Antisymmetric Part Research Articles

Magnon-Dragged Magnetoresistance and Spin Seebeck Effect in YIG/IrMn Thin Films

We report the magnon-dragged magnetoresistance and spin Seebeck effect simultaneously in lateral yttrium iron garnet (YIG)/Ir20Mn80 thin films, which are detected as $R_{{\text {drag}}}$ and $R_{{\text {SSE}}}$ , respectively, namely, the nonlocal inverse spin Hall voltages quantified by the injected current. According to their different dependences on applied current, $R_{{\text {drag}}}$ and $R_{{\text {SSE}}}$ can be separated as the antisymmetric and symmetric part of the nonlocal signals. By a simple magnon diffusion model, the diffusion length of electrically generated magnons is calculated which is comparable to the values reported in YIG/Pt structures. The low magnetic field and the temperature dependences of $R_{{\text {drag}}}$ and $R_{{\text {SSE}}}$ are found to be different, indicating that the origin and transport properties of magnons associated with these two effects are distinct.

Scalar-torsion theories of gravity. II. L(T, X, Y, ϕ) theory

We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such transformations map different theories in this class onto each other.

Cyclic sieving and plethysm coefficients

A combinatorial expression for the coefficient of the Schur function s λ s_{\lambda } in the expansion of the plethysm p n / d d ∘ s μ p_{n/d}^d \circ s_{\mu } is given for all d d dividing n n for the cases in which n = 2 n=2 or λ \lambda is rectangular. In these cases, the coefficient ⟨ p n / d d ∘ s μ , s λ ⟩ \langle p_{n/d}^d \circ s_{\mu }, s_{\lambda } \rangle is shown to count, up to sign, the number of fixed points of an ⟨ s μ n , s λ ⟩ \langle s_{\mu }^n, s_{\lambda } \rangle -element set under the d d th power of an order- n n cyclic action. If n = 2 n=2 , the action is the Schützenberger involution on semistandard Young tableaux (also known as evacuation), and, if λ \lambda is rectangular, the action is a certain power of Schützenberger and Shimozono’s jeu-de-taquin promotion. This work extends results of Stembridge and Rhoades linking fixed points of the Schützenberger actions to ribbon tableaux enumeration. The conclusion for the case n = 2 n=2 is equivalent to the domino tableaux rule of Carré and Leclerc for discriminating between the symmetric and antisymmetric parts of the square of a Schur function.

Ordered Rate Constitutive Theories for Non-classical Thermoviscoelastic Solids with Dissipation and Memory Incorporating Internal Rotations

This paper presents constitutive theories for non-classical thermoviscoelastic solids with dissipation and memory using thermodynamic framework based on entirety of the displacement gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric parts of the displacement gradient tensor. In this paper, we only consider small deformation small strain; hence, the constitutive theories are basis independent. The constitutive theories are derived in the presence as well as in the absence of balance of moment of moments balance law. It is shown that the energy storage, dissipation mechanism, and the fading memory in the non-classical thermoviscoelastic solids are due to strain rates, rotation rates, stress tensor, moment tensor, and their rates. Constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem. The constitutive theories derived using integrity are followed by simplified constitutive theories. Material coefficients are derived and discussed for both cases. Constitutive models parallel to non-classical Maxwell, Oldroyd-B, and Giesekus models for thermoviscoelastic fluids are derived and shown to be a subset of a more generalized simplified constitutive theory presented in the paper. Retardation moduli are derived for stress tensor as well as moment tensor and are compared with those in classical continuum theories for similar solids.

Experimental and numerical studies to estimate fatigue crack growth behavior of Ni-based super alloy

In this work, the fatigue crack growth behavior of the Nickel based super alloy is investigated at room (26 °C) and elevated temperature (650 °C). The fatigue crack growth experiments are performed to understand the effect of temperature and loading rate. The elasto plastic fracture toughness tests are performed to evaluate JIC. Paris law is used in conjunction with extended finite element method (XFEM) to numerically predict the fatigue life. The stress intensity factors of individual mode (KI and KII) are computed from J-integral by decomposing the stress, strain and strain derivatives into symmetric and antisymmetric parts. Few parametric studies are performed to show the mesh convergence and path independency of J-integral. Fatigue crack growth in an aero-engine turbine disc is predicted. The numerically predicted fatigue life is found in good match with the experimental results.

From geometry to non-geometry via T-duality**Supported by the Serbian Ministry of Education and Science (171031)

Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields and are T-dual to and respectively. We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable yμ and its double . This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.

