Arbitrary Scalar Field Research Articles

An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models

Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma flows. We discuss a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. Prescribing this flow, we derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics for the case of an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. Our solution procedure employs Euler potentials and Cauchy's integral formalism based on the flow's stream function and isochrones. Furthermore, we use a particular renormalization procedure that allows us to generate more general analytical expressions modeling the deformations experienced by arbitrary scalar or vector-valued fields embedded in the flow as they are advected first toward and then past the parabolic obstacle. Finally, both the velocity field and the magnetic field embedded therein are generalized from incompressible to mildly compressible flow, where the associated density distribution is found from Bernoulli's principle.

Blind people can actively manipulate virtual objects with a novel tactile device

Frequently in rehabilitation, visually impaired persons are passive agents of exercises with fixed environmental constraints. In fact, a printed tactile map, i.e. a particular picture with a specific spatial arrangement, can usually not be edited. Interaction with map content, instead, facilitates the learning of spatial skills because it exploits mental imagery, manipulation and strategic planning simultaneously. However, it has rarely been applied to maps, mainly because of technological limitations. This study aims to understand if visually impaired people can autonomously build objects that are completely virtual. Specifically, we investigated if a group of twelve blind persons, with a wide age range, could exploit mental imagery to interact with virtual content and actively manipulate it by means of a haptic device. The device is mouse-shaped and designed to jointly perceive, with one finger only, local tactile height and inclination cues of arbitrary scalar fields. Spatial information can be mentally constructed by integrating local tactile cues, given by the device, with global proprioceptive cues, given by hand and arm motion. The experiment consisted of a bi-manual task, in which one hand explored some basic virtual objects and the other hand acted on a keyboard to change the position of one object in real-time. The goal was to merge basic objects into more complex objects, like a puzzle. The experiment spanned different resolutions of the tactile information. We measured task accuracy, efficiency, usability and execution time. The average accuracy in solving the puzzle was 90.5%. Importantly, accuracy was linearly predicted by efficiency, measured as the number of moves needed to solve the task. Subjective parameters linked to usability and spatial resolutions did not predict accuracy; gender modulated the execution time, with men being faster than women. Overall, we show that building purely virtual tactile objects is possible in absence of vision and that the process is measurable and achievable in partial autonomy. Introducing virtual tactile graphics in rehabilitation protocols could facilitate the stimulation of mental imagery, a basic element for the ability to orient in space. The behavioural variable introduced in the current study can be calculated after each trial and therefore could be used to automatically measure and tailor protocols to specific user needs. In perspective, our experimental setup can inspire remote rehabilitation scenarios for visually impaired people.

Leading all-loop quantum contribution to the effective potential in general scalar field theory

The RG equation for the effective potential in the leading log (LL) approximation is constructed which is valid for an arbitrary scalar field theory in 4 dimensions. The solution to this equation sums up the leading log ϕ contributions to all orders of perturbation theory. In general, this is the second order nonlinear partial differential equation, but in some cases it can be reduced to the ordinary one. For particular examples, this equation is solved numerically and the LL effective potential is constructed. The solution has a characteristic discontinuity replacing the Landau pole typical for the ϕ4 theory. For a power-like potential no new minima appear due to the Coleman-Weinberg mechanism.

New inflationary exact solution from Lie symmetries

For the inflaton field, we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral indices for the density perturbations [Formula: see text] and the scalar-to-tensor ratio [Formula: see text] are related as [Formula: see text]. Function [Formula: see text] is classified according to the admitted Lie symmetries for the master equation. The possible admitted Lie symmetries form the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] Lie algebras. The new inflationary solution is recovered by the Lie symmetries of the [Formula: see text] algebra. Scalar field potential is derived explicitly, while we compare the resulting spectral indices with the observations.

Derivation and Evaluation of Satellite-Based Surface Current

Observations of real-time ocean surface currents allow one to search and rescue at ocean disaster sites and investigate the surface transport and fate of ocean contaminants. Although real-time surface currents have been mapped by high-frequency (HF) radar, shipboard instruments, satellite altimetry, and surface drifters, geostationary satellites have proved their capability in satisfying both basin-scale coverage and high spatiotemporal resolutions not offered by other observational platforms. In this paper, we suggest a strategy for the production of operational surface currents using geostationary satellite data, the particle image velocimetry (PIV) method, and deep learning-based evaluation. We used the model scalar field and its gradient to calculate the corresponding surface current via PIV, and we estimated the error between the true velocity field and calculated velocity field by the combined magnitude and relevance index (CMRI) error. We used the model datasets to train a convolutional neural network, which can be used to filter out bad vectors in the surface current produced by arbitrary model scalar fields. We also applied the pretrained network to the surface current generated from real-time Himawari-8 skin sea surface temperature (SST) data. The results showed that the deep learning network successfully filtered out bad vectors in a surface current when it was applied to model SST and created stronger dynamic features when the network was applied to Himawari SST. This strategy can help to provide a quality flag in satellite data to inform data users about the reliability of PIV-derived surface currents.

