Invariant Field Research Articles

Thermoelastic effect in modal shapes at high frequencies using infrared thermography

Infrared thermography is employed by different methodologies and techniques to perform characterisations and evaluations in solids, typically related to fracture mechanics and damage, based on monitoring heat generation or temperature changes. In this study, the limits of the current technology for Thermoelastic Stress Analysis (TSA), usually employed under low-frequency loads, are explored to characterise temperature fields associated to the first stress invariant in mode shapes. Higher frequencies are especially emphasised in this research. Eleven modes of a plate were analysed, reaching frequencies over 2000 Hz. High correlation coefficients were obtained in comparison with the first stress invariant fields of a finite element model, with a detriment as the mode’s order increases. In those cases, this study highlights the combined influence of the specimen response and mode shape stiffness as well as the progressively shorter integration time.

Fundamental scale invariance

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.

Entanglement renormalization for gauge invariant quantum fields

The continuous multiscale entaglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett., 110, 100402 (2013)] is a variational wavefunctional for ground states of quantum field theories. So far, only scalar bosons and fermions have been considered. In this paper we explain how to generalize the cMERA framework to gauge invariant quantum fields. The fundamental difficulty to be addressed is how to make the gauge constraints (local linear constraints in the Hilbert space) compatible with the UV structure of the cMERA wavefunctional (which is generated by a quasi-local entangler). For simplicity, we consider $U(1)$ gauge theory in $d+1$ spacetime dimensions, a non-interacting theory with massless Hamiltonian $H_{U(1)}$ and Gaussian scale invariant ground state $|\Psi_{U(1)}\rangle$. We propose a gauge invariant cMERA wavefunctional $|\Psi^{\Lambda}_{U(1)}\rangle$ that, by construction, accurately reproduces the long distance properties of $|\Psi_{U(1)}\rangle$ while remaining somewhat unentangled at short distances. Moreover, $|\Psi^{\Lambda}_{U(1)}\rangle$ is the exact ground state of a gauge invariant, local Hamiltonian $H^{\Lambda}_{U(1)}$ whose low energy properties coincide with those of $H_{U(1)}$. Our construction also extends the cMERA formalism to massive (non-gauge invariant) vector boson quantum fields.

Motions of Curves in 4-Dimensional Galilean Space G4

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers’ equations in 4-dimensional Galilean space.

Evolving traversable wormholes satisfying the energy conditions in the presence of pole dark energy

We consider the evolution of traversable wormhole geometries in the inflationary, radiation -- and matter -- dominated eras, and dynamic wormholes with a traceless energy-momentum tensor (EMT), within the recently proposed {\it pole dark energy} model. We show that the evolving radiation -- and matter -- dominated wormhole spacetimes satisfy the null energy condition (NEC), but possess negative energy densities at late times, thus violating the weak energy condition (WEC) in this specific domain. However, we demonstrate with a specific example that the traceless EMT evolving wormholes, supported by conformally invariant massless fields, in principle, could satisfy the WEC, and consequently the NEC, at all times and for all values of the radial coordinate. Thus, one may imagine a scenario in which these geometries originate in the Planckian era through quantum gravitational processes. Inflation could then provide a natural mechanism for the enlargement of these Planckian wormholes, where their FLRW background evolution is governed by pole dark energy. For the first time in the literature, specific dynamical $4$-dimensional solutions are presented that satisfy the NEC and WEC everywhere and everywhen.

Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds

We show that every sequence of torsion-free arithmetic congruence lattices in $\mathrm{PGL}(2,\mathbb R)$ or $\mathrm{PGL}(2,\mathbb C)$ satisfies a strong quantitative version of the Limit Multiplicity property. We deduce that for $R>0$ in certain range, growing linearly in the degree of the invariant trace field, the volume of the $R$-thin part of any congruence arithmetic hyperbolic surface or congruence arithmetic hyperbolic $3$-manifold $M$ is of order at most $\mathrm{Vol}(M)^{11/12}$. As an application we prove Gelander's conjecture on homotopy type of arithmetic hyperbolic $3$-manifolds: We show that there are constants $A,B$ such that every such manifold $M$ is homotopy equivalent to a simplicial complex with at most $A\mathrm{Vol}(M)$ vertices, all of degrees bounded by $B$.

On Modular Vector Invariant Fields

Let [Formula: see text] be a finite field of any characteristic and [Formula: see text] be the general linear group over [Formula: see text]. Suppose W denotes the standard representation of [Formula: see text], and [Formula: see text] acts diagonally on the direct sum of W and its dual space W∗. Let G be any subgroup of [Formula: see text]. Suppose the invariant field [Formula: see text], where [Formula: see text] in [Formula: see text] are homogeneous invariant polynomials. We prove that there exist homogeneous polynomials [Formula: see text] in the invariant ring [Formula: see text] such that the invariant field [Formula: see text] is generated by [Formula: see text] over [Formula: see text].

