Pseudo-duality

This paper describes an approach for interactive visualization of mixed scalar and vector fields, in which vector icons are generated from pre-voxelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field and the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. Subject Terms: data visualisation; interactive systems; graphical user interfaces; rendering (computer graphics); interactive visualization; scalar fields; vector fields; vector icons; pre-voxelized icon templates; volume-rendered; volumetric scalar data; incremental image update; real-time animation; zooming lens; local probe

In Part III we deal with some essential aspects of field theory. Except in the last two sections of the present chapter, the entire discussion is in flat spacetime. After a brief introduction to field theory in general, in this chapter we deal with the classical theory of scalar fields.

This paper discusses the reconstruction of the two-dimensional (2D) vector field topology (VFT) from a 2D scalar potential field and vice versa. The physical foundation of the proposed reconstruction method is the convection-type equation coupling a 2D vector field (e.g., skin friction) with a 2D potential field (e.g., surface pressure, temperature, or scalar concentration) in viscous flows. To reconstruct the VFT, a variational method is applied to this inverse problem, and then, an approximate method is proposed based on the linear superposition of some elemental potential field structures with simple analytical forms (source, vortex, saddle, etc.). As examples, the proposed method is applied to swept shock-wave/boundary-layer interaction and near-wall turbulence. Furthermore, in a reversed process to reconstruct a 2D potential field from a 2D vector field, a similar variational method is applied, and an approximate method with a constant source term in the convection-type relation is proposed, which is particularly applicable to reconstruction of a surface pressure field from global skin friction measurements in aerodynamics experiments. The significance of this work is that the complex VFT can be reconstructed based on a scalar potential field by using a semi-analytical approach. The proposed method can be used in fluid mechanics and other disciplines such as computer graphics and data visualization.

We explore the cosmological dynamics of a minimalistic yet generic string-inspired model for multifield dark energy. Adopting a supergravity four-dimensional viewpoint, we motivate the model’s structure arising from superstring compactifications involving a chiral superfield and a pure U(1) gauge sector. The chiral sector gives rise to a pair of scalar fields, such as the axio-dilaton, which are kinetically coupled. However, the scalar potential depends on only one of them, further entwined with the vector field through the gauge kinetic function. The model has two anisotropic attractor solutions that, despite a steep potential and thanks to multifield dynamics, could explain the current accelerated expansion of the Universe while satisfying observational constraints on the late-times cosmological anisotropy. Nevertheless, justifying the parameter space allowing for slow roll dynamics together with the correct cosmological parameters, would be challenging within the landscape of string theory. Intriguingly, we find that the vector field, particularly at one of the studied fixed points, plays a crucial role in enabling geodesic trajectories in the scalar field space while realizing slow-roll dynamics with a steep potential. This observation opens a new avenue for exploring multifield dark energy models within the superstring landscape.

A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein-Euler system. The resulting evolution system is used to show that small nonlinear perturbations of expanding Friedman-Lemaître-Robertson-Walker backgrounds, with scalar field potentials satisfying certain future asymptotic conditions, decay exponentially to zero, in synchronous time.

Feature-aware streamline generation of planar vector fields via topological methods

We discuss new models of an “affine” theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposal to specify the space-time geometry by the use of the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric” Lagrangian that is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields that can describe massive particles, tachyons, or even “phantoms.” In “natural” geometric theories, which are discussed here, dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly considering approximate cosmological models inspired by the geometric approach.

At energies higher than the brane tension, the dynamics of a scalar field rolling down a potential are modified relative to the predictions of General Relativity. The modifications imply, among other things, that steeper potentials can be used to drive an epoch of slow–roll inflation. We investigate the evolution of entropy and adiabatic modes during inflation driven by two scalar fields confined on the brane. We show that the amount of entropy perturbations produced during inflation is suppressed compared to the predictions made by General Relativity. As a consequence, the initial conditions do not matter in multiple field inflation in brane worlds if inflation is driven at energies much higher than the brane tension. DAMTP-2002-107 Inflation provides an explanation for the origin of structures in the universe. In its simplest form, inflation is driven by a single scalar field, called the inflaton, which slowly rolls down a potential. Perturbations in the inflaton field are adiabatic and obey Gaussian statistics [1]. However, this picture might be over simplistic as there is no reason to believe that inflation is driven solely by a single scalar field. Instead, the possibility that inflation is driven by a system of several scalar fields must be considered. In particular, perturbations are, in general, no longer purely adiabatic. Entropy (or isocurvature) per

