Bulk Terms Research Articles

Surface terms in effective action of O-plane at order alpha '^2

The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of alpha ' and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order alpha '^2 and for NS–NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.

Statistical treatment of nuclear clusters in the continuum

The evaluation of the sub-saturation nuclear equation of state at finite temperature requires a proper state counting of the internal partition sum of nuclei which are immersed in the background of their continuum states. This classical statistical problem is addressed within the self-consistent mean-field approximation, which naturally accounts for isospin and effective mass effects in the nuclear density of states. The nuclear free energy is decomposed into bulk and surface terms, allowing a simple analytical prescription for the subtraction of gas states from the nuclear partition sum, that avoids double counting of unbound single particle states. We show that this correction leads to a sizeable effect in the composition of matter at high temperature and low proton fractions, such as it is formed in supernova collapse, early proto-neutron star evolution, as well as laboratory experiments. Specifically, the energy stored in the internal nuclear degrees of freedom is reduced, as well as the mass fraction of heavy clusters in the statistical equilibrium. The gas subtraction prescription is compared to different phenomenological methods proposed in the literature, based on a high energy truncation of the partition sum. We show that none of these methods satisfactorily reproduces the gas subtracted level density, if the temperature overcomes ~4 MeV.

On the continuum limit of Benincasa–Dowker–Glaser causal set action

We study the continuum limit of the Benincasa–Dowker–Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of arbitrary curvature in various spacetime dimensions. In the continuum limit, we show that the action admits a finite limit. More importantly, the limit is composed by an Einstein–Hilbert bulk term as predicted by the Benincasa–Dowker–Glaser action, and a boundary term exactly proportional to the codimension-two joint volume. Our calculation provides strong evidence in support of the conjecture that the Benincasa–Dowker–Glaser action naturally includes codimension-two boundary terms when evaluated on causally convex regions.

Development of quadrupole susceptibility automatic calculator in sum frequency generation spectroscopy and application to methyl C-H vibrations.

Sum frequency generation (SFG) spectroscopy has been established as a powerful interface probe technique based on the electric dipole approximation, while possible signals of quadrupole and bulk origin have also been known for a long time. In this work, we developed a computational tool, namely, Qsac (quadrupole susceptibility automatic calculator), to evaluate the comprehensive contributions of the dipole/quadrupole and interface/bulk in the arbitrary vibrational bands of SFG spectra. The calculations of relevant susceptibility terms are performed on the basis of the theory of energy representation using quantum chemical calculation and molecular dynamics simulation, which allows for semi-quantitative comparison among these terms on the same footing. We applied the Qsac to the methyl C-H stretching bands of organic molecules and found a general trend that the weak asymmetric bands are more sensitive to the bulk contribution than the symmetric ones. The phases of interface and bulk terms tend to cancel in the asymmetric band, which results in the reduced band intensity in the SFG spectra.

Holographic complexity in general quadratic curvature theory of gravity

In the context of CA conjecture for holographic complexity, we study the action growth rate at late time approximation for general quadratic curvature theory of gravity. We show how the Lloyd’s bound saturates for charged and neutral black hole solutions. We observe that a second singular point may modify the action growth rate to a value other than the Lloyd’s bound. Moreover, we find the universal terms that appear in the divergent part of complexity from computing the bulk and joint terms on a regulated WDW patch.

Surface terms in the effective actions via duality constraints

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge transformations and under the string dualities. Using this proposal at the leading order of α′, the standard Gibbons-Hawking-York boundary term is reproduced.

Parametrization of the surface energy in the ETF approximation

We perform extended Thomas–Fermi calculations in the Wigner–Seitz cell below and above neutron drip with realistic functionals. The resulting energy density is decomposed as a sum of bulk terms and a surface term, and a compressible liquid drop analytical formula is used to fit the surface tension. The effect of curvature terms and neutron skin is studied in detail. A very good reproduction of the microscopic data is obtained using an expression that depends only on the mass and charge of the cluster, showing that the in-medium modifications of the nuclear energy in the presence of an external neutron gas can be effectively accounted for in the isospin dependence of the surface tension. In this first application, aimed at establishing the fitting protocol, we concentrate on the Sly4 energy functional, but the study can be easily generalized to different functionals, and the resulting parametrizations can be used for direct applications in pasta calculations in neutron star crusts and supernova matter.

