natural and unambiguous way. Some further extensions ...

Abstract

We study scattering of waves by black holes. Solving a massless scalar field with a point source in the Schwarzschild spacetime, waves scattered by the black hole is obtained numerically. We then reconstruct images of the black hole from scattered wave data for specified scattering angles. For the forward and the backward directions, obtained wave optical images of black holes show rings that correspond to the black hole glories associated with existence of the unstable circular photon orbit in the Schwarzschild spacetime. ...

Abstract

Beam propagation beyond the paraxial approximation is studied in an optically written waveguide structure. The waveguide structure that leads to diffractionless light propagation, is imprinted on a medium consisting of a five-level atomic vapor driven by an incoherent pump and two coherent spatially dependent control and plane-wave fields. We first study propagation in a single optically written waveguide, and find that the paraxial approximation does not provide an accurate description of the probe propagation. We then employ coherent control fields such that two parallel and one tilted Gaussian ...

Abstract

We discuss physical implications of the explicit method in numerical analysis. Numerical methods have there own condition for causality, known as the Courant-Friedrichs-Lewy condition. It is proposed that numerical causality merges with physical causality as the grid interval size approaches zero. We discuss the implications of this proposition on the numerical analysis of the wave equation. We also show that, insisting on physical causality, the numerical analysis of Schrodinger's equation implies that the minimum space interval should satisfy $Δ x ≥ a_0 λ_c$, where $λ_c$ is the reduced Compton ...

Abstract

We give an explicit solution to the phenomenon of internal waves with a still water surface, called dead water, on the basis of the Gerstner wave solution to the Euler equations. ...

Abstract

The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two Lorentz-invariant 2D surfaces in spacetime can be defined such that magnetic and electric field lines are determined, for any observer, by the intersection of those surfaces with spacelike hyperplanes. An instance of this type of field is constituted by the so-called Hopf-Ranada solutions of the source-free Maxwell equations, which have been studied because of their interesting topological properties, ...

Abstract

Newton's third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is thus zero. However, according to the principles of relativity a signal can not propagate at speeds exceeding the speed of light. Hence the action cannot be generated at the same time with the reaction because the information about the action has to reach the affected object and the affected object still needs additional time to react on ...

Abstract

That the universal constancy of the speed of light is a logical consequence of Maxwell's equations is common knowledge. Here we show that the converse is also true. That is, electromagnetism (EM) and electrodynamics (ED) in all their details can be derived from the simple assumption that the speed of light is a universal constant. The consequences reach far. Conventional EM and ED are observation based. The alternative we propose spares all observational foundations of EM, only to reintroduce them as theoretically derived and empiricism-free laws of Nature. ...

Abstract

We propose and verify experimentally a new concept for achieving strong nonlinear coupling between the electromagnetic and elastic properties in metamaterials. This coupling is provided through a novel degree of freedom in metamaterial design: internal rotation within structural elements. Our meta-atoms have high sensitivity to electromagnetic wave power, and the elastic and electromagnetic properties can be independently designed to optimise the response. We demonstrate a rich range of nonlinear phenomena including self-tuning and bistability, and provide a comprehensive experimental demonstration of the predicted effects. ...

Abstract

A precise definition of causality in physics has been missing so far, only supplemented by ad hoc assumptions based on empirical evidence. Causality has then been often confused with the notion of determinism. In view of the debate about quantum foundations, it is mandatory to separate the two notions with clear-cut definitions. Quantum theory provides an example of causal not-deterministic theory. Here we introduce a toy operational theory that is deterministic and non-causal, thus proving that the two notions of causality and determinism are totally independent. ...

Abstract

Metamaterials are patterned metallic structures which permit access to a novel electromagnetic response, negative index of refraction, impossible to achieve with naturally occurring materials. Using the Babinet principle, the complementary split ring resonator (SRR) is etched in a metallic plate to provide negative ε, with perpendicular direction. Here we propose a new design, etched in a metallic plate to provide negative magnetic permeability μ, with perpendicular direction. The combined electromagnetic response of this planar metamaterial, where the negative μ comes from ...

Abstract

The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to ...

Abstract

Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. ...

Abstract

Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in ...

Abstract

We present and discuss a selection of classical mechanics and thermodynamics problems. The discussion is based on the use of the impulse–momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or the first law of thermodynamics, depending on the nature of the problem. Thermodynamical aspects of classical mechanics, namely problems involving non-conservative forces or variation of mechanical energy are discussed in different reference frames, in connection with the use of one or other of the energy equations, and also compliance with the ...