The comparison of strain gradient effects for each component in static and dynamic analyses of FGM micro-beams

This paper proposes a spherical–deviatoric splitting of the strain gradient tensor to reinterpret the meanings of strain gradient components. The strain gradient theory of Zhou et al. is re-expressed in a more direct form, and, in parallel, the corresponding reduced theories are also obtained as comparisons. The effect of each strain gradient component is investigated by an application on static and dynamic analyses of an FGM micro-beam. To facilitate the modeling, the governing equation, initial condition and boundary conditions are derived by using Hamilton’s principle. The present model can reduce to the corresponding models based on the reduced strain gradient theories. The static bending and free vibration problems of a cantilever beam are solved. Numerical results reveal that the present model can predict a smaller deflection and a larger natural frequency compared with the reduced models, and the differences of results predicted by these different models are decreasing or even diminishing with the increase in beam thickness. The present theory predicts a stronger size effect since the contributions from all strain gradient components are considered. In addition, as far as the beam problems, the contributions from the symmetric part of strain gradient are ignorable compared with the contributions from the antisymmetric part of the strain gradient.

Common origin of nonzero θ13 and baryon asymmetry of the Universe in a TeV scale seesaw model with A4 flavor symmetry

We study the possibility of generating non-zero reactor mixing angle $\theta_{13}$ and baryon asymmetry of the Universe within the framework of an $A_4$ flavour symmetric model. Using the conventional type I seesaw mechanism we construct the Dirac and Majorana mass matrices which give rise to the correct light neutrino mass matrix. Keeping the right handed neutrino mass matrix structure trivial so that it gives rise to a (quasi) degenerate spectrum of heavy neutrinos suitable for resonant leptogenesis at TeV scale, we generate the non-trivial structure of Dirac neutrino mass matrix that can lead to the light neutrino mixing through type I seesaw formula. Interestingly, such a setup naturally leads to non-zero $\theta_{13}$ due to the existence of anti-symmetric contraction of the product of two triplet representations of $A_4$. Such antisymmetric part of triplet products usually vanish for right handed neutrino Majorana mass terms, leading to $\mu-\tau$ symmetric scenarios in the most economical setups. We constrain the model parameters from the requirement of producing the correct neutrino data as well as baryon asymmetry of the Universe for right handed neutrino mass scale around TeV. The $A_4$ symmetry is augmented by additional $Z_3 \times Z_2$ symmetry to make sure that the splitting between right handed neutrinos required for resonant leptogenesis is generated only by next to leading order terms, making it naturally small. We find that the inverted hierarchical light neutrino masses give more allowed parameter space consistent with neutrino and baryon asymmetry data.

A realization problem in statistical and affine geometry

A few realization results are proved in statistical and affine geometry in the 2-dimensional case. For instance, it is proved that each analytic metric tensor field on a 2-dimensional manifold M can be locally realized as the Blaschke metric on a Blaschke surface. It is not true, however, that each torsion-free connection (even analytic) can be locally realized on a Blaschke surface. But each analytic torsion-free, Ricci-symmetric, projectively flat connection on M can be locally realized as the dual connection on a Blaschke surface. Equiaffine versions of these theorems are also proved. A generalization of Amari–Armstrong theorem is proved. Namely, we prove that each analytic metric tensor field and an analytic 2-covariant tensor field whose anti-symmetric part is closed can be locally realized as a metric of a statistical structure and the Ricci tensor of the statistical connection of this structure, respectively.

Rotational strain in Weyl semimetals: A continuum approach

The coupling of lattice deformations to the low energy electronic excitations of Dirac matter involve novel types of electron--phonon couplings as the celebrated elastic gauge fields first analyzed in graphene. In the continuum low energy approach, lattice deformations coupling to the electronic degrees of freedom are characterized by the (symmetric) strain tensor defined in elasticity theory. We review these couplings in Weyl semimetals and examine the coupling of electronic excitations to the antisymmetric part of the deformation gradient tensor associated to rotational strain. The new couplings, absent in the two dimensional materials, have important physical implications: they give rise to new elastic gauge fields, contribute to the deformation potential, tilt the cones and generate new pseudo--Zeeman couplings.

Covariant formulation of scalar-torsion gravity

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, $f(T,\phi)$, thus encompassing the cases of $f(T)$ gravity and nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection compatible with a given tetrad. We discuss how the spin connection equation can be solved in general, and provide the cosmological and spherically symmetric examples. Finally we generalize the theory to an arbitrary number of scalar fields.