We construct a Lagrangian for the massive scalar multiplet, locally invariant under two types of spinorial transformations (N=2 supersymmetry). Our theory is based on the coupling of the global supermultiplet to N=2 supergravity and corrections generated iteratively in powers of Newton's constant. Consistency of the theory requires the vector field of supergravity to gauge the central charge represented in the massive sector of the multiplet. The same vector may alternatively gauge the internal 0(2) symmetry of the two supersymmetry generators. Furthermore, it may even gauge a linear combination of the generators of these two groups; we indicate the grounds for this compatibility. We discuss the hierarchy of internal symmetries characterizing each sector of the theory, ranging from U(1)xSU(2)xSU(2) down to 0(2)x0(2). This internal symmetry imposes tight constraints on the system. For instance, the nonpolynomial structure of the spinless fields at hand is considerably more restricted than that present in the general simple supersymmetric (N-1) theory. Furthermore, the vector field is forced to couple to the matter fields with gravitational strength, to the effect that the resulting Coulomb potential exactly cancels against the Newtonian potential of gravity, in the static limit. Our theory may be also viewed as a truncation of N=8 supergravity theory, compatibly with the SO (8) breakup scheme into SU(3)xU(1)xU(1). The potential of the spinless fields present has a local minimum at the origin, but further off it is not even bounded from below. However, we point out some indications that the tunneling out of the supersymmetric, metastable vacuum is negligibly small.

: Interactive visualization allows scientists and engineers to analyze massive data sets in new ways. They can prune useless data, identify important features, and see the science behind the data. We address computational tasks of image generation, dynamical visualization, and interactive manipulation and quantitative querying. The data sets comprise of scalar fields (volumetric histological scans of spinal cord injuries), vector fields (numerical simulation of turbulent flows) and tensor fields (Reynolds stresses produced by vortices in the flow). Image generation is the core of visualization. Dynamical visualization brings out time dependent features that are hard to recognize in static images. Interactive manipulation and querying allows users to focus and quantify key features in large data sets.

It is shown that ``${B}^{\ensuremath{\wedge}}F$'' theory in 3+1 dimensions with a Kalb-Ramond field is related by Buscher's duality transformation to two different versions of massive gauge-invariant spin-one theories of St\"uckelberg-type, one involving vector and scalar fields and the other antisymmetric tensor and vector fields. A similar construction for massive spin-zero theory is also shown. The implication of this equivalence to the five-dimensional theories from which these theories can be obtained is discussed.

The validity of running criterion for vector and scalar fields is analyzed. It is shown that such criterion may be used for scalar fields of any kind. This criterion may be implemented for relatively simple vector fields like heterogeneously polarized beams with central symmetry of their parameters and it cannot use for vector field of general type. The results of computer simulation are presented.

A classical relativistic approach based in the Vlasov equation is applied to the study of infinite nuclear matter. Hadronic matter couples to massive scalar and vector fields. The small-amplitude oscillations around a stationary state are studied. Orthogonality and completeness relations and the energy-weighted sum rule are obtained for the longitudinal modes. The appearance of the zero-sound mode and the distribution of the strength among the different modes are discussed. It is seen that the scalar field only couples to the low-energy excitations at high densities and for wavelengths not too long. The vector field couples strongly to the low-energy excitations. The long-wavelength limit and high-density limit are studied.

The extended scalar-tensor and vector-tensor theories admit black hole solutions with the nontrivial profiles of the scalar and vector fields, respectively. The disformal transformation maps a solution in a class of the scalar-tensor or vector-tensor theories to that in another class, and hence it can be a useful tool to construct a new nontrivial solution from the known one. First, we investigate how the stationary and axisymmetric solutions in the vector-tensor theories without and with the $U(1)$ gauge symmetry are disformally transformed. We start from a stationary and axisymmetric solution satisfying the circularity conditions, and show that in both the cases the metric of the disformed solution in general does not satisfy the circularity conditions. Using the fact that a solution in a class of the vector-tensor theories with the vanishing field strength is mapped to that in a class of the shift-symmetric scalar-tensor theories, we derive the disformed stationary and axisymmetric solutions in a class of these theories, and show that the metric of the disformed solutions does not satisfy the circularity conditions if the scalar field depends on the time or azimuthal coordinate. We also confirm that in the scalar-tensor theories without the shift symmetry, the disformed stationary and axisymmetric solutions satisfy the circularity conditions. Second, we investigate the disformal transformations of the stationary and axisymmetric black hole solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor, the shift-symmetric scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor, the Einstein-Maxwell theory, and the Einstein-conformally coupled scalar field theory. We show that the disformal transformations modify the causal properties of the spacetime.

The scalar and Einstein field equations are considered in the general symmetric comoving system. The self-gravitational interaction of the scalar field is expressed by identifying the energy momentum tensor with the one canonically associated to the scalar field. It is shown that the scalar field can depend only on the radial and time variables and that the energy momentum tensor is implicitly conserved. Two classes of solutions are then studied. A first class, that contains the static case previously considered and the complete time-dependent case, is determined by a priori assuming the unknown functions to depend on one only variable. This class is meaningful essentially for massless field. A second class of solutions refers to the a priori assumption that the scalar field alone depends on r or on t. In both cases some comments are developed for the massive scalar field and for a large class of massless fields we are able to determine the solutions.