ON $S$-CURVATURE OF A HOMOGENEOUS FINSLER SPACE WITH RANDERS CHANGED SQUARE METRIC

The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on a homogeneous Finsler space with Randers changed square metric has been proved. Further, an explicit formula for $S$-curvature of Randers changed square metric has been established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(\alpha, \beta)$-metric has been calculated.

Space regularity for evolution operators modeled on H\xf6rmander vector fields with time dependent measurable coefficients

We consider a heat-type operator mathcal {L} structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, with a uniformly positive matrix of bounded measurable coefficients depending only on time. We prove that if mathcal {L}u is smooth with respect to the space variables, the same is true for u, with quantitative regularity estimates in the scale of Sobolev spaces defined by right invariant vector fields. Moreover, the solution and its space derivatives of every order satisfy a 1/2-Hölder continuity estimate with respect to time. The result is proved both for weak solutions and for distributional solutions, in a suitable sense.

Buoyancy Effetcs On FalknerSkan Flow of a Maxwell Nanofluid Fluid With Activation Energy past a wedge: Finite Element Approach

A description of heat transportation in Maxwell fluids mixed with nanoparticles over a wedged wall is presented in this article. The porous and thermally convective boundary of the wedge undergoes a sudden movement. The physical mechanism is influenced by an invariant magnetic field. A transformed formulation is established in ordinary differential form by involving similarity functions. A robust coding based on finite element analysis is developed in Matlab script. The convergence and accuracy of the solution are tested against reliable criteria. The interest in computational effort centered on the formation of boundary layer patterns for fluid temperature, the volume fraction of nano-inclusions, and fluid velocity when influential parameters are varied. The larger Hartmann number Ha, unsteady parameter A, Deborah number β, and wedge parameter m made the flow along the wall faster and produced thinning of the boundary layer. The higher values of Hartmann number, mixed convection, buoyancy ratio parameter, thermophoresis parameter Nt, Brownian motion parameter Nb, wedge parameter m, and Biot number have raised the fluid temperature. The local heat transfer rate reduces against Nt and it is higher for stretching wedge and smaller for the shrinking wedge. An efficient heat transfer in macro-tech processes may utilize the procedure and findings of this study.

Covariants, Invariant Subsets, and First Integrals

Let $k$ be an algebraically closed field of characteristic 0, and let $V$ be a finite-dimensional vector space. Let $End(V)$ be the semigroup of all polynomial endomorphisms of $V$. Let $E$ be a subset of $End(V)$ which is a linear subspace and also a semi-subgroup. Both $End(V)$ and $E$ are ind-varieties which act on $V$ in the obvious way. In this paper, we study important aspects of such actions. We assign to $E$ a linear subspace $D_{E}$ of the vector fields on $V$. A subvariety $X$ of $V$ is said to $D_{E}$ -invariant if $h(x)$ is in the tangent space of $x$ for all $h$ in $D_{E}$ and $x$ in $X$. We show that $X$ is $D_{E}$ -invariant if and only if it is the union of $E$-orbits. For such $X$, we define first integrals and construct a quotient space for the $E$-action. An important case occurs when $G$ is an algebraic subgroup of $GL(V$) and $E$ consists of the $G$-equivariant polynomial endomorphisms. In this case, the associated $D_{E}$ is the space the $G$-invariant vector fields. A significant question here is whether there are non-constant $G$-invariant first integrals on $X$. As examples, we study the adjoint representation, orbit closures of highest weight vectors, and representations of the additive group. We also look at finite-dimensional irreducible representations of SL2 and its nullcone.

Conformal invariance from scale invariance in nonlinear sigma models

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+\epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+\epsilon$ dimension from the seminal work by Perelman on the Ricci flow.

Modular invariants of finite gluing groups

We use the gluing construction introduced by Jia Huang to explore the rings of invariants for a range of modular representations. We construct generating sets for the rings of invariants of the maximal parabolic subgroups of a finite symplectic group and their common Sylow p-subgroup. We also investigate the invariants of singular finite classical groups. We introduce parabolic gluing and use this construction to compute the invariant field of fractions for a range of representations. We use thin gluing to construct faithful representations of semidirect products and to determine the minimum dimension of a faithful representation of the semidirect product of a cyclic p-group acting on an elementary abelian p-group.