Abstract

This chapter discusses the relationships between current sources and the resulting electromagnetic waves in FDTD simulations. First, the "total-field/scattered-field" approach to creating incident plane waves is reviewed and seen to be a special case of the well-known principle of equivalence in electromagnetism: this can be used to construct "equivalent" current sources for any desired incident field, including waveguide modes. The effects of dispersion and discretization are discussed, and a simple technique to separate incident and scattered fields is described in order to compensate for imperfect equivalent currents. The important ...

Abstract

Employing a transformation to hyperbolic space, we derive in a simple way exact solutions for the Klein-Gordon equation in an infinite square-well potential with one boundary moving at constant velocity, for the massless as well as for the massive case. ...

Abstract

The method of conformal transformations is applied to the analysis of waveguide bends. Equivalent structures are obtained that permit solution by traditional methods of optical waveguide analysis. Losses associated with both curvature and with the transition from straight to curved guides are discussed and simple first-order expressions that describe the dependence of the losses on waveguide parameters are derived. ...

Abstract

We obtain analytical solutions for positive-to-negative transition materials with a smooth transition profile "$\tanh$". The fields are expressed in terms of hypergeometric functions. The final expressions for reflection and transmission coefficients are obtained in closed forms. The total absorption is nonzero even in the lossless limit in accordance with previous studies. Properties of the total absorption as function of controlling factors are also well studied. As an application of the analytical results, we analyze the effects of smooth transition on perfect imaging and, interestingly, find multiple images of the ...

Abstract

Plasmonic nanoantennas are key elements in nanophotonics capable of directing radiation or enhancing the transition rate of a quantum emitter. The magnetic-dipole-type nanoantennas, which are the Babinet complementary structures of typical electric-dipole-type, have received little attention leaving their antenna properties largely unexplored. We present a multi-slot nanoantenna with a magnetic dipole feed exhibiting highly unidirectional free-space radiation. This antenna does not suffer from the directivity limit arising from a natural tendency to radiate into high-refractive-index substrates. Its geometry is engineered to achieve an optimal front-to-back ratio by adjusting the phase ...

Abstract

We show that the Lorentz force law, F^L_1=q_1(E+v_1xB) being the charge on particle 1 interacting with the electromagnetic fields due to all other particles, can be written in a pure field form F^L_1=-∇_1 U^EM. In this expression U^EM is the total electromagnetic energy of the system of particle 1 and all other particles. In deriving this result we review the old but not widely known results that Maxwell's equations follow uniquely from Special Relativity, and that the Lorentz force law follows from applying Hamilton's variational principle to this ...

Abstract

The structure of a society depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society's hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined ...

Abstract

The stationary value problem of the dynamic action for the determination of the natural frequencies of the polygonal plates is transformed by a holomorphic function into an equivalent problem of another plate with a circular boundary. The equivalent problem is then solved by the Rayleigh‐Ritz method. Since the selected coordinate functions are independent of the actual shape of a plate, the formulation is valid for one plate and for all others with boundaries which are the conformal images of a unit ...

Abstract

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and optimization are used. Detailed numerical results are given and the connections between the different approaches are enlightened. ...

Abstract

There has existed a continuing dialogue concerning the proper identification of radiation forces and momenta in dielectric media. I argue herein that a sensible and consistent picture of these forces and momenta is available. That is, the density of electromagnetic momentum G⃗ is given by G⃗=S⃗/c2, where S⃗ is Poynting's vector. The forces which are exerted on material objects in dielectric media are associated with changes in both the electromagnetic and mechanical momenta of the media. In fairly broad circumstances, such ...

Abstract

It is shown that the use of the Riemann-Silberstein (RS) vector greatly simplifies the description of the electromagnetic field both in the classical domain and in the quantum domain. In this review we describe many specific examples where this vector enables one to significantly shorten the derivations and make them more transparent. We also argue why the RS vector may be considered as the best possible choice for the photon wave function. ...

Abstract

The systematic biases and errors seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory. We show the contrary: that these biases are a consequence of people correctly following probability theory, but with random variation or noise affecting the reasoning process. Taking P_E(A) to represent a person's estimate for the probability of some event A, this random variation account predicts that on average P_E(A)+P_E(B)- P_E(A or B)-P_E(A and B)=0 for all pairs of events A,B, ...