Optical properties of silicon and germanium determined by high-precision analysis of reflection electron energy loss spectroscopy spectra

We present a detailed analysis and comparison of four models describing the extension of the electron-energy loss function from the optical limit of q\ensuremath{\rightarrow}0 into the (q,\ensuremath{\omega}) plane to obtain the bulk and surface terms of differential inverse inelastic mean free paths. We found that the best model that describes accurately and times efficiently the calculation of the energy loss function of free-electron-like materials is the combination of the Penn algorithm [Phys. Rev. B 35, 482 (1987)] with the Ritchie-Howie method [Philos. Mag. 36, 463 (1977)]. Applying this model in our reverse Monte Carlo method, we determined, with high-precision, electron-energy loss functions of silicon and germanium based on the theoretical analysis of the high-energy resolution reflected electron energy loss spectroscopy (REELS) spectra, measured at 3, 4, and 5 keV incident electron energies. The refractive index $n$, the extinction coefficient $k$, and the complex dielectric function ($\ensuremath{\varepsilon}={\ensuremath{\varepsilon}}_{1}+i{\ensuremath{\varepsilon}}_{2}$) were calculated from the obtained energy loss function in a wide energy loss range of 0--200 eV. The accuracy of the obtained results is justified with various sum rules. We found that the calculated optical data of Si and Ge fulfill the sum rules with an average accuracy of 0.11% or even better. Therefore, the use of these optical data in materials science and surface analysis is highly recommended for further applications.

Self-stress on a dielectric ball and Casimir–Polder forces

It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir–Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt (2018), who find that the energy or self-stress of a homogeneous dielectric ball with permittivity ε begins with a term of order ε−1. Here we demonstrate that this cannot be correct. The only possible origin of a term linear in ε−1 lies in the bulk energy, that energy which would be present if either the material of the body, or of its surroundings, filled all space. Since Avni and Leonhardt correctly subtract the bulk terms, the linear term they find likely arises from their omission of an integral over the transverse stress tensor.

On Relation between Bulk, Surface and Curvature Parts of Nuclear Binding Energy within the Model of Hexagonal Clusters

Using the model of hexagonal clusters we express the surface, curvature and Gauss curvature coefficients of the nuclear binding energy in terms of its bulk coefficient. Using the derived values of these coefficients and a single fitting parameter we are able to reasonably well describe the experimental binding energies of nuclei with more than 100 nucleons. To improve the description of lighter nuclei we introduce the same correction for all the coefficients. In this way we determine the apparent values of the surface, curvature and Gauss curvature coefficients which may be used for infinite nuclear matter equation of state. This simple model allows us to fix the temperature dependence of all these coefficients, if the temperature dependence for the bulk term is known. The found estimates for critical temperature are well consistent both with experimental and with theoretical findings.

Holographic relationships in Lovelock type brane gravity

We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the and allowing to be determined completely by . In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geometric degrees of freedom in both bulk and surface space.

Rotation in galaxy clusters from MUSIC simulations with the kinetic Sunyaev–Zel’dovich effect

The Sunyaev-Zel’dovich effect in galaxy clusters is a unique probe for studying astrophysics and cosmology. We propose in this work its application for the detection of possible coherent rotational motions in the hot intra-cluster medium. We select a sample of massive, relaxed and rotating galaxy clusters from Marenostrum-mUltidark SImulations of galaxy Clusters (MUSIC), and we produce mock maps of the temperature distortion produced by the kinetic Sunyaev–Zel’dovich effect by exploring six different lines of sight, in the best observational condition. These maps are compared with the expected signal computed from a suitable theoretical model in two cases: (i) focusing only on the contribution from the rotation, and (ii) accounting also for the cluster bulk motion. We find that the parameters of the model assumed for the radial profile of the rotational velocity, averaged over the considered lines of sight, are in agreement within two standard deviations at most with independent estimates from the simulation data, without being significantly affected by the presence of the cluster bulk term. The amplitude of the rotational signal is, on average, of the order of 23 per cent of the total signal accounting also for the cluster bulk motion, and its values are consistent with the literature. The projected bulk velocity of the cluster is also recovered at the different lines of sight, with values in agreement with the simulation data.