Flat-space limit of extremal curves

According to the Ryu-Takayanagi prescription, the entanglement entropy of subsystems in the boundary conformal field theory (CFT) is proportional to the area of extremal surfaces in bulk asymptotically Anti-de Sitter (AdS) spacetimes. The flat-space limit of these surfaces is not well defined in the generic case. We introduce a new curve in the three-dimensional asymptotically AdS spacetimes with a well-defined flat-space limit. We find this curve by using a new vector, which is vanishing on it and is normal to the bulk modular flow of the original interval in the two-dimensional CFT. The flat-space limit of this new vector is well defined and gives rise to the bulk modular flow of the corresponding asymptotically flat spacetime. Moreover, after Rindler transformation, this new vector is the normal Killing vector of the BTZ inner horizon. We reproduce all known results about the holographic entanglement entropy of Bondi-Metzner-Sachs invariant field theories, which are dual to the asymptotically flat spacetimes.

Finite element simulation of bioconvection Falkner–Skan flow of a Maxwell nanofluid fluid along with activation energy over a wedge

A description of heat transportation in Maxwell nano-fluids mixed with self-motile thermophile microorganisms over a wedged wall is presented in this article. The porous and thermally convective boundary of the wedge undergoes a sudden movement. The physical mechanism is influenced by an invariant magnetic field. A transformed formulation is established in ordinary differential form by involving similarity functions. A robust coding based on finite element analysis is developed in Matlab script. The convergence and accuracy of the solution are tested against reliable criteria. The interest in computational effort centered on the formation of boundary layer patterns for microorganism distribution, fluid temperature, the volume fraction of nano-inclusions, and fluid velocity when influential parameters are varied. The larger Hartmann number Ha, unsteady parameter A, Deborah number β, and wedge parameter m made the flow along the wall faster and produced thinning of the boundary layer. The higher values of Hartmann number, mixed convection, buoyancy ratio parameter, thermophoresis parameter Nt, Brownian motion parameter Nb, wedge parameter m, radiation parameter Rd, and Biot number have raised the fluid temperature. The local heat transfer rate reduces against Nt and it is higher for stretching wedge and smaller for the shrinking wedge. An efficient heat transfer in macro-tech processes may utilize the procedure and findings of this study.

Soft surfaces and enhanced nonlinearity enabled via epsilon-near-zero media doped with zero-area perfect electric conductor inclusions.

Introducing a dielectric inclusion inside an epsilon-near-zero (ENZ) host has been shown to dramatically affect the effective permeability of the host for a TM-polarized incident wave, a concept coined as photonic doping [Science355, 1058 (2017)SCIEAS0036-807510.1126/science.aal2672]. Here, we theoretically study the prospect of doping the ENZ host with infinitesimally thin perfect electric conductor (PEC) inclusions, which we call "zero-area" PEC dopants. First, we theoretically demonstrate that zero-area PEC dopants enable the design of soft surfaces with an arbitrary cross-sectional geometry. Second, we illustrate the possibility of engineering the PEC dopants with the goal of transforming the electric field distribution inside the ENZ while maintaining a spatially invariant magnetic field. We exploit this property to enhance the effective nonlinearity of the ENZ host.

Bogomolov multipliers of some groups of order p 6

Let G be a finite group, V a faithful finite-dimensional representation of G over the complex field and be the corresponding invariant field. The Bogomolov multiplier of G is canonically isomorphic to the unramified cohomological group which has been used by Saltman in 1984 and Bogomolov in 1988 to provide counterexamples to the rationality problem of for finite p-groups P over In this paper, we investigate the vanishing property of where P denotes a p-group of order p 6 for

On the classification of finite-dimensional Henselian simple central algebras with unitary involutions

The purpose of this paper is to investigate the problem of the classification of finite-dimensional simple central K-algebras with unitary involutions. In this paper, K-isomorphism is proven for weakly ramified finite-dimensional central K-algebras with division and unitary K/k-involutions (where the invariant field k is Henselian). Earlier, in papers by J.-P. Tignol, V. V. Kursov and V. I. Yanchevskii, generalized Abelian crossed products were defined and the K-isomorphism of generalized Abelian crossed products (D1, G, (ω, f )) and (D2, G, (ϖ, g )), was proven for the case D1 = D2. In this paper, this criterion is proven when D1 and D2 are different. With the help of this criterion, the main result of this article is obtained.

Homogeneous Finsler spaces with exponential metric

Abstract We prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

Harmonicity of vector fields on the oscillator groups with neutral signature

In this paper, we mainly investigate curvature properties and harmonicity of invariant vector fields on the four-dimensional Oscillator groups endowed with three left-invariant pseudo-Riemannian metrics of signature (2,2). We determine all harmonic vector fields, vector fields which define harmonic maps and the vector fields which are critical points for the energy functional restricted to vector fields of the same length.