Enabling visually impaired people to learn three-dimensional tactile graphics with a 3DOF haptic mouse

BackgroundIn this work, we present a novel sensory substitution system that enables to learn three dimensional digital information via touch when vision is unavailable. The system is based on a mouse-shaped device, designed to jointly perceive, with one finger only, local tactile height and inclination cues of arbitrary scalar fields. The device hosts a tactile actuator with three degrees of freedom: elevation, roll and pitch. The actuator approximates the tactile interaction with a plane tangential to the contact point between the finger and the field. Spatial information can therefore be mentally constructed by integrating local and global tactile cues: the actuator provides local cues, whereas proprioception associated with the mouse motion provides the global cues.MethodsThe efficacy of the system is measured by a virtual/real object-matching task. Twenty-four gender and age-matched participants (one blind and one blindfolded sighted group) matched a tactile dictionary of virtual objects with their 3D-printed solid version. The exploration of the virtual objects happened in three conditions, i.e., with isolated or combined height and inclination cues. We investigated the performance and the mental cost of approximating virtual objects in these tactile conditions.ResultsIn both groups, elevation and inclination cues were sufficient to recognize the tactile dictionary, but their combination worked at best. The presence of elevation decreased a subjective estimate of mental effort. Interestingly, only visually impaired participants were aware of their performance and were able to predict it.ConclusionsThe proposed technology could facilitate the learning of science, engineering and mathematics in absence of vision, being also an industrial low-cost solution to make graphical user interfaces accessible for people with vision loss.

Cosmological reconstruction and energy constraints in generalized Gauss\u2013Bonnet-scalar\u2013kinetic\u2013matter couplings

Recently introduced f(mathcal {G},T) theory is generalized by adding dependence on the arbitrary scalar field phi and its kinetic term (nabla phi )^2, to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss–Bonnet theories. The field equations for the resulting fleft( mathcal {G},phi ,(nabla phi )^2,Tright) theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime are discussed for the generic function fleft( mathcal {G},phi ,(nabla phi )^2,Tright) . As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed fleft( mathcal {G},phi ,(nabla phi )^2,Tright) gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the fleft( mathcal {G},phi ,Tright) case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the f(R,phi ,(nabla phi )^2) and f=gamma (phi ,X)mathcal {G}+mu T^{1/2} approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.

Horndeski gravity and standard sirens

Standard sirens have been proposed as probes of alternative theories of gravity, such as Horndeski models. Hitherto, all studies have been conducted on a homogeneous-isotropic cosmological background, which is unable to consistently account for realistic distributions of matter, and for inhomogeneities in the Horndeski scalar field. Yet, the latter are essential for screening mechanisms. In this article, we comprehensively analyze the propagation of Horndeski gravitational waves in an arbitrary background spacetime and scalar field. We restrict to the class of theories in which gravitational waves propagate at light speed, and work in the geometric-optics regime. We find that kinetic braiding only produces a nonphysical longitudinal mode, whereas conformal coupling affects the amplitude of the standard transverse modes but not their polarization. We confirm that any observable deviation from general relativity depends on the local value of the effective Planck mass at emission and reception of the wave. This result is interpreted as the conservation of the number of gravitons.

Exact design of complex amplitude holograms for producing arbitrary scalar fields.

Typical methods to holographically encode arbitrary wavefronts assume the hologram medium only applies either phase shifts or amplitude attenuation to the wavefront. In many cases, phase cannot be introduced to the wavefront without also affecting the amplitude. Here we show how to encode an arbitrary wavefront into an off-axis transmission hologram that returns the exact desired arbitrary wavefunction in a diffracted beam for phase-only, amplitude-only, or mixed phase and amplitude holograms with any periodic groove profile. We apply this to design thin holograms for electrons in a TEM, but our results are generally applicable to light and X-ray optics. We employ a phase reconstruction from a series of focal plane images to qualitatively show the accuracy of this method to impart the expected amplitude and phase to a specific diffraction order.

