Antisymmetric Part Research Articles

Double bracket formulation for the distribution function approach to multibead-chain suspensions

A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains is described by a distribution function that evolves according to a Liouville or Fokker–Planck equation. The evolution of these multibead-chain suspensions is described using a double bracket formulation with a Hamiltonian functional. The conservative part of the dynamics is described by a Poisson bracket, and the dissipative part by an additional symmetric bracket. We treat the configuration space of multibead chains as a higher order tangent bundle. Lifting the fluid velocity field to the bundle leads naturally to a semidirect product Lie–Poisson bracket for the conservative dynamics. The elastic stress exerted by the multibead chains on the fluid then follows directly from the same Hamiltonian functional that governs the internal dissipative mechanics of the multibead chains. For chains with three or more beads, the possible bending of the chain introduces an angular momentum flux that is absent for chains with two beads. This flux appear as an asymmetric elastic stress whose antisymmetric part is the divergence of a rank-3 tensor, as in the Cosserats’ theory of couple stresses in media with no internal angular momentum density. We investigate the possibility of an exact closure, passing from a distribution function description to a closed internal state variable description of the fluid suspension, and obtain some sufficient conditions for their existence. The resulting exactly closable models are generalisations of the upper-convected Maxwell model to Hookean bead–spring chains instead of Hookean bead–spring pairs.

Antisymmetric Cross-correlation between H i and CO Line Intensity Maps as a New Probe of Cosmic Reionization

Abstract Intensity mapping of the H i 21 cm line and the CO 2.61 mm line from the epoch of reionization has emerged as powerful, complementary, probes of the high-redshift universe. However, both maps and their cross-correlation are dominated by foregrounds. We propose a new analysis by which the signal is unbiased by foregrounds, i.e., it can be measured without foreground mitigation. We construct the antisymmetric part of two-point cross-correlation between intensity maps of the H i 21 cm line and the CO 2.61 mm line, arising because the statistical fluctuations of two fields have different evolution in time. We show that the sign of this new signal can distinguish model independently whether inside-out reionization happens during some interval of time. More importantly, within the framework of the excursion-set model of reionization, we demonstrate that the slope of the dipole of H i–CO cross-power spectrum at large scales is linear to the rate of change of global neutral fraction of hydrogen in a manner independent of reionization parameters, until the slope levels out near the end of reionization, but this trend might possibly depend on the framework of reionization modeling. The H i–CO dipole may be a smoking-gun probe for the speed of reionization, or “standard speedometer” for cosmic reionization. Observations of this new signal will unveil the global reionization history from the midpoint to near the completion of reionization.

Exploring axial symmetry in modified teleparallel gravity

Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing independent connection components, the notion of symmetry concerns, not just the metric, but also the connection. As discovered recently, in teleparallel geometries, axial symmetry can be realised in two branches, while only one of these has a continuous spherically symmetric limit. In the current paper, we consider a very generic $f(T,B,\phi,X)$ family of teleparallel gravities, whose action depends on the torsion scalar $T$ and the boundary term $B$, as well as a scalar field $\phi$ with its kinetic term $X$. As the field equations can be decomposed into symmetric and antisymmetric (spin connection) parts, we thoroughly analyse the antisymmetric equations and look for solutions of axial spacetimes which could be used as ans\"atze to tackle the symmetric part of the field equations. In particular, we find solutions corresponding to a generalisation of the Taub-NUT metric, and the slowly rotating Kerr spacetime. Since this work also concerns a wider issue of how to determine the spin connection in teleparallel gravity, we also show that the method of "turning off gravity" proposed in the literature, does not always produce a solution to the antisymmetric equations.

Raman scattering model of the spin noise.