Necessity of law of balance of moment of moments in non-classical continuum theories for solid continua

In the non-classical continuum theories for solid continua the presence of internal rotations and their gradients arising due to Jacobian of deformation and/or consideration of Cosserat rotations as additional unknown degrees of freedom at a material point necessitate existence of moment tensor. For small deformation, small strains theories, in Lagrangian description the Cauchy moment tensor and the rates of rotation gradients are rate of work conjugate pair in addition to the rate of work conjugate Cauchy stress tensor and the strain rate tensor. It is well established that in such non-classical theories the Cauchy stress tensor is non-symmetric and the antisymmetric components of the Cauchy stress tensor are balanced by gradients of the Cauchy moment tensor, the balance of angular momenta balance law. In the non-classical continuum theories incorporating internal rotations and conjugate moment tensor that are absent in the classical continuum theories, the fundamental question is “are the conservation and balance laws used in classical continuum mechanics sufficient to ensure dynamic equilibrium of the deforming volume of matter”. At this stage the Cauchy moment tensor remains non-symmetric if we only consider standard balance laws that are used in classical continuum theories. Thus, requiring constitutive theories for the symmetric as well as anti-symmetric Cauchy moment tensors. The work presented in this paper shows that when the thermodynamically consistent constitutive theories are used for symmetric as well as antisymmetric Cauchy moment tensor non physical and spurious solutions result even in simple model problems. This suggests that perhaps the additional conjugate tensors resulting due to presence of internal rotations, namely the Cauchy moment tensor and the antisymmetric part of the Cauchy stress stress tensor must obey some additional law or restriction so that the spurious behavior is precluded. This paper demonstrates that in the non-classical theory with internal rotations considered here the law of balance of moment of moments and the consideration of the equilibrium of moment of moments are in fact identical. When this balance law is considered the Cauchy moment tensor becomes symmetric, hence eliminating the constitutive theory for the antisymmetric Cauchy moment tensor and thereby eliminating spurious and non physical solutions. The necessity of this balance law is established theoretically and is also demonstrated through model problems using thermoelastic solids with small strain small deformation as an example. The findings reported in this paper hold for thermoviscoelastic solids with and without memory as well as when deformation and strains are small. Extensions of the concepts presented here for finite deformation and finite strain will be presented in a follow up paper.

Current density tensors.

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Necessity of law of balance/equilibrium of moment of moments in non-classical continuum theories for fluent continua

In the non-classical theories for fluent continua, the presence of internal rotation rates and their gradients arising due to the velocity gradient tensor necessitate existence of moment tensor. The Cauchy moment tensor acting on the faces of the deformed tetrahedron (derived using Cauchy principle) and the gradients of the rates of total rotations are a rate of work conjugate pair in addition to the rate of work conjugate Cauchy stress tensor and rate of strain tensor. It is well established that in such non-classical continuum theories the Cauchy stress tensor is non-symmetric and the antisymmetric components of the Cauchy stress tensor are balanced by the gradients of the Cauchy moment tensor, balance of angular momenta balance law. In the non-classical continuum theories incorporating internal rotation rates and conjugate Cauchy moment tensor that are absent in classical continuum theories, the fundamental question is “are the conservation and balance laws used in classical continuum mechanics sufficient to ensure dynamic equilibrium of the deforming volume of matter?" If one only considers conservation and balance laws used in classical continuum theories, then the Cauchy moment tensor is non-symmetric. Thus, requiring constitutive theories for the symmetric as well as non-symmetric Cauchy moment tensors. The work presented in this paper shows that when the thermodynamically consistent constitutive theories are used for the symmetric as well as antisymmetric Cauchy moment tensors, non-physical and spurious solutions result even in simple flows. This suggests that perhaps the additional conjugate tensors resulting due to the presence of internal rotation rates, namely the Cauchy moment tensor and the antisymmetric part of Cauchy stress tensor, must obey some additional law or restriction so that the spurious behavior is precluded. The paper demonstrates that in the non-classical theory with internal rotation rates considered here the balance of moment of moments balance law and the equilibrium of moment of moments are in fact identical. When this balance law is considered, the Cauchy moment tensor becomes symmetric, hence eliminating the constitutive theory for the antisymmetric Cauchy moment tensor and thereby eliminating spurious and non-physical solutions. The necessity of this balance/equilibrium law is established theoretically, its derivation is presented using rate considerations, and its necessity is also demonstrated by a model problem using thermoviscous incompressible fluid as an example. The findings reported in this paper hold for all fluent continua, compressible as well as incompressible.