Gravitational backreaction on a cosmic string: Formalism

We develop a method for computing the linearized gravitational backreaction for Nambu-Goto strings using a fully covariant formalism. We work with equations of motion expressed in terms of a higher dimensional analog of the geodesic equation subject to self-generated forcing terms. The approach allows arbitrary spacetime and world sheet gauge choices for the background and perturbation. The perturbed spacetime metric may be expressed as an integral over a distributional stress-energy tensor supported on the string world sheet. By formally integrating out the distribution, this quantity may be reexpressed in terms of an integral over the retarded image of the string. In doing so, one must pay particular attention to contributions that arise from the field point and from nonsmooth regions of the string. Then, the gradient of the perturbed metric decomposes into a sum of boundary and bulk terms. The decomposition depends upon the world sheet coordinates used to describe the string, but the total is independent of those considerations. We illustrate the method with numerical calculations of the self-force at every point on the world sheet for loops with kinks, cusps and self-intersections using a variety of different coordinate choices. For field points on smooth parts of the world sheet the self-force is finite. As the field point approaches a kink or cusp the self-force diverges, but is integrable in the sense that the displacement of the world sheet remains finite. As a consistency check, we verify that the period-averaged flux of energy-momentum at infinity matches the direct work the self-force performs on the string. The methodology can be applied to address many fundamental questions for string loop evolution.

Structure of anomalies of 4d SCFTs from M5-branes, and anomaly inflow

We study the ’t Hooft anomalies of four-dimensional superconformal field theories that arise from M5-branes wrapped on a punctured Riemann surface. In general there are two independent contributions to the anomalies. There is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface; this contribution knows about the punctures only through its dependence on the Euler characteristic of the surface. The second set of contributions comes from local data at the punctures; these terms are independent from the bulk data of the surface. Using anomaly inflow in M-theory, we describe the general structure of the anomalies for cases when the four-dimensional theories preserve mathcal{N}=2 supersymmetry. We additionally discuss the anomalies corresponding to (p, q) punctures in mathcal{N}=1 theories.

Modern finite-size criticality: Dirichlet and Neumann boundary conditions

Finite-size critical systems defined on a parallel-plate geometry of finite extent along one single (z) direction with Dirichlet and Neumann boundary conditions at z = 0, L are analyzed in momentum space. We introduce a modified representation for the discrete eigenfunctions in a renormalized one-particle-irreducible (1PI) vertex part scalar field-theoretic framework using either massless or massive fields. The appearance of multiplicities in the Feynman rules to construct diagrams due to this choice of representation of the basis functions is discussed along with the modified normalization conditions. For nonvanishing external quasi-momenta, Dirichlet and Neumann boundary conditions are shown to be unified within a single formalism. We examine the dimensional crossover regimes for these and show a correspondence with those from antiperiodic and periodic boundary conditions. It is demonstrated that finite-size effects for Dirichlet and Neumann boundary conditions do not require surface fields necessarily but are implemented nontrivially from the Feynman rules involving only bulk terms in the Lagrangian. As an application, the critical exponents $\eta$ and $\nu$ are evaluated at least up to two-loop level through diagrammatic means. We show that the critical indices are the same as those from the bulk (infinite) system irrespective of the boundary conditions.

A Ginzburg--Landau-Type Problem for Highly Anisotropic Nematic Liquid Crystals

We carry out an asymptotic analysis of a variational problem relevant in the studies of nematic liquid crystalline films when one elastic constant dominates over the others, namely, $ \inf E_\varepsilon(u)$, where $E_\varepsilon(u) := \frac{1}{2}\int_\Omega \left\{\varepsilon\,|\nabla u|^2 + \frac{1}{\varepsilon} \,(|u|^2 - 1)^2 + L \,(\mathrm{div}\, u)^2\right\} \,dx. $ Here $u: \Omega \to \mathbb{R}^2$ is a vector field, $0 < \varepsilon \ll 1 $ is a small parameter, and $L > 0$ is a fixed constant, independent of $\varepsilon$. We identify a candidate for the $\Gamma$-limit $E_0$, which is a sum of a bulk term penalizing divergence and an Aviles--Giga-type wall energy involving the cube of the jump in the tangential component of the $\mathbb{S}^1$-valued nematic director. We establish the lower bound and provide the recovery sequence for this candidate within a restricted class. Then we consider a set of variational problems for $E_0$ arising from various choices of domain geometry and boundary conditions. We demonstrate that the criticality conditions for $E_0$ can be expressed as a pair of scalar conservation laws that share characteristics. We use the method of characteristics to analytically construct critical points of $E_0$ that we observe numerically.