The mechanism of formation of the polarimetric signal observed in the spin noise spectroscopy (SNS) is analyzed from the viewpoint of the light scattering theory. A rigorous calculation of the polarimetric signal (Faraday rotation or ellipticity) recorded in the SNS is presented in the approximation of single scattering. We show that it is most correctly to consider this noise as a result of scattering of the probe light beam by fluctuating susceptibility of the medium. Fluctuations of the gyrotropic (antisymmetric) part of the susceptibility tensor lead to appearance of the typical for the SNS Faraday rotation noise at the Larmor frequency. At the same time, fluctuations of linear anisotropy of the medium (symmetric part of the susceptibility tensor) give rise to the ellipticity noise of the probe beam spectrally localized at the double Larmor frequency. The results of the theoretical analysis well agree with the experimental data on the ellipticity noise in cesium vapor.

Mathcal{N} = 2 AdS4 supergravity, holography and Ward identities

We develop in detail the holographic framework for an mathcal{N} = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

Transfer equation for the strain rate tensor and description of an incompressible dispersed mixture (incompressible fluid) by a system of equations of dynamic type

It is known that the application of the vector operation rot to the equations of hydrodynamics leads to the Helmholtz-Friedman equation for a vortex. A dispersed mixture, tensor transformations are used, in a certain sense generalizing the vector operation rot, which gives more than one, a couple of equations. One of them describes the transfer of vorticity is the well-known Helmholtz-Friedman equation. The second equation was obtained for the first time, and it describes the transfer of the strain rate tensor. Any tensor decomposes into symmetric and antisymmetric parts. By definition, the symmetric part of the tensor U is the strain rate tensor. The antisymmetric part of U is a tensor whose components are related in a known manner to the pseudovector angular velocity.

The Quantum Geometric Tensor in Curved Space

We formulate the quantum geometric tensor in a curved space background, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. The quantum metric tensor is obtained in two different ways: By using the definition of the infinitesimal distance between two states in the parameter space and via the fidelity-susceptibility approach. The usual Berry connection is modified into an object that transforms as a connection and density of weight one due to the modification of the inner product. Finally, we provide three examples in one dimension: two gauge-transformed harmonic oscillators and one gauge-transformed generalized harmonic oscillator.

Beyond Pairwise Interactions: The Totally Antisymmetric Part of the Bispectrum as Coupling Measure of at Least Three Interacting Sources.

In this paper we make two contributions to the analysis of brain oscillations with CFC techniques. First, we introduce a new bispectral CFC measure which is selective to couplings between three or more brain sources. This measure can be derived from ordinary cross-bispectra by performing a total-antisymmetrization operation on them. Significant coupling values can then be attributed to at least three interacting signals. This selectivity to the number of sources can be helpful to test hypotheses on the number of brain sources involved in the generation of commonly observed brain oscillations, such as the alpha rhythm. In a second step we present the correct empirical distribution for the coupling measure, which is necessary to properly assess the significance of coupling results. More importantly however, this corrected statistic is not limited to our particular measure, but holds for all complex-valued coupling estimators. We illustrate how the very common misassumption of empirical normality of such estimators can lead to a systematic underestimation of p-values, the breakdown of multiple comparison control procedures and in consequence a drastic inflation of the number of false positives.

Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion

Nonlinear optical response is well studied in the context of semiconductors and has gained a renaissance in studies of topological materials in the recent decade. So far it mainly deals with non-magnetic materials and it is believed to root in the Berry curvature of the material band structure. In this work, we revisit the general formalism for the second-order optical response and focus on the consequences of the time-reversal-symmetry ($\mathcal{T}$) breaking, by a diagrammatic approach. We have identified three physical mechanisms to generate a dc photocurrent, i.e. the Berry curvature, the quantum metric, and the diabatic motion. All three effects can be understood intuitively from the anomalous acceleration. The first two terms are respectively the antisymmetric and symmetric parts of the quantum geometric tensor. The last term is due to the dynamical antilocalization that appears from the phase accumulation between time-reversed fermion loops. Additionally, we derive the semiclassical conductivity that includes both intra- and interband effects. We find that $\mathcal{T}$-breaking can lead to a greatly enhanced non-linear anomalous Hall effect that is beyond the contribution by the Berry curvature dipole.