Scalar, vector and tensor harmonics on the flat compact orientable three-manifolds

Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices for building cosmological models based on the present observations. This paper briefly describes these six manifolds and the harmonic basis functions previously developed for representing arbitrary scalar fields on them. The principal focus of this paper is the development of new harmonics for representing arbitrary vector and second-rank tensor fields on these manifolds. These new harmonics are designed to be useful tools for analyzing the dynamics of electromagnetic and gravitational fields on these spaces.

The imaginary Toda field theory

We consider the two-dimensional quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry (Wn algebra), a central charge and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a semi-degenerate field of Wyllard type. The solution obtained is not the analytic continuation of the usual Toda three-point function. Non-scalar primary fields and their three-point functions are also discussed. Non-scalar primary fields are classified by conjugacy classes of the permutation group , and their structure constants are computed explicitly, up to an overall factor.

Adaptive re-parameterization based on arbitrary scalar fields for shape optimization and surface fitting

This paper presents a method for re-parameterization based on an arbitrary scalar field named the relaxation field. The relaxation field is applied to re-distribute the control-points of a parametric surface towards the desired areas. The proposed method was developed for possible application in an intelligent shape optimization procedure where a sensitivity field with respect to an objective function (or some other physical field) would be used for constructing the relaxation field. It could hence contribute to the concentrating the control-points at areas where significant changes in the geometry are expected. The method can easily be used in shape optimization since it keeps the number of variables constant during the redistribution of control-points as opposed to adaptive insertion of control points when using T-spline and similar methods.The same method can also be used in surface fitting by choosing the relaxation field based on the geometric error. This leads to an adaptive iterative fitting method. The method was validated by fitting a single patch B-spline surface to triangulated point clouds. The point-clouds were obtained by 3D scanning or from a CAD model. Examples include several complex engineering objects. The proposed method uses a parameterization method based on a combination of harmonic mapping and a mapping method based on a spring mesh. By relaxation using a spring mesh, the method allocates more parametric space to the regions of interest, thus assigning them more control points. The combination of these two mapping methods provides for increased local control while keeping the global smoothness of the parameterization.

Proof of Renormalizability of Scalar Field Theories Using the Epstein-Glaser Scheme and Techniques of Microlocal Analysis

The renormalizability of QFT's is a vastly studied issue, and particularly the results concerning a scalar eld theory are well-known through the traditionalrenormalization approach in the literature. However, in this paper we analyze the problem through a less known approach, which justies in a more rigorousand mathematically neat manner, the heuristic arguments of standard treatments of divergencies in QFT's. This paper analyzes the renormalizability ofan arbitrary Scalar Field Theory with interaction Lagrangean L(x) =: 'm(x) : using the method of Epstein-Glaser and techniques of microlocal analysis, inparticular, the concept of scaling degree of a distribution. For a renormalizability proof of perturbative models in the Epstein-Glaser scheme one rst needs to dene an n-fold product of sub-Wick monomials of the interaction Lagrangean. This time ordering is an operator-valued distribution on R4n and the basic issue is its ill-denedness on a null set. The renormalization of a theory in this scheme amounts to the problem of extension of distributions across null sets.

First sound in holographic superuids at zero temperature

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed the case. Working at zero temperature, we explicitly find the quadratic action for the superfluid phonon at the boundary in an arbitrary number of dimensions and for an arbitrary scalar field potential, recovering the known dispersion relation for conformal first sound.

Scalar field cosmology via non-local integrals of motion

In re-parametrization invariant systems, such as mini-superspace Lagrangians, the existence of constraints can lead to the emergence of additional non-local integrals of motion defined in phase space. In the case of a FLRW flat/non-flat space-time minimally coupled to an arbitrary scalar field, we manage to use such conserved quantities to completely integrate the system of equations of motion. This is achieved without constraining the potential in any way. Thus, obtaining the most general solution that encompasses all possible cosmological scenarios which can be based on the existence of a scalar field.