Hall viscosity of a chiral two-orbital superconductor at finite temperatures

The Hall viscosity known as the anti-symmetric part of the viscosity fourth-rank tensor. Such dissipationless response which appears for systems with broken time reversal symmetry. We calculate this non-dissipative quantity for a chiral two-orbital superconductor placed in a viscoelastic magnetic field using the linear response theory and apply our calculations to the putative multiband chiral superconductor Sr2RuO4. The chirality origin of a multiband superconductor arises from the interorbital coupling of the superconducting state. This feature leads to the robustness of the Hall viscosity against temperature and impurity effects. We study the temperature effect on the Hall viscosity at the one-loop approximation.

A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction

Abstract The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin [2] and by Kim [18] to linear elasticity. In order to get a guaranteed reliability bound with respect to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in next-to-lowest order Raviart–Thomas spaces is modified in such a way that its anti-symmetric part vanishes in average on each element; (ii) the auxiliary conforming approximation is constructed under the constraint that its divergence coincides with the one for the nonconforming approximation. An important aspect of our construction is that all results hold uniformly in the incompressible limit. Global efficiency is also shown and the effectiveness is illustrated by adaptive computations involving different Lamé parameters including the incompressible limit case.

Rortex—A new vortex vector definition and vorticity tensor and vector decompositions

A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. In our previous work, a new vector quantity that is called vortex vector was proposed to accurately describe the local fluid rotation and clearly display vortical structures. In this paper, the definition of the vortex vector, named Rortex here, is revisited from the mathematical perspective. The existence of the possible rotational axis is proved through real Schur decomposition. Based on real Schur decomposition, a fast algorithm for calculating Rortex is also presented. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including the 2D Couette flow, 2D rigid rotational flow, and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex. It can be observed that Rortex identifies both the precise swirling strength and the rotational axis, and thus it can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research.

Computations of the chirality-sensitive effect induced by an antisymmetric indirect spin–spin coupling

ABSTRACTResults of quantum mechanical computations of the antisymmetric part of the indirect spin–spin coupling tensor, , performed using the coupled-cluster method, the second-order polarisation propagator approximation, and the density functional theory for 25 molecules and nearly 100 spin–spin couplings are reported. These results are used for an estimation of the magnitude of the recently proposed liquid-state nuclear magnetic resonance chirality-sensitive effect, which allows to determine the molecular chirality directly, i.e. without the need for the application of any chiral agent. The following were found: (i) the antisymmetry J⋆ is usually larger for the coupling between spins separated by two chemical bonds in comparison with the coupling through one bond, (ii) promising samples are those which contain fluorine, and (iii) the antisymmetry of the spin–spin coupling tensor is of the order of a few hertz for commercially available chemical compounds. Therefore, the relevant property of the experiment, the pseudoscalar Jc, for them is of the order of 1 nHz m/V.

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

Dark-matter-like solutions to Einstein’s unified field equations

Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we interpret it more modestly as an alternative to Einstein-Maxwell theory, approximating the coupling between the electromagnetic field and spacetime curvature in the macroscopic classical regime. Previously it was shown that the Lorentz force can be derived from this theory, albeit with deviation on the scale of a universal length constant $\ell$. Here we assume that $\ell$ is of galactic scale and show that the modified coupling of the electromagnetic field with charged particles allows a non-Maxwellian equilibrium of non-neutral plasma. The resulting electromagnetic field is "dark" in the sense that its modified Lorentz force on the plasma vanishes, yet through its modified coupling to the gravitational field it engenders a nonvanishing, effective mass density. We obtain a solution for which this mass density asymptotes approximately to that of the pseudo-isothermal model of dark matter. The resulting gravitational field produces radial acceleration, in the context of a post-Minkowskian approximation, which is negligible at small radius but yields a flat rotation curve at large radius. We further exhibit a family of such solutions which, like the pseudo-isothermal model, has a free parameter to set the mass scale (in this case related to the charge density) and a free parameter to set the length scale (in this case an integer multiple of $\ell$). Moreover, these solutions are members of a larger family with more general angular and radial dependence. They thus show promise as approximations of generalized pseudo-isothermal models, which in turn are known to fit a wide range of mass density profiles for galaxies and clusters.