Classical boundary field theory of Jacobi sigma models by Poissonization

In this paper, we are going to construct the classical field theory on the boundary of the embedding of \mathbb{R} \times S^{1}ℝ×S1 into the manifold MM by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.

PETROGENESIS, MAJOR OXIDES AND TRACE ELEMENTS GEOCHEMISTRY OF MIGMATITE IN AJUBA, KWARA STATE, NIGERIA

Petrogenesis, major oxides and trace elements geochemical study was carried out on migmatite in Ajuba. The study area is located on Latitudes 8° 05'N and 8°13'N and Longitudes 5°23'E and 5°30'E. Five rock samples were taken from the migmatite outcrops and used for petrographic and geochemical analyses. The geochemical analysis was done using X-ray Fluorescence Spectrometer technique. The dominant rock type is migmatite; gneiss and granite outcrops were also found in sparse distribution. Ptygmatic folds, which constitute the palaeosome, is the common structure observed on the migmatite rock. The petrographic analysis shows that the migmatite consists of quartz, biotite, plagioclase, hornblende and microcline. The major oxides analysis indicates SiO2 as the dominant oxide with concentration range values (70.71 wt. % - 79.32 wt. %) and average of 74.80 wt. %. Al2O3 (14.98 wt. % - 16.44 wt. %, average: 15.70 wt. %) and Fe2O3 (9.10 wt. % - 15.41 wt. %, average: 12.39 wt. %), K2O (6.67 wt. % - 8.86 wt. %, average: 7.50 wt. %) and CaO (0.49 Wt. % - 4.64 wt. %. average: 2.73 wt. %). P2O5, MnO and TiO2 are less than 1.0 wt. %. The trace elements analysis indicates the concentration distributions: Rb (0.11-0.15 ppm, average 0.13 ppm), Co (0.04-0.17 ppm, average 0.10 ppm). Trace elements ˂ 0.10 ppm are Zn, W, Ni, Cu, V and Pb. From the petrographic and geochemical assessment, the petrogenesis of the migmatite has silica-rich igneous parentage. Moreover, the plots of SiO2-CaO and K2O-SiO2 placed the migmatite on the “upper boundary field of Francisian Greywacke” protolith and Shoshonite series, respectively.

Bounds on Regge growth of flat space scattering from bounds on chaos

We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary

We characterise the boundary field line behaviour of Beltrami flows on compact, connected manifolds with vanishing first de Rham cohomology group. Namely we show that except for an at most nowhere dense subset of the boundary, on which the Beltrami field may vanish, all other field lines at the boundary are smoothly embedded 1-manifolds diffeomorphic to $${\mathbb {R}}$$ R , which approach the zero set as time goes to $$\pm \, \infty$$ ± ∞ . We then drop the assumptions of compactness and vanishing de Rham cohomology and prove that for almost every point on the given manifold, the field line passing through the point is either a non-constant, periodic orbit or a non-periodic orbit which comes arbitrarily close to the starting point as time goes to $$\pm \infty$$ ± ∞ . During the course of the proof, we in particular show that the set of points at which a Beltrami field vanishes in the interior of the manifold is countably 1-rectifiable in the sense of Federer and hence in particular has a Hausdorff dimension of at most 1. As a consequence, we conclude that for every eigenfield of the curl operator, corresponding to a non-zero eigenvalue, there always exists exactly one nodal domain.

Topological defects formation with momentum dissipation

We employ holographic techniques to explore the effects of momentum dissipation on the formation of topological defects during the critical dynamics of a strongly coupled superconductor after a linear quench of temperature. The gravity dual is the dRGT massive gravity in which the conservation of momentum in the boundary field theory is broken by the presence of a bulk graviton mass. From the scaling relations of defects number and “freeze-out” time to the quench rate for various graviton masses, we demonstrate that the momentum dissipation induced by graviton mass has little effect on the scaling laws compared to the Kibble-Zurek mechanism. Inspired from Pippard’s formula in condensed matter, we propose an analytic relation between the coherence length and the graviton mass, which agrees well with the numerical results from the quasi-normal modes analysis. As a result, the coherence length decreases with respect to the graviton mass, which indicates that the momentum dissipation will augment the number of topological defects.

A modified-boundary condition algorithm for efficient 3D forward modeling of CSEM data

<p>I present a newly developed 3D forward modeling algorithm for controlled-source electromagnetic data. The algorithm is based on the finite-difference method, where the source term vector is redefined by combining a modified boundary condition vector and source term vector. The forward modeling scheme includes a two-step modeling approach that exploits the smoothness of the electromagnetic field. The first step involves a coarse grid finite-difference modeling and the computation of a modified boundary field vector called radiation boundary field vector. In the second step, a relatively fine grid modeling is performed using radiation boundary conditions. The fine grid discretization does not include stretched grid and air medium. The proposed algorithm derives computational efficiency from a stretch-free discretization, air-free computational domain, and a better initial guess for an iterative solver. The numerical accuracy and efficiency of the algorithm are demonstrated using synthetic experiments. Numerical tests indicate that the developed algorithm is one order faster than the finite-difference modeling algorithm in most of the cases analyzed during the study. The radiation boundary method concept is very general; hence, it can be implemented in other numerical schemes such as finite-element algorithms.</p>

Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body that is immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided that an appropriate scaling factor is employed. As usual, based on estimates for solutions in the Laplace-transformed domain, we may obtain properties of corresponding solutions in the time-domain without having to perform the inversion of the Laplace-domain solutions.

Why boundary conditions do not generally determine the universality class for boundary critical behavior

Interacting field theories for systems with a free surface frequently exhibit distinct universality classes of boundary critical behaviors depending on gross surface properties. The boundary condition satisfied by the continuum field theory on some scale may or may not be decisive for the universality class that applies. In many recent papers on boundary field theories, it is taken for granted that Dirichlet or Neumann boundary conditions decide whether the ordinary or special boundary universality class is observed. While true in a certain sense for the Dirichlet boundary condition, this is not the case for the Neumann boundary condition. Building on results that have been worked out in the 1980s, but have not always been appropriately appreciated in the literature, the subtle role of boundary conditions and their scale dependence is elucidated and the question of whether or not they determine the observed boundary universality class is discussed. Graphical abstract

The dual of non-extremal area: differential entropy in higher dimensions

The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancelation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in AdS4. Our results suggest a candidate c-function for field theories in arbitrary dimensions.