Cosmological dynamics of scalar fields with kinetic corrections: Beyond the exponential potential

We expand the dynamical systems investigation of cosmological scalar fields characterised by kinetic corrections presented in [N. Tamanini, Phys. Rev. D 89 (2014) 083521]. In particular we do not restrict the analysis to exponential potentials only, but we consider arbitrary scalar field potentials and derive general results regarding the corresponding cosmological dynamics. Two specific potentials are then used as examples to show how these models can be employed not only to describe dark energy, but also to achieve dynamical crossing of the phantom barrier at late times. Stability and viability issues at the classical level are also discussed.

Trace anomaly and counterterms in designer gravity

We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS$_{4}$, so that the total action is finite on-shell and satisfy a well defined variational principle for an arbitrary scalar field potential. We focus on scalar fields with the conformal mass, $m^{2}=-2l^{-2}$, and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar field. When the anomaly vanishes, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of four-dimensional gauged $\mathcal{N}=8$ supergravity and its $\omega$-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric $ \widehat {g}_{\mu \nu }$ which is responsible to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associated $\widehat {g}$ geometry. Only recently, the method introduced by Einstein in general relativity was used beyond the domain of gravitational forces to map arbitrary accelerated bodies submitted to non-Newtonian attractions onto geodesics of a modified geometry. This process has its roots in the very ancient idea to treat any dynamical problem in Classical Mechanics as nothing but a problem of static where all forces acting on a body annihilates themselves including the inertial ones. This general procedure, that concerns arbitrary forces—beyond the uses of General Relativity that is limited only to gravitational processes—is nothing but the relativistic version of the d’Alembert method in classical mechanics and consists in the principle of Metric Relativity. The main difference between gravitational interaction and all other forces concerns the universality of gravity which added to the interpretation of the equivalence principle allows all associated geometries—one for each different body in the case of non-gravitational forces—to be unified into a unique Riemannian space-time structure. The same geometrical description appears for electromagnetic waves in the optical limit within the context of nonlinear theories or material medium. Once it is largely discussed in the literature, the so-called analogue models of gravity, we will dedicate few sections on this emphasizing their relation with the new concepts introduced here. Then, we pass to the description of the Dynamical Bridge formalism which states the dynamic equivalence of nonlinear theories (driven by arbitrary scalar, spinor or vector fields) that occur in Minkowski background to theories described in associated curved geometries generated by each one of these fields. We shall see that it is possible to map the dynamical properties of a theory, say Maxwell electrodynamics in Minkowski space-time, into Born-Infeld electrodynamics described in a curved space-time the metric of which is defined in terms of the electromagnetic field itself in such way that it yields the same dynamics. It is clear that when considered in whatever unique geometrical structure, these two theories are not the same; they do not describe the same phenomenon. However, we shall see that by a convenient modification of the metric of space-time, an equivalence appears that establishes a bridge between these two theories making they represent the same phenomenon. This method was recently used to achieve a successful geometric scalar theory of gravity. At the end, we briefly review the proposal of geometrization of quantum mechanics in the de Broglie-Bohm formulation using an enlarged non-Riemannian (Weyl) structure.

Design by Dragging: An Interface for Creative Forward and Inverse Design with Simulation Ensembles

We present an interface for exploring large design spaces as encountered in simulation-based engineering, design of visual effects, and other tasks that require tuning parameters of computationally-intensive simulations and visually evaluating results. The goal is to enable a style of design with simulations that feels as-direct-as-possible so users can concentrate on creative design tasks. The approach integrates forward design via direct manipulation of simulation inputs (e.g., geometric properties, applied forces) in the same visual space with inverse design via 'tugging' and reshaping simulation outputs (e.g., scalar fields from finite element analysis (FEA) or computational fluid dynamics (CFD)). The interface includes algorithms for interpreting the intent of users' drag operations relative to parameterized models, morphing arbitrary scalar fields output from FEA and CFD simulations, and in-place interactive ensemble visualization. The inverse design strategy can be extended to use multi-touch input in combination with an as-rigid-as-possible shape manipulation to support rich visual queries. The potential of this new design approach is confirmed via two applications: medical device engineering of a vacuum-assisted biopsy device and visual effects design using a physically based flame simulation.

Dust reference frame in quantum cosmology

We give a formulation of quantum cosmology with pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time gauge, leading to a physical Hamiltonian that is not a square root. Quantization leads to a Schrödinger equation for which unitary evolution is directly linked to geodesic completeness. Our approach simplifies the analysis of both Wheeler–deWitt and loop quantum cosmology (LQC) models and significantly broadens the applicability of the latter. This is demonstrated for arbitrary scalar field potential and cosmological constant in LQC.