Subgrid-scale model based on the vorticity gradient tensor for rotating turbulent flows

A new subgrid-scale (SGS) stress model is proposed for rotating turbulent flows, and the new model is based on the traceless symmetric part of the square of the velocity gradient tensor and the symmetric part of the vorticity gradient tensor (or the so-called vorticity strain rate tensor). The new subgrid-scale stress model is taken into account the effect of the vortex motions in turbulence, which is reflected on the anti-symmetric part of the velocity gradient tensor. In addition, the eddy viscosity of the new model reproduces the proper scaling as O(y3) near the wall. Then, the new SGS model is applied in large-eddy simulation of the spanwise rotating turbulent channel flow. Different simulating cases are selected to test the new model. The results demonstrate that the present model can well predict the mean velocity profiles, the turbulence intensities, and the rotating turbulence structures. In addition, it needs no a second filter, and is convenient to be used in the engineering rotational flows.

Principal coordinates and principal velocity gradient tensor decomposition

Helmholtz velocity decomposition and Cauchy-Stokes tensor decomposition have been widely accepted as the foundation of fluid kinematics for a long time. However, there are some problems with these decompositions which cannot be ignored. Firstly, Cauchy-Stokes decomposition itself is not Galilean invariant which means under different coordinates, the stretching (compression) and deformation are quite different. Another problem is that the anti-symmetric part of the velocity gradient tensor is not the proper quantity to represent fluid rotation. To show these two drawbacks, two counterexamples are given in this paper. Then “principal coordinate” and “principal decomposition” are introduced to solve the problems of Helmholtz decomposition. An easy way is given to find the Principal decomposition which has the property of Galilean invariance.

Instabilities in metric-affine theories of gravity with higher order curvature terms

We discuss the presence of ghostly instabilities for metric-affine theories constructed with higher order curvature terms. We mainly focus on theories containing only the Ricci tensor and show the crucial role played by the projective symmetry. The pathological modes arise from the absence of a pure kinetic term for the projective mode and the non-minimal coupling of a 2-form field contained in the connection, and which can be related to the antisymmetric part of the metric in non-symmetric gravity theories. The couplings to matter are considered at length and cannot be used to render the theories stable. We discuss different procedures to avoid the ghosts by adding additional constraints. We finally argue how these pathologies are expected to be present in general metric-affine theories unless much care is taken in their construction.

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo.

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality.

This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works.

Minimal model of torsion mediated dark matter

We present a minimal model of fermionic dark matter (DM), where a singlet Dirac fermion can interact with the Standard Model (SM) particles via the torsion field of gravitational origin. In general, torsion can be realized as an antisymmetric part of the affine connection associated with the spacetime diffeomorphism symmetry and thus can be thought of as a massive axial vector field. Because of its gravitational origin, the torsion field couples to all the fermion fields including the DM with equal strength, which makes the model quite predictive. The DM is naturally stable without any imposition of ad-hoc symmetry {\it e.g.,} $\mathcal{Z}_2$. Apart from producing the correct thermal abundance, singlet fermion can easily evade the stringent bounds on the spin-independent DM-nucleon direct detection cross-section due to its axial nature. However, in the allowed parameter space, strong bounds can be placed on the torsion mass and its couplings to fermions from the recent LHC searches. Assuming a non universal torsion-DM and torsion-SM coupling, smaller values of torsion masses may become allowed. In both cases we also study the reach of spin-dependent direct detection searches of the DM.

Interplay of Elementary Interactions Causing Social Traps in Evolutionary Games

In evolutionary games, pair interactions are defined by payoff matrices that can be decomposed into four types of orthogonal elementary games that represent fundamentally different interaction situations. The four classes of elementary interactions are formed by games with self- and cross-dependent payoffs, coordination games, and cyclic games. At the level of two-person games, social traps (dilemmas) can not occur for symmetric payoff matrices, which are combinations of coordination games and symmetrically paired self- and cross-dependent components, because individual and common interests coincide in them. In spatial evolutionary games that follow the logit evolutionary dynamics, however, the total payoff is still not maximized at certain noise levels in certain combinations of symmetric components. This phenomenon is similar to the appearance of partially ordered phases in solid state physics, which are stabilized by their higher entropy. In contrast, it is the antisymmetric part of their self- and cross-dependent components that is responsible for the emergence of traditional social dilemmas in games like the two-strategy donation game or the prisoner's dilemma. The general features of these social dilemmas are inherited by $n$-strategy games in the absence of cyclic components, which would prevent the existence of a potential and thus thermodynamic behavior. Using the mathematical framework of matrix decomposition, we survey the ways in which the interplay of elementary games can lead to a loss of total payoff for a society of selfish players. We describe the general features of different illustrative combinations of elementary games, including a game in which the presence of a cyclic component gives rise to the the tragedy of the commons via a paradoxical effect.