Abstract

The Maxwell fish eye lens has previously been reported as being capable of the much sought after phenomenon of subwavelength imaging. The inclusion of a drain in this system is considered crucial to the imaging ability, although its role is the topic of much debate. This paper provides a numerical investigation into a practical implementation of a drain in such systems, and analyzes the strong frequency dependence of both the Maxwell fish eye lens and an alternative, the Miñano lens. The ...

Abstract

The Open Researcher & Contributor ID (ORCID) registry presents a unique opportunity to solve the problem of author name ambiguity. At its core the value of the ORCID registry is that it crosses disciplines, organizations, and countries, linking ORCID with both existing identifier schemes as well as publications and other research activities. By supporting linkages across multiple datasets - clinical trials, publications, patents, datasets - such a registry becomes a switchboard for researchers and publishers alike in managing the dissemination of ...

Abstract

The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity [refractive index (RI) less than unity] and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the RI. This transformation preserves the ray trajectories but leads to a uniform phase delay. We show ...

Abstract

We introduce a general framework in performing transformation optics by purely rotating the optical axis of the same anisotropic dielectric material on the subwavelength scale. The transformation medium realizes any area-preserving maps with maximum anisotropy only limited by the original material. By applying different optical-axis profiles on the same medium, a wave expander and a virtual shifter are constructed as examples. The investigations are potentially useful for designing transformation optical devices using only one type of material. ...

Abstract

Hyperbolic metamaterials may be used to model a 2+1 dimensional Minkowski spacetime in which the role of time is played by one of the spatial coordinates. When a metamaterial is built and illuminated with a coherent extraordinary laser beam, the stationary pattern of light propagation inside the metamaterial may be treated as a collection of particle world lines, which represents a complete history of this 2+1 dimensional spacetime. While this model may be used to build interesting spacetime analogs, such as metamaterial black holes and big bang, it ...

Abstract

The method of transformation optics (TO) has recently been applied to the problem of manipulating the flow of surface plasmon polaritons (SPPs) along metal–dielectric interfaces. Although it allows one to theoretically control the flow in any manner desired, it usually leads to material properties not found in nature, thus making the realization of theoretical potentialities impractical. Therefore, artificial materials (called metamaterials), with both inhomogeneous and anisotropic electromagnetic response, are normally required to create the optical space designed with the TO method. ...

Abstract

Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. We introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation. It extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm). The approach is illustrated both by simple models (where, in contrast to the real world, we know the underlying equations/relations and so can check the validity of our method) ...

Abstract

This paper discusses the Monte Carlo and Molecular Dynamics methods. Both methods are, in principle, simple. However, simple does not mean risk-free. In the literature, many of the pitfalls in the field are mentioned, but usually as a footnote - and these footnotes are scattered over many papers. The present paper focuses on the `dark side' of simulation: it is one big footnote. I should stress that `dark', in this context, has no negative moral implication. It just means: under-exposed. ...

Abstract

The optical radiation of a magnetic dipole coupled to a plasmonic nanoantenna composed of stacked gold nanodisks is investigated. The nanoantenna is fed by a point magnetic dipole properly situated between two nanodisks. It is found that the magnetic dipole efficiently couples to the antenna due to the excitation of an antiphase localized surface plasmon resonance mode. This leads to a remarkable enhancement of the optical radiation at the resonant wavelength associated with the hybridized mode of the nanoantenna. By introducing ...

Abstract

Three-dimensional pentamode metamaterials are artificial solids that approximately behave like liquids, which have vanishing shear modulus. Pentamodes have recently become experimental reality. Here, we calculate their phonon band structures for various parameters. Consistent with static continuum mechanics, we find that compression and shear waves exhibit phase velocities that can realistically be different by more than one order of magnitude. Interestingly, we also find frequency intervals with more than two octaves bandwidth in which pure single-mode behavior is obtained. Herein, exclusively compression ...

Abstract

The speed of integrated circuits is ultimately limited by the mobility of electrons or holes, which depend on the effective mass in a semiconductor. Here, building on an analogy with electromagnetic metamaterials and transformation optics, we describe a transport regime in a semiconductor superlattice characterized by extreme anisotropy of the effective mass and a low intrinsic resistance to movement—with zero effective mass—along some preferred direction of electron motion. We theoretically demonstrate that such a regime may permit an ultrafast, extremely strong ...

Note (first note only)

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