Antiferromagnetic domain wall creep driven by magnetoelectric effect

We observed the magnetoelectric induced domain wall propagation in a Pt/Co/Au/Cr2O3/Pt stacked thin film based on magnetic domain observations using scanning soft X-ray magnetic circular dichroism microscopy. The antiferromagnetic (Cr2O3) domain wall velocity was estimated by a quasi-static approach using a pulsed voltage. At a pulse voltage amplitude of −12 V, corresponding to an electric field of −8.0 × 102 kV/cm, the domain wall velocity was very low, at 0.3 m/s. The domain wall velocity increased with increasing voltage amplitude, reaching 22 m/s at −20 V (−1.3 × 103 kV/cm). The change in the domain wall velocity with the applied voltage amplitude indicates the creep motion of the domain wall. Using a phenomenological model, we estimated the domain wall depinning energy, and found that the bulk and interface terms of the magnetic anisotropy affect the effective magnetic field to the same degree, suggesting that the magnetic domain wall motion may be controllable by the antiferromagnetic layer thickness.

Phase-Field Modeling of Equilibrium Precipitate Shapes Under the Influence of Coherency Stresses

Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in order to investigate the mechanical response of a material which undergoes precipitation during heat treatment, it is important to derive the range of precipitate shapes that evolve. In this regard, several studies have been conducted in the past using sharp interface approaches where the influence of elastic energy anisotropy on the precipitate shapes has been investigated. In this paper, we propose a diffuse interface approach which allows us to minimize grid-anisotropy related issues applicable in sharp-interface methods. In this context, we introduce a novel phase-field method where we minimize the functional consisting of the elastic and surface energy contributions while preserving the precipitate volume. Using this method we reproduce the shape-bifurcation diagrams for the cases of pure dilatational misfit that have been studied previously using sharp interface methods and then extend them to include interfacial energy anisotropy with different anisotropy strengths which has not been a part of previous sharp-interface models. While we restrict ourselves to cubic anisotropies in both elastic and interfacial energies in this study, the model is generic enough to handle any combination of anisotropies in both the bulk and interfacial terms. Further, we have examined the influence of asymmetry in dilatational misfit strains along with interfacial energy anisotropy on precipitate morphologies.

Combined supramolecular and mesoscale modelling of liquid–liquid extraction of rare earth salts

We develop a minimal model of weak aggregation in water in the case of neutral extractant in a Winsor II regime, i.e. dispersed microemulsions in thermodynamic equilibrium with concentrated brine. All the terms involved in the free energy associated with the transfer of ions from a concentrated aqueous to an organised organic phase have been estimated: supramolecular effects, bulk terms, extractant film bending and electric polarisation terms. This allows the rationalization of the paradoxical observation of apparent stoichiometry: “constant” associated with the phase transfer that varies with the nature of the solvent and the bending properties of the surfactant. The extractant film is characterized by its spontaneous packing parameter (of the order of 4) and its intrinsic rigidity of the order of 6.25 kJ mol−1 (2.5 kBT). This multi-scale study combining supramolecular chemistry and mesoscale modelling approach allows a large reduction of the number of parallel apparent equilibria currently used for dimensioning extraction devices. Prediction power versus variations of water activity and temperature is in reasonable agreement with observations made in typical pilot cascades.

Topological sources of soliton mass and supersymmetry breaking

We derive the Smarr formulae for two five-dimensional solutions of supergravity, which are asymptotically ; in particular, one has a magnetic ‘bolt’ in its center, and one is a two-center solution. We show for both spacetimes that supersymmetry—and so the BPS-bound—is broken by the holonomy and how each topological feature of a space-like hypersurface enters Smarr’s mass formula, with emphasis on the ones that give rise to the stated violation of the BPS-bound. In this light, we question if any violating extra-mass term in a spacetime with such asymptotics is only evident in the ADM mass while the Komar mass per se ‘tries’ to preserve BPS. Finally, we derive the cohomological fluxes for each situation and examine in a more general fashion how the breaking of supersymmetry—and so the BPS-bound violation—is associated with their topologies. In the second (and more complicated) scenario, we especially focus on the compact cycle linking the centers, and the contribution of non-vanishing bulk terms in the mass formula to the breaking of supersymmetry.