On the constitution of polar fiber-reinforced materials

This article presents important constitutive refinements and simplifications in the theory of polar elasticity of materials reinforced by a single family of fibers resistant in bending. One of these simplifications is achieved by paying attention to forms of the strain energy which are symmetric with respect to the symmetric and the antisymmetric parts of the fiber gradient tensor. This leads to the identification of a restricted version of the theory that is predominantly influenced by the fiber-splay mode of deformation. The lack of ellipticity of the governing equations of polar elasticity and the anticipation of existence of weak discontinuity surfaces even in the small deformation regime are also investigated. The manner in which potential activation of such surfaces is related with the action of either the fiber-bending or the fiber-splay deformation mode, as well as with their conjoined combination and coupling with their fiber-twist counterpart, is examined. The proposed constitutive equations can be simplified via the use of a new set of fourteen independent spectral invariants of the deformation. This set serves as an irreducible functional basis of relevant invariants or as an irreducible integrity basis of polynomial invariants. For instance, its use here enables identification of fourteen classical invariants that emerge as mutually independent from the known set of thirty-three in total classical invariants. In the special case of polynomial invariants, this result paves the way for identification of a corresponding minimal integrity basis.

Scattering of water waves by thick rectangular barriers in presence of ice cover

Assuming linear theory, the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover, is investigated here. Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate. May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water. The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function. The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function. The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity. These coefficients are depicted graphically against the wave number in a number of figures. Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover, thereby confirming the correctness of the results presented here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.

A Diagnosis of Anisotropic Eddy Diffusion From a High‐Resolution Global Ocean Model

AbstractOceanic mesoscale eddies are known to diffuse and stir tracers, and the development of skillful eddy closures is aided considerably by the accurate diagnosis of these processes from eddy‐resolving model statistics. In this work a multiple‐tracers inversion method is applied to a global mesoscale eddy‐resolving simulation, with the intent to solve for the eddy transport tensor that describes the eddy diffusion (symmetric part) and stirring (antisymmetric part). Special emphasis is placed on diagnosing the anisotropy of the horizontal transport, which is described by the eigenvalues and eigenvectors of the horizontal symmetric subtensor. Global diagnoses of these quantities, along with an examination of their vertical structures, are used to recommend an algorithm for extending the Gent and McWilliams and Redi parameterizations to include anisotropic effects.

On a micropolar theory of growing solids

Обсуждается принцип вывода граничных условий в краевых задачах механики растущих микрополярных тел. Приводится вывод уравнений динамики микрополярного континуума в терминах относительных тензоров для тел постоянного состава. Указана определяющая квадратичная форма упругого потенцила (абсолютного скаляра) для линейного гемитропного микрополярного тела. Выведены определяющие соотношения для симметричных и антисимметричных частей тензоров силовых и моментных напряжений. Получены конечные формы уравнений динамики гемитропного микрополярного континуума в терминах скоростей перемещений и микровращений. Полученные динамические уравнения для тел постоянного состава остаются справедливыми и в теориях растущих тел. Предложена процедура преобразования уравнений равновесия для получения граничных условий на поверхности наращивания в терминах относительных тензоров в форме дифференциальных ограничений. Полученные условия справедливы для весьма широкого круга материалов и метаматериалов. При выводе определяющих соотношений на поверхности наращивания активно используется аппарат алгебры рациональных относительных инвариантов. Получены полные системы совместных относительных инвариантов для тензоров силовых, моментных напряжений и единичного вектора нормали, в том числе системы инвариантов, не выдерживающие зеркальных отражений.